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# skopt module

Scikit-Optimize, or skopt, is a simple and efficient library to minimize (very) expensive and noisy black-box functions. It implements several methods for sequential model-based optimization. skopt is reusable in many contexts and accessible.

## Install

pip install numpy
pip install scikit-optimize


## Getting started

Find the minimum of the noisy function f(x) over the range -2 < x < 2 with skopt:

import numpy as np
from skopt import gp_minimize

def f(x):
return (np.sin(5 * x[0]) * (1 - np.tanh(x[0] ** 2)) *
np.random.randn() * 0.1)

res = gp_minimize(f, [(-2.0, 2.0)])


For more read our introduction to bayesian optimization and the other examples.

## Development

The library is still experimental and under heavy development.

The development version can be installed through:

git clone https://github.com/scikit-optimize/scikit-optimize.git
cd scikit-optimize
pip install -r requirements.txt
python setup.py develop


Run the tests by executing pytest in the top level directory.

"""
Scikit-Optimize, or skopt, is a simple and efficient library to
minimize (very) expensive and noisy black-box functions. It implements
several methods for sequential model-based optimization. skopt is reusable
in many contexts and accessible.

[![Build Status](https://travis-ci.org/scikit-optimize/scikit-optimize.svg?branch=master)](https://travis-ci.org/scikit-optimize/scikit-optimize)

## Install


pip install numpy
pip install scikit-optimize


## Getting started

Find the minimum of the noisy function f(x) over the range -2 < x < 2
with skopt:

python
import numpy as np
from skopt import gp_minimize

def f(x):
return (np.sin(5 * x[0]) * (1 - np.tanh(x[0] ** 2)) *
np.random.randn() * 0.1)

res = gp_minimize(f, [(-2.0, 2.0)])


For more read our [introduction to bayesian optimization](https://scikit-optimize.github.io/notebooks/bayesian-optimization.html)
and the other [examples](https://github.com/scikit-optimize/scikit-optimize/tree/master/examples).

## Development

The library is still experimental and under heavy development.

The development version can be installed through:

git clone https://github.com/scikit-optimize/scikit-optimize.git
cd scikit-optimize
pip install -r requirements.txt
python setup.py develop

Run the tests by executing pytest in the top level directory.
"""

from . import acquisition
from . import benchmarks
from . import callbacks
from . import learning
from . import optimizer
from . import plots
from . import space
from .optimizer import dummy_minimize
from .optimizer import forest_minimize
from .optimizer import gbrt_minimize
from .optimizer import gp_minimize
from .optimizer import Optimizer
from .searchcv import BayesSearchCV
from .space import Space
from .utils import dump
from .utils import expected_minimum
from .utils import load

__version__ = "0.4rc1"

__all__ = (
"acquisition",
"benchmarks",
"callbacks",
"learning",
"optimizer",
"plots",
"space",
"gp_minimize",
"dummy_minimize",
"forest_minimize",
"gbrt_minimize",
"Optimizer",
"dump",
"load",
"expected_minimum",
"BayesSearchCV",
"Space"
)


## Functions

def dummy_minimize(

func, dimensions, n_calls=100, x0=None, y0=None, random_state=None, verbose=False, callback=None)

Random search by uniform sampling within the given bounds.

## Parameters

• func [callable]: Function to minimize. Should take a array of parameters and return the function values.

• dimensions [list, shape=(n_dims,)]: List of search space dimensions. Each search dimension can be defined either as

• a (upper_bound, lower_bound) tuple (for Real or Integer dimensions),
• a (upper_bound, lower_bound, prior) tuple (for Real dimensions),
• as a list of categories (for Categorical dimensions), or
• an instance of a Dimension object (Real, Integer or Categorical).
• n_calls [int, default=100]: Number of calls to func to find the minimum.

• x0 [list, list of lists or None]: Initial input points.

• If it is a list of lists, use it as a list of input points.
• If it is a list, use it as a single initial input point.
• If it is None, no initial input points are used.
• y0 [list, scalar or None]: Evaluation of initial input points.

• If it is a list, then it corresponds to evaluations of the function at each element of x0 : the i-th element of y0 corresponds to the function evaluated at the i-th element of x0.
• If it is a scalar, then it corresponds to the evaluation of the function at x0.
• If it is None and x0 is provided, then the function is evaluated at each element of x0.
• random_state [int, RandomState instance, or None (default)]: Set random state to something other than None for reproducible results.

• verbose [boolean, default=False]: Control the verbosity. It is advised to set the verbosity to True for long optimization runs.

• callback [callable, list of callables, optional] If callable then callback(res) is called after each call to func. If list of callables, then each callable in the list is called.

## Returns

• res [OptimizeResult, scipy object]: The optimization result returned as a OptimizeResult object. Important attributes are:

• x [list]: location of the minimum.
• fun [float]: function value at the minimum.
• x_iters [list of lists]: location of function evaluation for each iteration.
• func_vals [array]: function value for each iteration.
• space [Space]: the optimisation space.
• specs [dict]: the call specifications.
• rng [RandomState instance]: State of the random state at the end of minimization.

For more details related to the OptimizeResult object, refer http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.OptimizeResult.html

def dummy_minimize(func, dimensions, n_calls=100, x0=None, y0=None,
random_state=None, verbose=False, callback=None):
"""Random search by uniform sampling within the given bounds.

Parameters
----------
* func [callable]:
Function to minimize. Should take a array of parameters and
return the function values.

* dimensions [list, shape=(n_dims,)]:
List of search space dimensions.
Each search dimension can be defined either as

- a (upper_bound, lower_bound) tuple (for Real or Integer
dimensions),
- a (upper_bound, lower_bound, prior) tuple (for Real
dimensions),
- as a list of categories (for Categorical dimensions), or
- an instance of a Dimension object (Real, Integer or
Categorical).

* n_calls [int, default=100]:
Number of calls to func to find the minimum.

* x0 [list, list of lists or None]:
Initial input points.

- If it is a list of lists, use it as a list of input points.
- If it is a list, use it as a single initial input point.
- If it is None, no initial input points are used.

* y0 [list, scalar or None]:
Evaluation of initial input points.

- If it is a list, then it corresponds to evaluations of the function
at each element of x0 : the i-th element of y0 corresponds
to the function evaluated at the i-th element of x0.
- If it is a scalar, then it corresponds to the evaluation of the
function at x0.
- If it is None and x0 is provided, then the function is evaluated
at each element of x0.

* random_state [int, RandomState instance, or None (default)]:
Set random state to something other than None for reproducible
results.

* verbose [boolean, default=False]:
Control the verbosity. It is advised to set the verbosity to True
for long optimization runs.

* callback [callable, list of callables, optional]
If callable then callback(res) is called after each call to func.
If list of callables, then each callable in the list is called.

Returns
-------
* res [OptimizeResult, scipy object]:
The optimization result returned as a OptimizeResult object.
Important attributes are:

- x [list]: location of the minimum.
- fun [float]: function value at the minimum.
- x_iters [list of lists]: location of function evaluation for each
iteration.
- func_vals [array]: function value for each iteration.
- space [Space]: the optimisation space.
- specs [dict]: the call specifications.
- rng [RandomState instance]: State of the random state
at the end of minimization.

For more details related to the OptimizeResult object, refer
http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.OptimizeResult.html
"""
# all our calls want random suggestions, except if we need to evaluate
# some initial points
if x0 is not None and y0 is None:
n_random_calls = n_calls - len(x0)
else:
n_random_calls = n_calls

return base_minimize(func, dimensions, base_estimator="dummy",
# explicitly set optimizer to sampling as "dummy"
# minimizer does not provide gradients.
acq_optimizer="sampling",
n_calls=n_calls, n_random_starts=n_random_calls,
x0=x0, y0=y0, random_state=random_state,
verbose=verbose,
callback=callback)


def dump(

res, filename, store_objective=True, **kwargs)

Store an skopt optimization result into a file.

## Parameters

• res [OptimizeResult, scipy object]: Optimization result object to be stored.

• filename [string or pathlib.Path]: The path of the file in which it is to be stored. The compression method corresponding to one of the supported filename extensions ('.z', '.gz', '.bz2', '.xz' or '.lzma') will be used automatically.

• store_objective [boolean, default=True]: Whether the objective function should be stored. Set store_objective to False if your objective function (.specs['args']['func']) is unserializable (i.e. if an exception is raised when trying to serialize the optimization result).

Notice that if store_objective is set to False, a deep copy of the optimization result is created, potentially leading to performance problems if res is very large. If the objective function is not critical, one can delete it before calling skopt.dump() and thus avoid deep copying of res.

• **kwargs [other keyword arguments]: All other keyword arguments will be passed to joblib.dump.

def dump(res, filename, store_objective=True, **kwargs):
"""
Store an skopt optimization result into a file.

Parameters
----------
* res [OptimizeResult, scipy object]:
Optimization result object to be stored.

* filename [string or pathlib.Path]:
The path of the file in which it is to be stored. The compression
method corresponding to one of the supported filename extensions ('.z',
'.gz', '.bz2', '.xz' or '.lzma') will be used automatically.

* store_objective [boolean, default=True]:
Whether the objective function should be stored. Set store_objective
to False if your objective function (.specs['args']['func']) is
unserializable (i.e. if an exception is raised when trying to serialize
the optimization result).

Notice that if store_objective is set to False, a deep copy of the
optimization result is created, potentially leading to performance
problems if res is very large. If the objective function is not
critical, one can delete it before calling skopt.dump() and thus
avoid deep copying of res.

* **kwargs [other keyword arguments]:
All other keyword arguments will be passed to joblib.dump.
"""
if store_objective:
dump_(res, filename, **kwargs)

elif 'func' in res.specs['args']:
# If the user does not want to store the objective and it is indeed
# present in the provided object, then create a deep copy of it and
# remove the objective function before dumping it with joblib.dump.
res_without_func = deepcopy(res)
del res_without_func.specs['args']['func']
dump_(res_without_func, filename, **kwargs)

else:
# If the user does not want to store the objective and it is already
# missing in the provided object, dump it without copying.
dump_(res, filename, **kwargs)


def expected_minimum(

res, n_random_starts=20, random_state=None)

Compute the minimum over the predictions of the last surrogate model.

Note that the returned minimum may not necessarily be an accurate prediction of the minimum of the true objective function.

## Parameters

• res [OptimizeResult, scipy object]: The optimization result returned by a skopt minimizer.

• n_random_starts [int, default=20]: The number of random starts for the minimization of the surrogate model.

• random_state [int, RandomState instance, or None (default)]: Set random state to something other than None for reproducible results.

## Returns

• x [list]: location of the minimum.

• fun [float]: the surrogate function value at the minimum.

def expected_minimum(res, n_random_starts=20, random_state=None):
"""
Compute the minimum over the predictions of the last surrogate model.

Note that the returned minimum may not necessarily be an accurate
prediction of the minimum of the true objective function.

Parameters
----------
* res  [OptimizeResult, scipy object]:
The optimization result returned by a skopt minimizer.

* n_random_starts [int, default=20]:
The number of random starts for the minimization of the surrogate
model.

* random_state [int, RandomState instance, or None (default)]:
Set random state to something other than None for reproducible
results.

Returns
-------
* x [list]: location of the minimum.

* fun [float]: the surrogate function value at the minimum.
"""
def func(x):
reg = res.models[-1]
return reg.predict(x.reshape(1, -1))[0]

xs = [res.x]
if n_random_starts > 0:
xs.extend(res.space.rvs(n_random_starts, random_state=random_state))

best_x = None
best_fun = np.inf

for x0 in xs:
r = sp_minimize(func, x0=x0, bounds=res.space.bounds)

if r.fun < best_fun:
best_x = r.x
best_fun = r.fun

return [v for v in best_x], best_fun


def forest_minimize(

func, dimensions, base_estimator='ET', n_calls=100, n_random_starts=10, acq_func='EI', x0=None, y0=None, random_state=None, verbose=False, callback=None, n_points=10000, xi=0.01, kappa=1.96, n_jobs=1)

Sequential optimisation using decision trees.

A tree based regression model is used to model the expensive to evaluate function func. The model is improved by sequentially evaluating the expensive function at the next best point. Thereby finding the minimum of func with as few evaluations as possible.

The total number of evaluations, n_calls, are performed like the following. If x0 is provided but not y0, then the elements of x0 are first evaluated, followed by n_random_starts evaluations. Finally, n_calls - len(x0) - n_random_starts evaluations are made guided by the surrogate model. If x0 and y0 are both provided then n_random_starts evaluations are first made then n_calls - n_random_starts subsequent evaluations are made guided by the surrogate model.

## Parameters

• func [callable]: Function to minimize. Should take a array of parameters and return the function values.

• dimensions [list, shape=(n_dims,)]: List of search space dimensions. Each search dimension can be defined either as

• a (upper_bound, lower_bound) tuple (for Real or Integer dimensions),
• a (upper_bound, lower_bound, prior) tuple (for Real dimensions),
• as a list of categories (for Categorical dimensions), or
• an instance of a Dimension object (Real, Integer or Categorical).

NOTE: The upper and lower bounds are inclusive for Integer dimensions.

• base_estimator [string or Regressor, default="ET"]: The regressor to use as surrogate model. Can be either

• "RF" for random forest regressor
• "ET" for extra trees regressor
• instance of regressor with support for return_std in its predict method

The predefined models are initilized with good defaults. If you want to adjust the model parameters pass your own instance of a regressor which returns the mean and standard deviation when making predictions.

• n_calls [int, default=100]: Number of calls to func.

• n_random_starts [int, default=10]: Number of evaluations of func with random points before approximating it with base_estimator.

• acq_func [string, default="LCB"]: Function to minimize over the forest posterior. Can be either

• "LCB" for lower confidence bound.
• "EI" for negative expected improvement.
• "PI" for negative probability of improvement.
• "EIps" for negated expected improvement per second to take into account the function compute time. Then, the objective function is assumed to return two values, the first being the objective value and the second being the time taken in seconds.
• "PIps" for negated probability of improvement per second. The return type of the objective function is assumed to be similar to that of "EIps"
• x0 [list, list of lists or None]: Initial input points.

• If it is a list of lists, use it as a list of input points.
• If it is a list, use it as a single initial input point.
• If it is None, no initial input points are used.
• y0 [list, scalar or None]: Evaluation of initial input points.

• If it is a list, then it corresponds to evaluations of the function at each element of x0 : the i-th element of y0 corresponds to the function evaluated at the i-th element of x0.
• If it is a scalar, then it corresponds to the evaluation of the function at x0.
• If it is None and x0 is provided, then the function is evaluated at each element of x0.
• random_state [int, RandomState instance, or None (default)]: Set random state to something other than None for reproducible results.

• verbose [boolean, default=False]: Control the verbosity. It is advised to set the verbosity to True for long optimization runs.

• callback [callable, optional] If provided, then callback(res) is called after call to func.

• n_points [int, default=10000]: Number of points to sample when minimizing the acquisition function.

• xi [float, default=0.01]: Controls how much improvement one wants over the previous best values. Used when the acquisition is either "EI" or "PI".

• kappa [float, default=1.96]: Controls how much of the variance in the predicted values should be taken into account. If set to be very high, then we are favouring exploration over exploitation and vice versa. Used when the acquisition is "LCB".

• n_jobs [int, default=1]: The number of jobs to run in parallel for fit and predict. If -1, then the number of jobs is set to the number of cores.

## Returns

• res [OptimizeResult, scipy object]: The optimization result returned as a OptimizeResult object. Important attributes are:

• x [list]: location of the minimum.
• fun [float]: function value at the minimum.
• models: surrogate models used for each iteration.
• x_iters [list of lists]: location of function evaluation for each iteration.
• func_vals [array]: function value for each iteration.
• space [Space]: the optimization space.
• specs [dict]: the call specifications.

For more details related to the OptimizeResult object, refer http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.OptimizeResult.html

def forest_minimize(func, dimensions, base_estimator="ET", n_calls=100,
n_random_starts=10, acq_func="EI",
x0=None, y0=None, random_state=None, verbose=False,
callback=None, n_points=10000, xi=0.01, kappa=1.96,
n_jobs=1):
"""Sequential optimisation using decision trees.

A tree based regression model is used to model the expensive to evaluate
function func. The model is improved by sequentially evaluating
the expensive function at the next best point. Thereby finding the
minimum of func with as few evaluations as possible.

The total number of evaluations, n_calls, are performed like the
following. If x0 is provided but not y0, then the elements of x0
are first evaluated, followed by n_random_starts evaluations.
Finally, n_calls - len(x0) - n_random_starts evaluations are
made guided by the surrogate model. If x0 and y0 are both
provided then n_random_starts evaluations are first made then
n_calls - n_random_starts subsequent evaluations are made
guided by the surrogate model.

Parameters
----------
* func [callable]:
Function to minimize. Should take a array of parameters and
return the function values.

* dimensions [list, shape=(n_dims,)]:
List of search space dimensions.
Each search dimension can be defined either as

- a (upper_bound, lower_bound) tuple (for Real or Integer
dimensions),
- a (upper_bound, lower_bound, prior) tuple (for Real
dimensions),
- as a list of categories (for Categorical dimensions), or
- an instance of a Dimension object (Real, Integer or
Categorical).

NOTE: The upper and lower bounds are inclusive for Integer
dimensions.

* base_estimator [string or Regressor, default="ET"]:
The regressor to use as surrogate model. Can be either

- "RF" for random forest regressor
- "ET" for extra trees regressor
- instance of regressor with support for return_std in its predict
method

The predefined models are initilized with good defaults. If you
want to adjust the model parameters pass your own instance of
a regressor which returns the mean and standard deviation when
making predictions.

* n_calls [int, default=100]:
Number of calls to func.

* n_random_starts [int, default=10]:
Number of evaluations of func with random points before
approximating it with base_estimator.

* acq_func [string, default="LCB"]:
Function to minimize over the forest posterior. Can be either

- "LCB" for lower confidence bound.
- "EI" for negative expected improvement.
- "PI" for negative probability of improvement.
- "EIps" for negated expected improvement per second to take into
account the function compute time. Then, the objective function is
assumed to return two values, the first being the objective value and
the second being the time taken in seconds.
- "PIps" for negated probability of improvement per second. The
return type of the objective function is assumed to be similar to
that of "EIps"

* x0 [list, list of lists or None]:
Initial input points.

- If it is a list of lists, use it as a list of input points.
- If it is a list, use it as a single initial input point.
- If it is None, no initial input points are used.

* y0 [list, scalar or None]:
Evaluation of initial input points.

- If it is a list, then it corresponds to evaluations of the function
at each element of x0 : the i-th element of y0 corresponds
to the function evaluated at the i-th element of x0.
- If it is a scalar, then it corresponds to the evaluation of the
function at x0.
- If it is None and x0 is provided, then the function is evaluated
at each element of x0.

* random_state [int, RandomState instance, or None (default)]:
Set random state to something other than None for reproducible
results.

* verbose [boolean, default=False]:
Control the verbosity. It is advised to set the verbosity to True
for long optimization runs.

* callback [callable, optional]
If provided, then callback(res) is called after call to func.

* n_points [int, default=10000]:
Number of points to sample when minimizing the acquisition function.

* xi [float, default=0.01]:
Controls how much improvement one wants over the previous best
values. Used when the acquisition is either "EI" or "PI".

* kappa [float, default=1.96]:
Controls how much of the variance in the predicted values should be
taken into account. If set to be very high, then we are favouring
exploration over exploitation and vice versa.
Used when the acquisition is "LCB".

* n_jobs [int, default=1]:
The number of jobs to run in parallel for fit and predict.
If -1, then the number of jobs is set to the number of cores.

Returns
-------
* res [OptimizeResult, scipy object]:
The optimization result returned as a OptimizeResult object.
Important attributes are:

- x [list]: location of the minimum.
- fun [float]: function value at the minimum.
- models: surrogate models used for each iteration.
- x_iters [list of lists]: location of function evaluation for each
iteration.
- func_vals [array]: function value for each iteration.
- space [Space]: the optimization space.
- specs [dict]: the call specifications.

For more details related to the OptimizeResult object, refer
http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.OptimizeResult.html
"""
rng = check_random_state(random_state)

if isinstance(base_estimator, str):
base_estimator = cook_estimator(base_estimator, n_jobs=n_jobs,
random_state=rng)

return base_minimize(func, dimensions, base_estimator,
n_calls=n_calls, n_points=n_points,
n_random_starts=n_random_starts,
x0=x0, y0=y0, random_state=random_state,
acq_func=acq_func,
xi=xi, kappa=kappa, verbose=verbose,
callback=callback, acq_optimizer="sampling")


def gbrt_minimize(

func, dimensions, base_estimator=None, n_calls=100, n_random_starts=10, acq_func='EI', acq_optimizer='auto', x0=None, y0=None, random_state=None, verbose=False, callback=None, n_points=10000, xi=0.01, kappa=1.96, n_jobs=1)

Sequential optimization using gradient boosted trees.

Gradient boosted regression trees are used to model the (very) expensive to evaluate function func. The model is improved by sequentially evaluating the expensive function at the next best point. Thereby finding the minimum of func with as few evaluations as possible.

The total number of evaluations, n_calls, are performed like the following. If x0 is provided but not y0, then the elements of x0 are first evaluated, followed by n_random_starts evaluations. Finally, n_calls - len(x0) - n_random_starts evaluations are made guided by the surrogate model. If x0 and y0 are both provided then n_random_starts evaluations are first made then n_calls - n_random_starts subsequent evaluations are made guided by the surrogate model.

## Parameters

• func [callable]: Function to minimize. Should take a array of parameters and return the function values.

• dimensions [list, shape=(n_dims,)]: List of search space dimensions. Each search dimension can be defined either as

• a (upper_bound, lower_bound) tuple (for Real or Integer dimensions),
• a (upper_bound, lower_bound, "prior") tuple (for Real dimensions),
• as a list of categories (for Categorical dimensions), or
• an instance of a Dimension object (Real, Integer or Categorical).
• base_estimator [GradientBoostingQuantileRegressor]: The regressor to use as surrogate model

• n_calls [int, default=100]: Number of calls to func.

• n_random_starts [int, default=10]: Number of evaluations of func with random points before approximating it with base_estimator.

• acq_func [string, default="LCB"]: Function to minimize over the forest posterior. Can be either

• "LCB" for lower confidence bound.
• "EI" for negative expected improvement.
• "PI" for negative probability of improvement.
• "EIps" for negated expected improvement per second to take into account the function compute time. Then, the objective function is assumed to return two values, the first being the objective value and the second being the time taken.
• "PIps" for negated probability of improvement per second.
• x0 [list, list of lists or None]: Initial input points.

• If it is a list of lists, use it as a list of input points.
• If it is a list, use it as a single initial input point.
• If it is None, no initial input points are used.
• y0 [list, scalar or None]: Evaluation of initial input points.

• If it is a list, then it corresponds to evaluations of the function at each element of x0 : the i-th element of y0 corresponds to the function evaluated at the i-th element of x0.
• If it is a scalar, then it corresponds to the evaluation of the function at x0.
• If it is None and x0 is provided, then the function is evaluated at each element of x0.
• random_state [int, RandomState instance, or None (default)]: Set random state to something other than None for reproducible results.

• verbose [boolean, default=False]: Control the verbosity. It is advised to set the verbosity to True for long optimization runs.

• callback [callable, optional] If provided, then callback(res) is called after call to func.

• n_points [int, default=10000]: Number of points to sample when minimizing the acquisition function.

• xi [float, default=0.01]: Controls how much improvement one wants over the previous best values. Used when the acquisition is either "EI" or "PI".

• kappa [float, default=1.96]: Controls how much of the variance in the predicted values should be taken into account. If set to be very high, then we are favouring exploration over exploitation and vice versa. Used when the acquisition is "LCB".

• n_jobs [int, default=1]: The number of jobs to run in parallel for fit and predict. If -1, then the number of jobs is set to the number of cores.

## Returns

• res [OptimizeResult, scipy object]: The optimization result returned as a OptimizeResult object. Important attributes are:

• x [list]: location of the minimum.
• fun [float]: function value at the minimum.
• models: surrogate models used for each iteration.
• x_iters [list of lists]: location of function evaluation for each iteration.
• func_vals [array]: function value for each iteration.
• space [Space]: the optimization space.
• specs [dict]: the call specifications.
• rng [RandomState instance]: State of the random state at the end of minimization.

For more details related to the OptimizeResult object, refer http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.OptimizeResult.html

def gbrt_minimize(func, dimensions, base_estimator=None,
n_calls=100, n_random_starts=10,
acq_func="EI", acq_optimizer="auto",
x0=None, y0=None, random_state=None, verbose=False,
callback=None, n_points=10000, xi=0.01, kappa=1.96,
n_jobs=1):
"""Sequential optimization using gradient boosted trees.

Gradient boosted regression trees are used to model the (very)
expensive to evaluate function func. The model is improved
by sequentially evaluating the expensive function at the next
best point. Thereby finding the minimum of func with as
few evaluations as possible.

The total number of evaluations, n_calls, are performed like the
following. If x0 is provided but not y0, then the elements of x0
are first evaluated, followed by n_random_starts evaluations.
Finally, n_calls - len(x0) - n_random_starts evaluations are
made guided by the surrogate model. If x0 and y0 are both
provided then n_random_starts evaluations are first made then
n_calls - n_random_starts subsequent evaluations are made
guided by the surrogate model.

Parameters
----------
* func [callable]:
Function to minimize. Should take a array of parameters and
return the function values.

* dimensions [list, shape=(n_dims,)]:
List of search space dimensions.
Each search dimension can be defined either as

- a (upper_bound, lower_bound) tuple (for Real or Integer
dimensions),
- a (upper_bound, lower_bound, "prior") tuple (for Real
dimensions),
- as a list of categories (for Categorical dimensions), or
- an instance of a Dimension object (Real, Integer or
Categorical).

* base_estimator [GradientBoostingQuantileRegressor]:
The regressor to use as surrogate model

* n_calls [int, default=100]:
Number of calls to func.

* n_random_starts [int, default=10]:
Number of evaluations of func with random points before
approximating it with base_estimator.

* acq_func [string, default="LCB"]:
Function to minimize over the forest posterior. Can be either

- "LCB" for lower confidence bound.
- "EI" for negative expected improvement.
- "PI" for negative probability of improvement.
- "EIps" for negated expected improvement per second to take into
account the function compute time. Then, the objective function is
assumed to return two values, the first being the objective value and
the second being the time taken.
- "PIps" for negated probability of improvement per second.

* x0 [list, list of lists or None]:
Initial input points.

- If it is a list of lists, use it as a list of input points.
- If it is a list, use it as a single initial input point.
- If it is None, no initial input points are used.

* y0 [list, scalar or None]:
Evaluation of initial input points.

- If it is a list, then it corresponds to evaluations of the function
at each element of x0 : the i-th element of y0 corresponds
to the function evaluated at the i-th element of x0.
- If it is a scalar, then it corresponds to the evaluation of the
function at x0.
- If it is None and x0 is provided, then the function is evaluated
at each element of x0.

* random_state [int, RandomState instance, or None (default)]:
Set random state to something other than None for reproducible
results.

* verbose [boolean, default=False]:
Control the verbosity. It is advised to set the verbosity to True
for long optimization runs.

* callback [callable, optional]
If provided, then callback(res) is called after call to func.

* n_points [int, default=10000]:
Number of points to sample when minimizing the acquisition function.

* xi [float, default=0.01]:
Controls how much improvement one wants over the previous best
values. Used when the acquisition is either "EI" or "PI".

* kappa [float, default=1.96]:
Controls how much of the variance in the predicted values should be
taken into account. If set to be very high, then we are favouring
exploration over exploitation and vice versa.
Used when the acquisition is "LCB".

* n_jobs [int, default=1]:
The number of jobs to run in parallel for fit and predict.
If -1, then the number of jobs is set to the number of cores.

Returns
-------
* res [OptimizeResult, scipy object]:
The optimization result returned as a OptimizeResult object.
Important attributes are:

- x [list]: location of the minimum.
- fun [float]: function value at the minimum.
- models: surrogate models used for each iteration.
- x_iters [list of lists]: location of function evaluation for each
iteration.
- func_vals [array]: function value for each iteration.
- space [Space]: the optimization space.
- specs [dict]: the call specifications.
- rng [RandomState instance]: State of the random state
at the end of minimization.

For more details related to the OptimizeResult object, refer
http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.OptimizeResult.html
"""
# Check params
rng = check_random_state(random_state)

if base_estimator is None:
base_estimator = cook_estimator("GBRT", random_state=rng,
n_jobs=n_jobs)
return base_minimize(func, dimensions, base_estimator,
n_calls=n_calls, n_points=n_points,
n_random_starts=n_random_starts,
x0=x0, y0=y0, random_state=random_state, xi=xi,
kappa=kappa, acq_func=acq_func, verbose=verbose,
callback=callback, acq_optimizer="sampling")


def gp_minimize(

func, dimensions, base_estimator=None, n_calls=100, n_random_starts=10, acq_func='gp_hedge', acq_optimizer='auto', x0=None, y0=None, random_state=None, verbose=False, callback=None, n_points=10000, n_restarts_optimizer=5, xi=0.01, kappa=1.96, noise='gaussian', n_jobs=1)

Bayesian optimization using Gaussian Processes.

If every function evaluation is expensive, for instance when the parameters are the hyperparameters of a neural network and the function evaluation is the mean cross-validation score across ten folds, optimizing the hyperparameters by standard optimization routines would take for ever!

The idea is to approximate the function using a Gaussian process. In other words the function values are assumed to follow a multivariate gaussian. The covariance of the function values are given by a GP kernel between the parameters. Then a smart choice to choose the next parameter to evaluate can be made by the acquisition function over the Gaussian prior which is much quicker to evaluate.

The total number of evaluations, n_calls, are performed like the following. If x0 is provided but not y0, then the elements of x0 are first evaluated, followed by n_random_starts evaluations. Finally, n_calls - len(x0) - n_random_starts evaluations are made guided by the surrogate model. If x0 and y0 are both provided then n_random_starts evaluations are first made then n_calls - n_random_starts subsequent evaluations are made guided by the surrogate model.

## Parameters

• func [callable]: Function to minimize. Should take a array of parameters and return the function values.

• dimensions [list, shape=(n_dims,)]: List of search space dimensions. Each search dimension can be defined either as

• a (upper_bound, lower_bound) tuple (for Real or Integer dimensions),
• a (upper_bound, lower_bound, "prior") tuple (for Real dimensions),
• as a list of categories (for Categorical dimensions), or
• an instance of a Dimension object (Real, Integer or Categorical).

NOTE: The upper and lower bounds are inclusive for Integer dimensions.

• base_estimator [a Gaussian process estimator]: The Gaussian process estimator to use for optimization. By default, a Matern kernel is used with the following hyperparameters tuned.

• All the length scales of the Matern kernel.
• The covariance amplitude that each element is multiplied with.
• Noise that is added to the matern kernel. The noise is assumed to be iid gaussian.
• n_calls [int, default=100]: Number of calls to func.

• n_random_starts [int, default=10]: Number of evaluations of func with random points before approximating it with base_estimator.

• acq_func [string, default="EI"]: Function to minimize over the gaussian prior. Can be either

• "LCB" for lower confidence bound.
• "EI" for negative expected improvement.
• "PI" for negative probability of improvement.
• "gp_hedge" Probabilistically choose one of the above three acquisition functions at every iteration. The weightage given to these gains can be set by \eta through acq_func_kwargs.
• The gains g_i are initialized to zero.
• At every iteration,
• Each acquisition function is optimised independently to propose an candidate point X_i.
• Out of all these candidate points, the next point X_best is chosen by softmax(\eta g_i)
• After fitting the surrogate model with (X_best, y_best), the gains are updated such that g_i -= \mu(X_i)
• "EIps" for negated expected improvement per second to take into account the function compute time. Then, the objective function is assumed to return two values, the first being the objective value and the second being the time taken in seconds.
• "PIps" for negated probability of improvement per second. The return type of the objective function is assumed to be similar to that of "EIps
• acq_optimizer [string, "sampling" or "lbfgs", default="lbfgs"]: Method to minimize the acquistion function. The fit model is updated with the optimal value obtained by optimizing acq_func with acq_optimizer.

The acq_func is computed at n_points sampled randomly.

• If set to "auto", then acq_optimizer is configured on the basis of the space searched over. If the space is Categorical then this is set to be "sampling".
• If set to "sampling", then the point among these n_points where the acq_func is minimum is the next candidate minimum.
• If set to "lbfgs", then
• The n_restarts_optimizer no. of points which the acquisition function is least are taken as start points.
• "lbfgs" is run for 20 iterations with these points as initial points to find local minima.
• The optimal of these local minima is used to update the prior.
• x0 [list, list of lists or None]: Initial input points.

• If it is a list of lists, use it as a list of input points.
• If it is a list, use it as a single initial input point.
• If it is None, no initial input points are used.
• y0 [list, scalar or None] Evaluation of initial input points.

• If it is a list, then it corresponds to evaluations of the function at each element of x0 : the i-th element of y0 corresponds to the function evaluated at the i-th element of x0.
• If it is a scalar, then it corresponds to the evaluation of the function at x0.
• If it is None and x0 is provided, then the function is evaluated at each element of x0.
• random_state [int, RandomState instance, or None (default)]: Set random state to something other than None for reproducible results.

• verbose [boolean, default=False]: Control the verbosity. It is advised to set the verbosity to True for long optimization runs.

• callback [callable, list of callables, optional] If callable then callback(res) is called after each call to func. If list of callables, then each callable in the list is called.

• n_points [int, default=10000]: Number of points to sample to determine the next "best" point. Useless if acq_optimizer is set to "lbfgs".

• n_restarts_optimizer [int, default=5]: The number of restarts of the optimizer when acq_optimizer is "lbfgs".

• kappa [float, default=1.96]: Controls how much of the variance in the predicted values should be taken into account. If set to be very high, then we are favouring exploration over exploitation and vice versa. Used when the acquisition is "LCB".

• xi [float, default=0.01]: Controls how much improvement one wants over the previous best values. Used when the acquisition is either "EI" or "PI".

• noise [float, default="gaussian"]:

• Use noise="gaussian" if the objective returns noisy observations. The noise of each observation is assumed to be iid with mean zero and a fixed variance.
• If the variance is known before-hand, this can be set directly to the variance of the noise.
• Set this to a value close to zero (1e-10) if the function is noise-free. Setting to zero might cause stability issues.
• n_jobs [int, default=1] Number of cores to run in parallel while running the lbfgs optimizations over the acquisition function. Valid only when acq_optimizer is set to "lbfgs." Defaults to 1 core. If n_jobs=-1, then number of jobs is set to number of cores.

## Returns

• res [OptimizeResult, scipy object]: The optimization result returned as a OptimizeResult object. Important attributes are:

• x [list]: location of the minimum.
• fun [float]: function value at the minimum.
• models: surrogate models used for each iteration.
• x_iters [list of lists]: location of function evaluation for each iteration.
• func_vals [array]: function value for each iteration.
• space [Space]: the optimization space.
• specs [dict]: the call specifications.
• rng [RandomState instance]: State of the random state at the end of minimization.

For more details related to the OptimizeResult object, refer http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.OptimizeResult.html

def gp_minimize(func, dimensions, base_estimator=None,
n_calls=100, n_random_starts=10,
acq_func="gp_hedge", acq_optimizer="auto", x0=None, y0=None,
random_state=None, verbose=False, callback=None,
n_points=10000, n_restarts_optimizer=5, xi=0.01, kappa=1.96,
noise="gaussian", n_jobs=1):
"""Bayesian optimization using Gaussian Processes.

If every function evaluation is expensive, for instance
when the parameters are the hyperparameters of a neural network
and the function evaluation is the mean cross-validation score across
ten folds, optimizing the hyperparameters by standard optimization
routines would take for ever!

The idea is to approximate the function using a Gaussian process.
In other words the function values are assumed to follow a multivariate
gaussian. The covariance of the function values are given by a
GP kernel between the parameters. Then a smart choice to choose the
next parameter to evaluate can be made by the acquisition function
over the Gaussian prior which is much quicker to evaluate.

The total number of evaluations, n_calls, are performed like the
following. If x0 is provided but not y0, then the elements of x0
are first evaluated, followed by n_random_starts evaluations.
Finally, n_calls - len(x0) - n_random_starts evaluations are
made guided by the surrogate model. If x0 and y0 are both
provided then n_random_starts evaluations are first made then
n_calls - n_random_starts subsequent evaluations are made
guided by the surrogate model.

Parameters
----------
* func [callable]:
Function to minimize. Should take a array of parameters and
return the function values.

* dimensions [list, shape=(n_dims,)]:
List of search space dimensions.
Each search dimension can be defined either as

- a (upper_bound, lower_bound) tuple (for Real or Integer
dimensions),
- a (upper_bound, lower_bound, "prior") tuple (for Real
dimensions),
- as a list of categories (for Categorical dimensions), or
- an instance of a Dimension object (Real, Integer or
Categorical).

NOTE: The upper and lower bounds are inclusive for Integer
dimensions.

* base_estimator [a Gaussian process estimator]:
The Gaussian process estimator to use for optimization.
By default, a Matern kernel is used with the following
hyperparameters tuned.
- All the length scales of the Matern kernel.
- The covariance amplitude that each element is multiplied with.
- Noise that is added to the matern kernel. The noise is assumed
to be iid gaussian.

* n_calls [int, default=100]:
Number of calls to func.

* n_random_starts [int, default=10]:
Number of evaluations of func with random points before
approximating it with base_estimator.

* acq_func [string, default="EI"]:
Function to minimize over the gaussian prior. Can be either

- "LCB" for lower confidence bound.
- "EI" for negative expected improvement.
- "PI" for negative probability of improvement.
- "gp_hedge" Probabilistically choose one of the above three
acquisition functions at every iteration. The weightage
given to these gains can be set by \eta through acq_func_kwargs.
- The gains g_i are initialized to zero.
- At every iteration,
- Each acquisition function is optimised independently to
propose an candidate point X_i.
- Out of all these candidate points, the next point X_best is
chosen by softmax(\eta g_i)
- After fitting the surrogate model with (X_best, y_best),
the gains are updated such that g_i -= \mu(X_i)
- "EIps" for negated expected improvement per second to take into
account the function compute time. Then, the objective function is
assumed to return two values, the first being the objective value and
the second being the time taken in seconds.
- "PIps" for negated probability of improvement per second. The
return type of the objective function is assumed to be similar to
that of "EIps

* acq_optimizer [string, "sampling" or "lbfgs", default="lbfgs"]:
Method to minimize the acquistion function. The fit model
is updated with the optimal value obtained by optimizing acq_func
with acq_optimizer.

The acq_func is computed at n_points sampled randomly.

- If set to "auto", then acq_optimizer is configured on the
basis of the space searched over.
If the space is Categorical then this is set to be "sampling".
- If set to "sampling", then the point among these n_points
where the acq_func is minimum is the next candidate minimum.
- If set to "lbfgs", then
- The n_restarts_optimizer no. of points which the acquisition
function is least are taken as start points.
- "lbfgs" is run for 20 iterations with these points as initial
points to find local minima.
- The optimal of these local minima is used to update the prior.

* x0 [list, list of lists or None]:
Initial input points.

- If it is a list of lists, use it as a list of input points.
- If it is a list, use it as a single initial input point.
- If it is None, no initial input points are used.

* y0 [list, scalar or None]
Evaluation of initial input points.

- If it is a list, then it corresponds to evaluations of the function
at each element of x0 : the i-th element of y0 corresponds
to the function evaluated at the i-th element of x0.
- If it is a scalar, then it corresponds to the evaluation of the
function at x0.
- If it is None and x0 is provided, then the function is evaluated
at each element of x0.

* random_state [int, RandomState instance, or None (default)]:
Set random state to something other than None for reproducible
results.

* verbose [boolean, default=False]:
Control the verbosity. It is advised to set the verbosity to True
for long optimization runs.

* callback [callable, list of callables, optional]
If callable then callback(res) is called after each call to func.
If list of callables, then each callable in the list is called.

* n_points [int, default=10000]:
Number of points to sample to determine the next "best" point.
Useless if acq_optimizer is set to "lbfgs".

* n_restarts_optimizer [int, default=5]:
The number of restarts of the optimizer when acq_optimizer
is "lbfgs".

* kappa [float, default=1.96]:
Controls how much of the variance in the predicted values should be
taken into account. If set to be very high, then we are favouring
exploration over exploitation and vice versa.
Used when the acquisition is "LCB".

* xi [float, default=0.01]:
Controls how much improvement one wants over the previous best
values. Used when the acquisition is either "EI" or "PI".

* noise [float, default="gaussian"]:
- Use noise="gaussian" if the objective returns noisy observations.
The noise of each observation is assumed to be iid with
mean zero and a fixed variance.
- If the variance is known before-hand, this can be set directly
to the variance of the noise.
- Set this to a value close to zero (1e-10) if the function is
noise-free. Setting to zero might cause stability issues.

* n_jobs [int, default=1]
Number of cores to run in parallel while running the lbfgs
optimizations over the acquisition function. Valid only
when acq_optimizer is set to "lbfgs."
Defaults to 1 core. If n_jobs=-1, then number of jobs is set
to number of cores.

Returns
-------
* res [OptimizeResult, scipy object]:
The optimization result returned as a OptimizeResult object.
Important attributes are:

- x [list]: location of the minimum.
- fun [float]: function value at the minimum.
- models: surrogate models used for each iteration.
- x_iters [list of lists]: location of function evaluation for each
iteration.
- func_vals [array]: function value for each iteration.
- space [Space]: the optimization space.
- specs [dict]: the call specifications.
- rng [RandomState instance]: State of the random state
at the end of minimization.

For more details related to the OptimizeResult object, refer
http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.OptimizeResult.html
"""
# Check params
rng = check_random_state(random_state)
space = normalize_dimensions(dimensions)
base_estimator = cook_estimator("GP", space=space, random_state=rng,
noise=noise)

return base_minimize(
func, space, base_estimator=base_estimator,
acq_func=acq_func,
xi=xi, kappa=kappa, acq_optimizer=acq_optimizer, n_calls=n_calls,
n_points=n_points, n_random_starts=n_random_starts,
n_restarts_optimizer=n_restarts_optimizer,
x0=x0, y0=y0, random_state=random_state, verbose=verbose,
callback=callback, n_jobs=n_jobs)


def load(

filename, **kwargs)

Reconstruct a skopt optimization result from a file persisted with skopt.dump.

Notice that the loaded optimization result can be missing the objective function (.specs['args']['func']) if dump was called with store_objective=False.

## Parameters

• filename [string or pathlib.Path]: The path of the file from which to load the optimization result.

• **kwargs [other keyword arguments]: All other keyword arguments will be passed to joblib.load.

## Returns

• res [OptimizeResult, scipy object]: Reconstructed OptimizeResult instance.
def load(filename, **kwargs):
"""
Reconstruct a skopt optimization result from a file
persisted with skopt.dump.

Notice that the loaded optimization result can be missing
the objective function (.specs['args']['func']) if skopt.dump
was called with store_objective=False.

Parameters
----------
* filename [string or pathlib.Path]:
The path of the file from which to load the optimization result.

* **kwargs [other keyword arguments]:
All other keyword arguments will be passed to joblib.load.

Returns
-------
* res [OptimizeResult, scipy object]:
Reconstructed OptimizeResult instance.
"""
return load_(filename, **kwargs)


## Classes

class BayesSearchCV

Bayesian optimization over hyper parameters.

BayesSearchCV implements a "fit" and a "score" method. It also implements "predict", "predict_proba", "decision_function", "transform" and "inverse_transform" if they are implemented in the estimator used.

The parameters of the estimator used to apply these methods are optimized by cross-validated search over parameter settings.

In contrast to GridSearchCV, not all parameter values are tried out, but rather a fixed number of parameter settings is sampled from the specified distributions. The number of parameter settings that are tried is given by n_iter.

Parameters are presented as a list of skopt.space.Dimension objects.

## Parameters

estimator : estimator object. A object of that type is instantiated for each search point. This object is assumed to implement the scikit-learn estimator api. Either estimator needs to provide a score function, or scoring must be passed.

search_spaces : dict, list of dict or list of tuple containing (dict, int), or None. One of 4 following cases: 1. dictionary, where keys are parameter names (strings) and values are skopt.space.Dimension instances (Real, Integer or Categorical) or any other valid value that defines skopt dimension (see skopt.Optimizer docs). Represents search space over parameters of the provided estimator. 2. list of dictionaries: a list of dictionaries, where every dictionary fits the description given in case 1 above. If a list of dictionary objects is given, then the search is performed sequentially for every parameter space with maximum number of evaluations set to self.n_iter. 3. list of (dict, int > 0): an extension of case 2 above, where first element of every tuple is a dictionary representing some search subspace, similarly as in case 2, and second element is a number of iterations that will be spent optimizing over this subspace. 4. None, in which case it is assumed that a user will provide search space via the add_spaces function.

n_iter : int, default=128 Number of parameter settings that are sampled. n_iter trades off runtime vs quality of the solution.

surrogate : string or skopt surrogate, default='auto' Surrogate to use for optimization of score of estimator. By default skopt.learning.GaussianProcessRegressor() is used.

scoring : string, callable or None, default=None A string (see model evaluation documentation) or a scorer callable object / function with signature scorer(estimator, X, y). If None, the score method of the estimator is used.

fit_params : dict, optional Parameters to pass to the fit method.

n_jobs : int, default=1 Number of jobs to run in parallel.

pre_dispatch : int, or string, optional Controls the number of jobs that get dispatched during parallel execution. Reducing this number can be useful to avoid an explosion of memory consumption when more jobs get dispatched than CPUs can process. This parameter can be:

    - None, in which case all the jobs are immediately
created and spawned. Use this for lightweight and
fast-running jobs, to avoid delays due to on-demand
spawning of the jobs

- An int, giving the exact number of total jobs that are
spawned

- A string, giving an expression as a function of n_jobs,
as in '2*n_jobs'


iid : boolean, default=True If True, the data is assumed to be identically distributed across the folds, and the loss minimized is the total loss per sample, and not the mean loss across the folds.

cv : int, cross-validation generator or an iterable, optional Determines the cross-validation splitting strategy. Possible inputs for cv are: - None, to use the default 3-fold cross validation, - integer, to specify the number of folds in a (Stratified)KFold, - An object to be used as a cross-validation generator. - An iterable yielding train, test splits.

For integer/None inputs, if the estimator is a classifier and y is
either binary or multiclass, :class:StratifiedKFold is used. In all
other cases, :class:KFold is used.

Refer :ref:User Guide <cross_validation> for the various
cross-validation strategies that can be used here.


refit : boolean, default=True Refit the best estimator with the entire dataset. If "False", it is impossible to make predictions using this RandomizedSearchCV instance after fitting.

verbose : integer Controls the verbosity: the higher, the more messages.

random_state : int or RandomState Pseudo random number generator state used for random uniform sampling from lists of possible values instead of scipy.stats distributions.

error_score : 'raise' (default) or numeric Value to assign to the score if an error occurs in estimator fitting. If set to 'raise', the error is raised. If a numeric value is given, FitFailedWarning is raised. This parameter does not affect the refit step, which will always raise the error.

return_train_score : boolean, default=True If 'False', the cv_results_ attribute will not include training scores.

## Example

from skopt import BayesSearchCV

# parameter ranges are specified by one of below

from skopt.space import Real, Categorical, Integer

from sklearn.datasets import load_iris from sklearn.svm import SVC from sklearn.model_selection import train_test_split

X, y = load_iris(True) X_train, X_test, y_train, y_test = train_test_split(X, y, train_size=0.75, random_state=0)

# log-uniform: understand as search over p = exp(x) by varying x

opt = BayesSearchCV( SVC(), { 'C': Real(1e-6, 1e+6, prior='log-uniform'), 'gamma': Real(1e-6, 1e+1, prior='log-uniform'), 'degree': Integer(1,8), 'kernel': Categorical(['linear', 'poly', 'rbf']), }, n_iter=32 )

# executes bayesian optimization

opt.fit(X_train, y_train)

# model can be saved, used for predictions or scoring

print(opt.score(X_test, y_test))

## Attributes

cv_results_ : dict of numpy (masked) ndarrays A dict with keys as column headers and values as columns, that can be imported into a pandas DataFrame.

For instance the below given table

+--------------+-------------+-------------------+---+---------------+
| param_kernel | param_gamma | split0_test_score |...|rank_test_score|
+==============+=============+===================+===+===============+
|    'rbf'     |     0.1     |        0.8        |...|       2       |
+--------------+-------------+-------------------+---+---------------+
|    'rbf'     |     0.2     |        0.9        |...|       1       |
+--------------+-------------+-------------------+---+---------------+
|    'rbf'     |     0.3     |        0.7        |...|       1       |
+--------------+-------------+-------------------+---+---------------+

will be represented by a cv_results_ dict of::

{
'param_kernel' : masked_array(data = ['rbf', 'rbf', 'rbf'],
mask = False),
'param_gamma'  : masked_array(data = [0.1 0.2 0.3], mask = False),
'split0_test_score'  : [0.8, 0.9, 0.7],
'split1_test_score'  : [0.82, 0.5, 0.7],
'mean_test_score'    : [0.81, 0.7, 0.7],
'std_test_score'     : [0.02, 0.2, 0.],
'rank_test_score'    : [3, 1, 1],
'split0_train_score' : [0.8, 0.9, 0.7],
'split1_train_score' : [0.82, 0.5, 0.7],
'mean_train_score'   : [0.81, 0.7, 0.7],
'std_train_score'    : [0.03, 0.03, 0.04],
'mean_fit_time'      : [0.73, 0.63, 0.43, 0.49],
'std_fit_time'       : [0.01, 0.02, 0.01, 0.01],
'mean_score_time'    : [0.007, 0.06, 0.04, 0.04],
'std_score_time'     : [0.001, 0.002, 0.003, 0.005],
'params' : [{'kernel' : 'rbf', 'gamma' : 0.1}, ...],
}

NOTE that the key 'params' is used to store a list of parameter
settings dict for all the parameter candidates.

The mean_fit_time, std_fit_time, mean_score_time and
std_score_time are all in seconds.


best_estimator_ : estimator Estimator that was chosen by the search, i.e. estimator which gave highest score (or smallest loss if specified) on the left out data. Not available if refit=False.

best_score_ : float Score of best_estimator on the left out data.

best_params_ : dict Parameter setting that gave the best results on the hold out data.

best_index_ : int The index (of the cv_results_ arrays) which corresponds to the best candidate parameter setting.

The dict at search.cv_results_['params'][search.best_index_] gives
the parameter setting for the best model, that gives the highest
mean score (search.best_score_).


scorer_ : function Scorer function used on the held out data to choose the best parameters for the model.

n_splits_ : int The number of cross-validation splits (folds/iterations).

## Notes

The parameters selected are those that maximize the score of the held-out data, according to the scoring parameter.

If n_jobs was set to a value higher than one, the data is copied for each parameter setting(and not n_jobs times). This is done for efficiency reasons if individual jobs take very little time, but may raise errors if the dataset is large and not enough memory is available. A workaround in this case is to set pre_dispatch. Then, the memory is copied only pre_dispatch many times. A reasonable value for pre_dispatch is 2 * n_jobs.

## See Also

:class:GridSearchCV: Does exhaustive search over a grid of parameters.

class BayesSearchCV(sklearn.model_selection._search.BaseSearchCV):
"""Bayesian optimization over hyper parameters.

BayesSearchCV implements a "fit" and a "score" method.
It also implements "predict", "predict_proba", "decision_function",
"transform" and "inverse_transform" if they are implemented in the
estimator used.

The parameters of the estimator used to apply these methods are optimized
by cross-validated search over parameter settings.

In contrast to GridSearchCV, not all parameter values are tried out, but
rather a fixed number of parameter settings is sampled from the specified
distributions. The number of parameter settings that are tried is
given by n_iter.

Parameters are presented as a list of skopt.space.Dimension objects.

Parameters
----------
estimator : estimator object.
A object of that type is instantiated for each search point.
This object is assumed to implement the scikit-learn estimator api.
Either estimator needs to provide a score function,
or scoring must be passed.

search_spaces : dict, list of dict or list of tuple containing
(dict, int), or None.
One of 4 following cases:
1. dictionary, where keys are parameter names (strings)
and values are skopt.space.Dimension instances (Real, Integer
or Categorical) or any other valid value that defines skopt
dimension (see skopt.Optimizer docs). Represents search space
over parameters of the provided estimator.
2. list of dictionaries: a list of dictionaries, where every
dictionary fits the description given in case 1 above.
If a list of dictionary objects is given, then the search is
performed sequentially for every parameter space with maximum
number of evaluations set to self.n_iter.
3. list of (dict, int > 0): an extension of case 2 above,
where first element of every tuple is a dictionary representing
some search subspace, similarly as in case 2, and second element
is a number of iterations that will be spent optimizing over
this subspace.
4. None, in which case it is assumed that a user will provide
search space via the add_spaces function.

n_iter : int, default=128
Number of parameter settings that are sampled. n_iter trades
off runtime vs quality of the solution.

surrogate : string or skopt surrogate, default='auto'
Surrogate to use for optimization of score of estimator.
By default skopt.learning.GaussianProcessRegressor() is used.

scoring : string, callable or None, default=None
A string (see model evaluation documentation) or
a scorer callable object / function with signature
scorer(estimator, X, y).
If None, the score method of the estimator is used.

fit_params : dict, optional
Parameters to pass to the fit method.

n_jobs : int, default=1
Number of jobs to run in parallel.

pre_dispatch : int, or string, optional
Controls the number of jobs that get dispatched during parallel
execution. Reducing this number can be useful to avoid an
explosion of memory consumption when more jobs get dispatched
than CPUs can process. This parameter can be:

- None, in which case all the jobs are immediately
created and spawned. Use this for lightweight and
fast-running jobs, to avoid delays due to on-demand
spawning of the jobs

- An int, giving the exact number of total jobs that are
spawned

- A string, giving an expression as a function of n_jobs,
as in '2*n_jobs'

iid : boolean, default=True
If True, the data is assumed to be identically distributed across
the folds, and the loss minimized is the total loss per sample,
and not the mean loss across the folds.

cv : int, cross-validation generator or an iterable, optional
Determines the cross-validation splitting strategy.
Possible inputs for cv are:
- None, to use the default 3-fold cross validation,
- integer, to specify the number of folds in a (Stratified)KFold,
- An object to be used as a cross-validation generator.
- An iterable yielding train, test splits.

For integer/None inputs, if the estimator is a classifier and y is
either binary or multiclass, :class:StratifiedKFold is used. In all
other cases, :class:KFold is used.

Refer :ref:User Guide <cross_validation> for the various
cross-validation strategies that can be used here.

refit : boolean, default=True
Refit the best estimator with the entire dataset.
If "False", it is impossible to make predictions using
this RandomizedSearchCV instance after fitting.

verbose : integer
Controls the verbosity: the higher, the more messages.

random_state : int or RandomState
Pseudo random number generator state used for random uniform sampling
from lists of possible values instead of scipy.stats distributions.

error_score : 'raise' (default) or numeric
Value to assign to the score if an error occurs in estimator fitting.
If set to 'raise', the error is raised. If a numeric value is given,
FitFailedWarning is raised. This parameter does not affect the refit
step, which will always raise the error.

return_train_score : boolean, default=True
If 'False', the cv_results_ attribute will not include training
scores.

Example
-------

from skopt import BayesSearchCV
# parameter ranges are specified by one of below
from skopt.space import Real, Categorical, Integer

from sklearn.datasets import load_iris
from sklearn.svm import SVC
from sklearn.model_selection import train_test_split

X, y = load_iris(True)
X_train, X_test, y_train, y_test = train_test_split(X, y, train_size=0.75, random_state=0)

# log-uniform: understand as search over p = exp(x) by varying x
opt = BayesSearchCV(
SVC(),
{
'C': Real(1e-6, 1e+6, prior='log-uniform'),
'gamma': Real(1e-6, 1e+1, prior='log-uniform'),
'degree': Integer(1,8),
'kernel': Categorical(['linear', 'poly', 'rbf']),
},
n_iter=32
)

# executes bayesian optimization
opt.fit(X_train, y_train)

# model can be saved, used for predictions or scoring
print(opt.score(X_test, y_test))

Attributes
----------
cv_results_ : dict of numpy (masked) ndarrays
A dict with keys as column headers and values as columns, that can be
imported into a pandas DataFrame.

For instance the below given table

+--------------+-------------+-------------------+---+---------------+
| param_kernel | param_gamma | split0_test_score |...|rank_test_score|
+==============+=============+===================+===+===============+
|    'rbf'     |     0.1     |        0.8        |...|       2       |
+--------------+-------------+-------------------+---+---------------+
|    'rbf'     |     0.2     |        0.9        |...|       1       |
+--------------+-------------+-------------------+---+---------------+
|    'rbf'     |     0.3     |        0.7        |...|       1       |
+--------------+-------------+-------------------+---+---------------+

will be represented by a cv_results_ dict of::

{
'param_kernel' : masked_array(data = ['rbf', 'rbf', 'rbf'],
mask = False),
'param_gamma'  : masked_array(data = [0.1 0.2 0.3], mask = False),
'split0_test_score'  : [0.8, 0.9, 0.7],
'split1_test_score'  : [0.82, 0.5, 0.7],
'mean_test_score'    : [0.81, 0.7, 0.7],
'std_test_score'     : [0.02, 0.2, 0.],
'rank_test_score'    : [3, 1, 1],
'split0_train_score' : [0.8, 0.9, 0.7],
'split1_train_score' : [0.82, 0.5, 0.7],
'mean_train_score'   : [0.81, 0.7, 0.7],
'std_train_score'    : [0.03, 0.03, 0.04],
'mean_fit_time'      : [0.73, 0.63, 0.43, 0.49],
'std_fit_time'       : [0.01, 0.02, 0.01, 0.01],
'mean_score_time'    : [0.007, 0.06, 0.04, 0.04],
'std_score_time'     : [0.001, 0.002, 0.003, 0.005],
'params' : [{'kernel' : 'rbf', 'gamma' : 0.1}, ...],
}

NOTE that the key 'params' is used to store a list of parameter
settings dict for all the parameter candidates.

The mean_fit_time, std_fit_time, mean_score_time and
std_score_time are all in seconds.

best_estimator_ : estimator
Estimator that was chosen by the search, i.e. estimator
which gave highest score (or smallest loss if specified)
on the left out data. Not available if refit=False.

best_score_ : float
Score of best_estimator on the left out data.

best_params_ : dict
Parameter setting that gave the best results on the hold out data.

best_index_ : int
The index (of the cv_results_ arrays) which corresponds to the best
candidate parameter setting.

The dict at search.cv_results_['params'][search.best_index_] gives
the parameter setting for the best model, that gives the highest
mean score (search.best_score_).

scorer_ : function
Scorer function used on the held out data to choose the best
parameters for the model.

n_splits_ : int
The number of cross-validation splits (folds/iterations).

Notes
-----
The parameters selected are those that maximize the score of the held-out
data, according to the scoring parameter.

If n_jobs was set to a value higher than one, the data is copied for each
parameter setting(and not n_jobs times). This is done for efficiency
reasons if individual jobs take very little time, but may raise errors if
the dataset is large and not enough memory is available.  A workaround in
this case is to set pre_dispatch. Then, the memory is copied only
pre_dispatch many times. A reasonable value for pre_dispatch is 2 *
n_jobs.

See Also
--------
:class:GridSearchCV:
Does exhaustive search over a grid of parameters.

"""

def __init__(self, estimator, search_spaces=None, optimizer_kwargs=None,
n_iter=50, scoring=None, fit_params=None, n_jobs=1,
iid=True, refit=True, cv=None, verbose=0,
pre_dispatch='2*n_jobs', random_state=None,
error_score='raise', return_train_score=True):

# set of space name: space dict. Stored as a dict, in order
# to make it easy to add or remove search spaces, in case
# user wants to use step function directly.
self.search_spaces_ = {}

# can be None if user intends to provide spaces later manually
if search_spaces is not None:
# account for the case when search space is a dict
if isinstance(search_spaces, dict):
search_spaces = [search_spaces]
self.add_spaces(list(range(len(search_spaces))), search_spaces)

self.n_iter = n_iter
self.random_state = random_state

if optimizer_kwargs is None:
self.optimizer_kwargs = {}
else:
self.optimizer_kwargs = optimizer_kwargs

# this dict is used in order to keep track of skopt Optimizer
# instances for different search spaces. str(space) is used as key
# as space is a dict, which is unhashable. however, str(space)
# is fixed and unique if space is not changed.
self.optimizer_ = {}
self.cv_results_ = defaultdict(list)

self.best_index_ = None
self.multimetric_ = False

super(BayesSearchCV, self).__init__(
estimator=estimator, scoring=scoring, fit_params=fit_params,
n_jobs=n_jobs, iid=iid, refit=refit, cv=cv, verbose=verbose,
pre_dispatch=pre_dispatch, error_score=error_score,
return_train_score=return_train_score)

def _check_search_space(self, search_space):
"""Checks whether the search space argument is correct"""

# check if space is a single dict, convert to list if so
if isinstance(search_space, dict):
search_space = [search_space]

# check if the structure of the space is proper
if isinstance(search_space, list):
# convert to just a list of dicts
dicts_only = []

# 1. check the case when a tuple of space, n_iter is provided
for elem in search_space:
if isinstance(elem, tuple):
if len(elem) != 2:
raise ValueError(
"All tuples in list of search spaces should have"
"length 2, and contain (dict, int), got %s" % elem
)
subspace, n_iter = elem

if (not isinstance(n_iter, int)) or n_iter < 0:
raise ValueError(
"Number of iterations in search space should be"
"positive integer, got %s in tuple %s " %
(n_iter, elem)
)

# save subspaces here for further checking
dicts_only.append(subspace)
elif isinstance(elem, dict):
dicts_only.append(elem)
else:
raise TypeError(
"A search space should be provided as a dict or"
"tuple (dict, int), got %s" % elem)

# 2. check all the dicts for correctness of contents
for subspace in dicts_only:
for k, v in subspace.items():
check_dimension(v)
else:
raise TypeError(
"Search space should be provided as a dict or list of dict,"
"got %s" % search_space)

def add_spaces(self, names, search_spaces):
"""
Add a parameter search space over which to search for parameter
values. Naming of search subspaces is necessary in order to specify
for the step function over which subspace to perform search step.

names: str or list of str
Define names for the parameter search subspaces.
if search_spaces is a single dict, then names should be str
representing name of the single search subspace.
if search_spaces is a list of dicts, defines names for every
search subspace in the list.

search_spaces : dict, list of dict or list of tuple (dict, int)
Define search subspaces over which to search for parameters
of the model.
One of 3 following cases:
1. dictionary, where keys are parameter names (strings)
and values are skopt.space.Dimension instances (Real, Integer
or Categorical) or any other valid value that defines skopt
dimension (see skopt.Optimizer docs). Represents search space
over parameters of the provided estimator.
2. list of dictionaries: a list of dictionaries, where every
dictionary fits the description given in case 1 above.
If a list of dictionary objects is given, then the search is
performed sequentially for every parameter space with maximum
number of evaluations set to self.n_iter.
3. list of (dict, int > 0): an extension of case 2 above,
where first element of every tuple is a dictionary representing
some search subspace, similarly as in case 2, and second element
is a number of iterations that will be spent optimizing over
this subspace.
"""

self._check_search_space(search_spaces)

if not isinstance(search_spaces, list):
search_spaces = [search_spaces]
if not isinstance(names, list):
names = [names]

# first check whether space already exits ...
for space, name in zip(search_spaces, names):
if name in self.search_spaces_:
raise ValueError("Search space %s already exists!" % name)

for space, name in zip(search_spaces, names):
self.search_spaces_[name] = space

# copied for compatibility with 0.19 sklearn from 0.18 BaseSearchCV
@property
def best_score_(self):
check_is_fitted(self, 'cv_results_')
return self.cv_results_['mean_test_score'][self.best_index_]

# copied for compatibility with 0.19 sklearn from 0.18 BaseSearchCV
@property
def best_params_(self):
check_is_fitted(self, 'cv_results_')
return self.cv_results_['params'][self.best_index_]

# copied for compatibility with 0.19 sklearn from 0.18 BaseSearchCV
def _fit(self, X, y, groups, parameter_iterable):
"""
Actual fitting,  performing the search over parameters.
Taken from https://github.com/scikit-learn/scikit-learn/blob/0.18.X
.../sklearn/model_selection/_search.py
"""

estimator = self.estimator
cv = sklearn.model_selection._validation.check_cv(self.cv, y, classifier=
is_classifier(estimator))
self.scorer_ = check_scoring(
self.estimator, scoring=self.scoring)

X, y, groups = indexable(X, y, groups)
n_splits = cv.get_n_splits(X, y, groups)
if self.verbose > 0 and isinstance(parameter_iterable, Sized):
n_candidates = len(parameter_iterable)
print("Fitting {0} folds for each of {1} candidates, totalling"
" {2} fits".format(n_splits, n_candidates,
n_candidates * n_splits))

base_estimator = clone(self.estimator)
pre_dispatch = self.pre_dispatch

cv_iter = list(cv.split(X, y, groups))
out = Parallel(
n_jobs=self.n_jobs, verbose=self.verbose,
pre_dispatch=pre_dispatch
)(delayed(sklearn.model_selection._validation._fit_and_score)(
clone(base_estimator),
X, y, self.scorer_,
train, test, self.verbose, parameters,
fit_params=self.fit_params,
return_train_score=self.return_train_score,
return_n_test_samples=True,
return_times=True, return_parameters=True,
error_score=self.error_score
)
for parameters in parameter_iterable
for train, test in cv_iter
)

# if one choose to see train score, "out" will contain train score info
if self.return_train_score:
(train_scores, test_scores, test_sample_counts,
fit_time, score_time, parameters) = zip(*out)
else:
(test_scores, test_sample_counts,
fit_time, score_time, parameters) = zip(*out)

candidate_params = parameters[::n_splits]
n_candidates = len(candidate_params)

results = dict()

def _store(key_name, array, weights=None, splits=False, rank=False):
"""A small helper to store the scores/times to the cv_results_"""
array = np.array(array, dtype=np.float64).reshape(n_candidates,
n_splits)
if splits:
for split_i in range(n_splits):
results["split%d_%s"
% (split_i, key_name)] = array[:, split_i]

array_means = np.average(array, axis=1, weights=weights)
results['mean_%s' % key_name] = array_means
# Weighted std is not directly available in numpy
array_stds = np.sqrt(np.average((array -
array_means[:, np.newaxis]) ** 2,
axis=1, weights=weights))
results['std_%s' % key_name] = array_stds

if rank:
results["rank_%s" % key_name] = np.asarray(
rankdata(-array_means, method='min'), dtype=np.int32)

# Computed the (weighted) mean and std for test scores alone
# NOTE test_sample counts (weights) remain the same for all candidates
test_sample_counts = np.array(test_sample_counts[:n_splits],
dtype=np.int)

_store('test_score', test_scores, splits=True, rank=True,
weights=test_sample_counts if self.iid else None)
if self.return_train_score:
_store('train_score', train_scores, splits=True)
_store('fit_time', fit_time)
_store('score_time', score_time)

best_index = np.flatnonzero(results["rank_test_score"] == 1)[0]
best_parameters = candidate_params[best_index]

# Use one MaskedArray and mask all the places where the param is not
# applicable for that candidate. Use defaultdict as each candidate may
# not contain all the params
param_results = defaultdict(partial(
MaskedArray,
np.empty(n_candidates,),
mask=True,
dtype=object))
for cand_i, params in enumerate(candidate_params):
for name, value in params.items():
# An all masked empty array gets created for the key
# "param_%s" % name at the first occurence of name.
# Setting the value at an index also unmasks that index
param_results["param_%s" % name][cand_i] = value

results.update(param_results)

# Store a list of param dicts at the key 'params'
results['params'] = candidate_params

self.cv_results_ = results
self.best_index_ = best_index
self.n_splits_ = n_splits

if self.refit:
# fit the best estimator using the entire dataset
# clone first to work around broken estimators
best_estimator = clone(base_estimator).set_params(
**best_parameters)
if y is not None:
best_estimator.fit(X, y, **self.fit_params)
else:
best_estimator.fit(X, **self.fit_params)
self.best_estimator_ = best_estimator
return self

def _fit_best_model(self, X, y):
"""Fit the estimator copy with best parameters found to the
provided data.

Parameters
----------
X : array-like, shape = [n_samples, n_features]
Input data, where n_samples is the number of samples and
n_features is the number of features.

y : array-like, shape = [n_samples] or [n_samples, n_output],
Target relative to X for classification or regression.

Returns
-------
self
"""
self.best_estimator_ = clone(self.estimator)
self.best_estimator_.set_params(**self.best_params_)
self.best_estimator_.fit(X, y)
return self

def _make_optimizer(self, params_space):
"""Instantiate skopt Optimizer class.

Parameters
----------
params_space : dict
Represents parameter search space. The keys are parameter
names (strings) and values are skopt.space.Dimension instances,
one of Real, Integer or Categorical.

Returns
-------
optimizer: Instance of the Optimizer class used for for search
in some parameter space.

"""

kwargs = self.optimizer_kwargs.copy()
kwargs['dimensions'] = dimensions_aslist(params_space)
optimizer = Optimizer(**kwargs)

return optimizer

def step(self, X, y, space_id, groups=None, n_jobs=1):
"""Generate n_jobs parameters and evaluate them in parallel.

Having a separate function for a single step for search allows to
save easily checkpoints for the parameter search and restore from
possible failures.

Parameters
----------
X : array-like or sparse matrix, shape = [n_samples, n_features]
The training input samples. Internally, it will be converted to
dtype=np.float32 and if a sparse matrix is provided
to a sparse csc_matrix.

y : array-like, shape = [n_samples] or [n_samples, n_outputs]
The target values (class labels) as integers or strings.

space_id : hashable
Identifier of parameter search space. Add search spaces with

groups : array-like, with shape (n_samples,), optional
Group labels for the samples used while splitting the dataset into
train/test set.

n_jobs : int, default=1
Number of parameters to evaluate in parallel.

Returns
-------
params_dict: dictionary with parameter values.
"""

# convert n_jobst to int > 0 if necessary
if n_jobs < 0:
n_jobs = max(1, cpu_count() + n_jobs + 1)

# use the cached optimizer for particular parameter space
if space_id not in self.search_spaces_:
raise ValueError("Unknown space %s" % space_id)

# get the search space for a step
search_space = self.search_spaces_[space_id]
if isinstance(search_space, tuple):
search_space, _ = search_space

# create optimizer if not created already
if space_id not in self.optimizer_:
self.optimizer_[space_id] = self._make_optimizer(search_space)
optimizer = self.optimizer_[space_id]

# get parameter values to evaluate
params = optimizer.ask(n_points=n_jobs)
params_dict = [point_asdict(search_space, p) for p in params]

# self.cv_results_ is reset at every call to _fit, keep current
all_cv_results = self.cv_results_

# record performances with different points
refit = self.refit
self.refit = False  # do not fit yet - will be fit later

# this adds compatibility with different versions of sklearn

self._fit(X, y, groups, params_dict)

self.refit = refit

# merge existing and new cv_results_
for k in self.cv_results_:
all_cv_results[k].extend(self.cv_results_[k])

self.cv_results_ = all_cv_results
self.best_index_ = np.argmax(self.cv_results_['mean_test_score'])

# feed the point and objective back into optimizer
local_results = self.cv_results_['mean_test_score'][-len(params):]

# optimizer minimizes objective, hence provide negative score
optimizer.tell(params, [-score for score in local_results])

# fit the best model if necessary
if self.refit:
self._fit_best_model(X, y)

def fit(self, X, y=None, groups=None):
"""Run fit on the estimator with randomly drawn parameters.

Parameters
----------
X : array-like, shape = [n_samples, n_features]
Training vector, where n_samples in the number of samples and
n_features is the number of features.

y : array-like, shape = [n_samples] or [n_samples, n_output]
Target relative to X for classification or regression;

groups : array-like, with shape (n_samples,), optional
Group labels for the samples used while splitting the dataset into
train/test set.
"""

# check if the list of parameter spaces is provided. If not, then
# only step in manual mode can be used.

if len(self.search_spaces_) == 0:
raise ValueError(
"Please provide search space using add_spaces first before"
"calling fit method."
)

n_jobs = self.n_jobs

# account for case n_jobs < 0
if n_jobs < 0:
n_jobs = max(1, cpu_count() + n_jobs + 1)

for space_id in sorted(self.search_spaces_.keys()):
elem = self.search_spaces_[space_id]

# if not provided with search subspace, n_iter is taken as
# self.n_iter
if isinstance(elem, tuple):
space, n_iter = elem
else:
n_iter = self.n_iter

# do the optimization for particular search space
while n_iter > 0:
# when n_iter < n_jobs points left for evaluation
n_jobs_adjusted = min(n_iter, self.n_jobs)

self.step(
X, y, space_id,
groups=groups, n_jobs=n_jobs_adjusted
)
n_iter -= n_jobs


### Ancestors (in MRO)

• BayesSearchCV
• sklearn.model_selection._search.BaseSearchCV
• abc.NewBase
• sklearn.base.BaseEstimator
• sklearn.base.MetaEstimatorMixin
• builtins.object

### Static methods

def __init__(

self, estimator, search_spaces=None, optimizer_kwargs=None, n_iter=50, scoring=None, fit_params=None, n_jobs=1, iid=True, refit=True, cv=None, verbose=0, pre_dispatch='2*n_jobs', random_state=None, error_score='raise', return_train_score=True)

Initialize self. See help(type(self)) for accurate signature.

def __init__(self, estimator, search_spaces=None, optimizer_kwargs=None,
n_iter=50, scoring=None, fit_params=None, n_jobs=1,
iid=True, refit=True, cv=None, verbose=0,
pre_dispatch='2*n_jobs', random_state=None,
error_score='raise', return_train_score=True):
# set of space name: space dict. Stored as a dict, in order
# to make it easy to add or remove search spaces, in case
# user wants to use step function directly.
self.search_spaces_ = {}
# can be None if user intends to provide spaces later manually
if search_spaces is not None:
# account for the case when search space is a dict
if isinstance(search_spaces, dict):
search_spaces = [search_spaces]
self.add_spaces(list(range(len(search_spaces))), search_spaces)
self.n_iter = n_iter
self.random_state = random_state
if optimizer_kwargs is None:
self.optimizer_kwargs = {}
else:
self.optimizer_kwargs = optimizer_kwargs
# this dict is used in order to keep track of skopt Optimizer
# instances for different search spaces. str(space) is used as key
# as space is a dict, which is unhashable. however, str(space)
# is fixed and unique if space is not changed.
self.optimizer_ = {}
self.cv_results_ = defaultdict(list)
self.best_index_ = None
self.multimetric_ = False
super(BayesSearchCV, self).__init__(
estimator=estimator, scoring=scoring, fit_params=fit_params,
n_jobs=n_jobs, iid=iid, refit=refit, cv=cv, verbose=verbose,
pre_dispatch=pre_dispatch, error_score=error_score,
return_train_score=return_train_score)


def add_spaces(

self, names, search_spaces)

Add a parameter search space over which to search for parameter values. Naming of search subspaces is necessary in order to specify for the step function over which subspace to perform search step.

names: str or list of str Define names for the parameter search subspaces. if search_spaces is a single dict, then names should be str representing name of the single search subspace. if search_spaces is a list of dicts, defines names for every search subspace in the list.

search_spaces : dict, list of dict or list of tuple (dict, int) Define search subspaces over which to search for parameters of the model. One of 3 following cases: 1. dictionary, where keys are parameter names (strings) and values are skopt.space.Dimension instances (Real, Integer or Categorical) or any other valid value that defines skopt dimension (see skopt.Optimizer docs). Represents search space over parameters of the provided estimator. 2. list of dictionaries: a list of dictionaries, where every dictionary fits the description given in case 1 above. If a list of dictionary objects is given, then the search is performed sequentially for every parameter space with maximum number of evaluations set to self.n_iter. 3. list of (dict, int > 0): an extension of case 2 above, where first element of every tuple is a dictionary representing some search subspace, similarly as in case 2, and second element is a number of iterations that will be spent optimizing over this subspace.

def add_spaces(self, names, search_spaces):
"""
Add a parameter search space over which to search for parameter
values. Naming of search subspaces is necessary in order to specify
for the step function over which subspace to perform search step.
names: str or list of str
Define names for the parameter search subspaces.
if search_spaces is a single dict, then names should be str
representing name of the single search subspace.
if search_spaces is a list of dicts, defines names for every
search subspace in the list.
search_spaces : dict, list of dict or list of tuple (dict, int)
Define search subspaces over which to search for parameters
of the model.
One of 3 following cases:
1. dictionary, where keys are parameter names (strings)
and values are skopt.space.Dimension instances (Real, Integer
or Categorical) or any other valid value that defines skopt
dimension (see skopt.Optimizer docs). Represents search space
over parameters of the provided estimator.
2. list of dictionaries: a list of dictionaries, where every
dictionary fits the description given in case 1 above.
If a list of dictionary objects is given, then the search is
performed sequentially for every parameter space with maximum
number of evaluations set to self.n_iter.
3. list of (dict, int > 0): an extension of case 2 above,
where first element of every tuple is a dictionary representing
some search subspace, similarly as in case 2, and second element
is a number of iterations that will be spent optimizing over
this subspace.
"""
self._check_search_space(search_spaces)
if not isinstance(search_spaces, list):
search_spaces = [search_spaces]
if not isinstance(names, list):
names = [names]
# first check whether space already exits ...
for space, name in zip(search_spaces, names):
if name in self.search_spaces_:
raise ValueError("Search space %s already exists!" % name)
for space, name in zip(search_spaces, names):
self.search_spaces_[name] = space


def fit(

self, X, y=None, groups=None)

Run fit on the estimator with randomly drawn parameters.

## Parameters

X : array-like, shape = [n_samples, n_features] Training vector, where n_samples in the number of samples and n_features is the number of features.

y : array-like, shape = [n_samples] or [n_samples, n_output] Target relative to X for classification or regression;

groups : array-like, with shape (n_samples,), optional Group labels for the samples used while splitting the dataset into train/test set.

def fit(self, X, y=None, groups=None):
"""Run fit on the estimator with randomly drawn parameters.
Parameters
----------
X : array-like, shape = [n_samples, n_features]
Training vector, where n_samples in the number of samples and
n_features is the number of features.
y : array-like, shape = [n_samples] or [n_samples, n_output]
Target relative to X for classification or regression;
groups : array-like, with shape (n_samples,), optional
Group labels for the samples used while splitting the dataset into
train/test set.
"""
# check if the list of parameter spaces is provided. If not, then
# only step in manual mode can be used.
if len(self.search_spaces_) == 0:
raise ValueError(
"Please provide search space using add_spaces first before"
"calling fit method."
)
n_jobs = self.n_jobs
# account for case n_jobs < 0
if n_jobs < 0:
n_jobs = max(1, cpu_count() + n_jobs + 1)
for space_id in sorted(self.search_spaces_.keys()):
elem = self.search_spaces_[space_id]
# if not provided with search subspace, n_iter is taken as
# self.n_iter
if isinstance(elem, tuple):
space, n_iter = elem
else:
n_iter = self.n_iter
# do the optimization for particular search space
while n_iter > 0:
# when n_iter < n_jobs points left for evaluation
n_jobs_adjusted = min(n_iter, self.n_jobs)
self.step(
X, y, space_id,
groups=groups, n_jobs=n_jobs_adjusted
)
n_iter -= n_jobs


def step(

self, X, y, space_id, groups=None, n_jobs=1)

Generate n_jobs parameters and evaluate them in parallel.

Having a separate function for a single step for search allows to save easily checkpoints for the parameter search and restore from possible failures.

## Parameters

X : array-like or sparse matrix, shape = [n_samples, n_features] The training input samples. Internally, it will be converted to dtype=np.float32 and if a sparse matrix is provided to a sparse csc_matrix.

y : array-like, shape = [n_samples] or [n_samples, n_outputs] The target values (class labels) as integers or strings.

space_id : hashable Identifier of parameter search space. Add search spaces with

groups : array-like, with shape (n_samples,), optional Group labels for the samples used while splitting the dataset into train/test set.

n_jobs : int, default=1 Number of parameters to evaluate in parallel.

## Returns

params_dict: dictionary with parameter values.

def step(self, X, y, space_id, groups=None, n_jobs=1):
"""Generate n_jobs parameters and evaluate them in parallel.
Having a separate function for a single step for search allows to
save easily checkpoints for the parameter search and restore from
possible failures.
Parameters
----------
X : array-like or sparse matrix, shape = [n_samples, n_features]
The training input samples. Internally, it will be converted to
dtype=np.float32 and if a sparse matrix is provided
to a sparse csc_matrix.
y : array-like, shape = [n_samples] or [n_samples, n_outputs]
The target values (class labels) as integers or strings.
space_id : hashable
Identifier of parameter search space. Add search spaces with
groups : array-like, with shape (n_samples,), optional
Group labels for the samples used while splitting the dataset into
train/test set.
n_jobs : int, default=1
Number of parameters to evaluate in parallel.
Returns
-------
params_dict: dictionary with parameter values.
"""
# convert n_jobst to int > 0 if necessary
if n_jobs < 0:
n_jobs = max(1, cpu_count() + n_jobs + 1)
# use the cached optimizer for particular parameter space
if space_id not in self.search_spaces_:
raise ValueError("Unknown space %s" % space_id)
# get the search space for a step
search_space = self.search_spaces_[space_id]
if isinstance(search_space, tuple):
search_space, _ = search_space
# create optimizer if not created already
if space_id not in self.optimizer_:
self.optimizer_[space_id] = self._make_optimizer(search_space)
optimizer = self.optimizer_[space_id]
# get parameter values to evaluate
params = optimizer.ask(n_points=n_jobs)
params_dict = [point_asdict(search_space, p) for p in params]
# self.cv_results_ is reset at every call to _fit, keep current
all_cv_results = self.cv_results_
# record performances with different points
refit = self.refit
self.refit = False  # do not fit yet - will be fit later
# this adds compatibility with different versions of sklearn
self._fit(X, y, groups, params_dict)
self.refit = refit
# merge existing and new cv_results_
for k in self.cv_results_:
all_cv_results[k].extend(self.cv_results_[k])
self.cv_results_ = all_cv_results
self.best_index_ = np.argmax(self.cv_results_['mean_test_score'])
# feed the point and objective back into optimizer
local_results = self.cv_results_['mean_test_score'][-len(params):]
# optimizer minimizes objective, hence provide negative score
optimizer.tell(params, [-score for score in local_results])
# fit the best model if necessary
if self.refit:
self._fit_best_model(X, y)


### Instance variables

var best_index_

var best_params_

var best_score_

var classes_

var cv_results_

var grid_scores_

var multimetric_

var n_iter

var optimizer_

var random_state

var search_spaces_

class Optimizer

Run bayesian optimisation loop.

An Optimizer represents the steps of a bayesian optimisation loop. To use it you need to provide your own loop mechanism. The various optimisers provided by skopt use this class under the hood.

Use this class directly if you want to control the iterations of your bayesian optimisation loop.

## Parameters

• dimensions [list, shape=(n_dims,)]: List of search space dimensions. Each search dimension can be defined either as

• a (upper_bound, lower_bound) tuple (for Real or Integer dimensions),
• a (upper_bound, lower_bound, "prior") tuple (for Real dimensions),
• as a list of categories (for Categorical dimensions), or
• an instance of a Dimension object (Real, Integer or Categorical).
• base_estimator ["GP", "RF", "ET", "GBRT" or sklearn regressor, default="GP"]: Should inherit from sklearn.base.RegressorMixin. In addition the predict method, should have an optional return_std argument, which returns std(Y | x) along withE[Y | x]. If base_estimator is one of ["GP", "RF", "ET", "GBRT"], a default surrogate model of the corresponding type is used corresponding to what is used in the minimize functions.

• n_random_starts [int, default=10]: DEPRECATED, use n_initial_points instead.

• n_initial_points [int, default=10]: Number of evaluations of func with initialization points before approximating it with base_estimator. Points provided as x0 count as initialization points. If len(x0) < n_initial_points additional points are sampled at random.

• acq_func [string, default="EI"]: Function to minimize over the posterior distribution. Can be either

• "LCB" for lower confidence bound.
• "EI" for negative expected improvement.
• "PI" for negative probability of improvement.
• "gp_hedge" Probabilistically choose one of the above three acquisition functions at every iteration.
• The gains g_i are initialized to zero.
• At every iteration,
• Each acquisition function is optimised independently to propose an candidate point X_i.
• Out of all these candidate points, the next point X_best is chosen by $softmax(\eta g_i)$
• After fitting the surrogate model with (X_best, y_best), the gains are updated such that $g_i -= \mu(X_i)$
• "EIps" for negated expected improvement per second to take into account the function compute time. Then, the objective function is assumed to return two values, the first being the objective value and the second being the time taken in seconds.
• "PIps" for negated probability of improvement per second. The return type of the objective function is assumed to be similar to that of "EIps
• acq_optimizer [string, "sampling" or "lbfgs", default="auto"]: Method to minimize the acquistion function. The fit model is updated with the optimal value obtained by optimizing acq_func with acq_optimizer.

• If set to "auto", then acq_optimizer is configured on the basis of the base_estimator and the space searched over. If the space is Categorical or if the estimator provided based on tree-models then this is set to be "sampling".
• If set to "sampling", then acq_func is optimized by computing acq_func at n_points randomly sampled points.
• If set to "lbfgs", then acq_func is optimized by
• Sampling n_restarts_optimizer points randomly.
• "lbfgs" is run for 20 iterations with these points as initial points to find local minima.
• The optimal of these local minima is used to update the prior.
• random_state [int, RandomState instance, or None (default)]: Set random state to something other than None for reproducible results.

• acq_func_kwargs [dict]: Additional arguments to be passed to the acquistion function.

• acq_optimizer_kwargs [dict]: Additional arguments to be passed to the acquistion optimizer.

## Attributes

• Xi [list]: Points at which objective has been evaluated.
• yi [scalar]: Values of objective at corresponding points in Xi.
• models [list]: Regression models used to fit observations and compute acquisition function.
• space An instance of skopt.space.Space. Stores parameter search space used to sample points, bounds, and type of parameters.
class Optimizer(object):
"""Run bayesian optimisation loop.

An Optimizer represents the steps of a bayesian optimisation loop. To
use it you need to provide your own loop mechanism. The various
optimisers provided by skopt use this class under the hood.

Use this class directly if you want to control the iterations of your
bayesian optimisation loop.

Parameters
----------
* dimensions [list, shape=(n_dims,)]:
List of search space dimensions.
Each search dimension can be defined either as

- a (upper_bound, lower_bound) tuple (for Real or Integer
dimensions),
- a (upper_bound, lower_bound, "prior") tuple (for Real
dimensions),
- as a list of categories (for Categorical dimensions), or
- an instance of a Dimension object (Real, Integer or
Categorical).

* base_estimator ["GP", "RF", "ET", "GBRT" or sklearn regressor, default="GP"]:
Should inherit from sklearn.base.RegressorMixin.
In addition the predict method, should have an optional return_std
argument, which returns std(Y | x) along with E[Y | x].
If base_estimator is one of ["GP", "RF", "ET", "GBRT"], a default
surrogate model of the corresponding type is used corresponding to what
is used in the minimize functions.

* n_random_starts [int, default=10]:
DEPRECATED, use n_initial_points instead.

* n_initial_points [int, default=10]:
Number of evaluations of func with initialization points
before approximating it with base_estimator. Points provided as
x0 count as initialization points. If len(x0) < n_initial_points
additional points are sampled at random.

* acq_func [string, default="EI"]:
Function to minimize over the posterior distribution. Can be either

- "LCB" for lower confidence bound.
- "EI" for negative expected improvement.
- "PI" for negative probability of improvement.
- "gp_hedge" Probabilistically choose one of the above three
acquisition functions at every iteration.
- The gains g_i are initialized to zero.
- At every iteration,
- Each acquisition function is optimised independently to
propose an candidate point X_i.
- Out of all these candidate points, the next point X_best is
chosen by $softmax(\eta g_i)$
- After fitting the surrogate model with (X_best, y_best),
the gains are updated such that $g_i -= \mu(X_i)$
- "EIps" for negated expected improvement per second to take into
account the function compute time. Then, the objective function is
assumed to return two values, the first being the objective value and
the second being the time taken in seconds.
- "PIps" for negated probability of improvement per second. The
return type of the objective function is assumed to be similar to
that of "EIps

* acq_optimizer [string, "sampling" or "lbfgs", default="auto"]:
Method to minimize the acquistion function. The fit model
is updated with the optimal value obtained by optimizing acq_func
with acq_optimizer.

- If set to "auto", then acq_optimizer is configured on the
basis of the base_estimator and the space searched over.
If the space is Categorical or if the estimator provided based on
tree-models then this is set to be "sampling".
- If set to "sampling", then acq_func is optimized by computing
acq_func at n_points randomly sampled points.
- If set to "lbfgs", then acq_func is optimized by
- Sampling n_restarts_optimizer points randomly.
- "lbfgs" is run for 20 iterations with these points as initial
points to find local minima.
- The optimal of these local minima is used to update the prior.

* random_state [int, RandomState instance, or None (default)]:
Set random state to something other than None for reproducible
results.

* acq_func_kwargs [dict]:
Additional arguments to be passed to the acquistion function.

* acq_optimizer_kwargs [dict]:
Additional arguments to be passed to the acquistion optimizer.

Attributes
----------
* Xi [list]:
Points at which objective has been evaluated.
* yi [scalar]:
Values of objective at corresponding points in Xi.
* models [list]:
Regression models used to fit observations and compute acquisition
function.
* space
An instance of skopt.space.Space. Stores parameter search space used
to sample points, bounds, and type of parameters.

"""
def __init__(self, dimensions, base_estimator="gp",
n_random_starts=None, n_initial_points=10,
acq_func="gp_hedge",
acq_optimizer="auto",
random_state=None, acq_func_kwargs=None,
acq_optimizer_kwargs=None):
# Arguments that are just stored not checked
self.acq_func = acq_func
self.rng = check_random_state(random_state)
self.acq_func_kwargs = acq_func_kwargs

allowed_acq_funcs = ["gp_hedge", "EI", "LCB", "PI", "EIps", "PIps"]
if self.acq_func not in allowed_acq_funcs:
raise ValueError("expected acq_func to be in %s, got %s" %
(",".join(allowed_acq_funcs), self.acq_func))
if self.acq_func == "gp_hedge":
self.cand_acq_funcs_ = ["EI", "LCB", "PI"]
self.gains_ = np.zeros(3)
else:
self.cand_acq_funcs_ = [self.acq_func]

if acq_func_kwargs is None:
acq_func_kwargs = dict()
self.eta = acq_func_kwargs.get("eta", 1.0)

if acq_optimizer_kwargs is None:
acq_optimizer_kwargs = dict()

self.n_points = acq_optimizer_kwargs.get("n_points", 10000)
self.n_restarts_optimizer = acq_optimizer_kwargs.get(
"n_restarts_optimizer", 5)
n_jobs = acq_optimizer_kwargs.get("n_jobs", 1)
self.acq_optimizer_kwargs = acq_optimizer_kwargs

if n_random_starts is not None:
warnings.warn(("n_random_starts will be removed in favour of "
"n_initial_points."),
DeprecationWarning)
n_initial_points = n_random_starts

self._check_arguments(base_estimator, n_initial_points, acq_optimizer,
dimensions)

if isinstance(self.base_estimator_, GaussianProcessRegressor):
dimensions = normalize_dimensions(dimensions)

self.space = Space(dimensions)
self.models = []
self.Xi = []
self.yi = []

self._cat_inds = []
self._non_cat_inds = []
for ind, dim in enumerate(self.space.dimensions):
if isinstance(dim, Categorical):
self._cat_inds.append(ind)
else:
self._non_cat_inds.append(ind)

self.n_jobs = n_jobs

# The cache of responses of ask method for n_points not None.
# This ensures that multiple calls to ask with n_points set
# return same sets of points.
# The cache is reset to {} at every call to tell.
self.cache_ = {}

def _check_arguments(self, base_estimator, n_initial_points,
acq_optimizer, dimensions):
"""Check arguments for sanity."""

if isinstance(base_estimator, str):
base_estimator = cook_estimator(
base_estimator, space=dimensions, random_state=self.rng)

if not is_regressor(base_estimator) and base_estimator is not None:
raise ValueError(
"%s has to be a regressor." % base_estimator)

if "ps" in self.acq_func:
self.base_estimator_ = MultiOutputRegressor(base_estimator)
else:
self.base_estimator_ = base_estimator

if n_initial_points < 0:
raise ValueError(
"Expected n_initial_points >= 0, got %d" % n_initial_points)
self._n_initial_points = n_initial_points
self.n_initial_points_ = n_initial_points

if acq_optimizer == "auto":
if has_gradients(self.base_estimator_):
acq_optimizer = "lbfgs"
else:
acq_optimizer = "sampling"

if acq_optimizer not in ["lbfgs", "sampling"]:
raise ValueError("Expected acq_optimizer to be 'lbfgs' or "
"'sampling', got {0}".format(acq_optimizer))

if (not has_gradients(self.base_estimator_) and
acq_optimizer != "sampling"):
raise ValueError("The regressor {0} should run with "
"acq_optimizer"
"='sampling'.".format(type(base_estimator)))

self.acq_optimizer = acq_optimizer

def copy(self, random_state=None):
"""Create a shallow copy of an instance of the optimizer.

Parameters
----------
* random_state [int, RandomState instance, or None (default)]:
Set the random state of the copy.
"""

optimizer = Optimizer(
dimensions=self.space.dimensions,
base_estimator=self.base_estimator_,
n_initial_points=self.n_initial_points_,
acq_func=self.acq_func,
acq_optimizer=self.acq_optimizer,
acq_func_kwargs=self.acq_func_kwargs,
acq_optimizer_kwargs=self.acq_optimizer_kwargs,
random_state=random_state,
)

if hasattr(self, "gains_"):
optimizer.gains_ = np.copy(self.gains_)

if self.Xi:
optimizer.tell(self.Xi, self.yi)

return optimizer

def ask(self, n_points=None, strategy="cl_min"):
"""Query point or multiple points at which objective should be evaluated.

* n_points [int or None, default=None]:
Number of points returned by the ask method.
If the value is None, a single point to evaluate is returned.
Otherwise a list of points to evaluate is returned of size
n_points. This is useful if you can evaluate your objective in
parallel, and thus obtain more objective function evaluations per
unit of time.

* strategy [string, default="cl_min"]:
Method to use to sample multiple points (see also n_points
description). This parameter is ignored if n_points = None.
Supported options are "cl_min", "cl_mean" or "cl_max".

- If set to "cl_min", then constant liar strtategy is used
with lie objective value being minimum of observed objective
values. "cl_mean" and "cl_max" means mean and max of values
respectively. For details on this strategy see:

https://hal.archives-ouvertes.fr/hal-00732512/document

With this strategy a copy of optimizer is created, which is
then asked for a point, and the point is told to the copy of
optimizer with some fake objective (lie), the next point is
asked from copy, it is also told to the copy with fake
objective and so on. The type of lie defines different
flavours of cl_x strategies.

"""
if n_points is None:
return self._ask()

supported_strategies = ["cl_min", "cl_mean", "cl_max"]

if not (isinstance(n_points, int) and n_points > 0):
raise ValueError(
"n_points should be int > 0, got " + str(n_points)
)

if strategy not in supported_strategies:
raise ValueError(
"Expected parallel_strategy to be one of " +
str(supported_strategies) + ", " + "got %s" % strategy
)

# Caching the result with n_points not None. If some new parameters
# are provided to the ask, the cache_ is not used.
if (n_points, strategy) in self.cache_:
return self.cache_[(n_points, strategy)]

# Copy of the optimizer is made in order to manage the
# deletion of points with "lie" objective (the copy of
# oiptimizer is simply discarded)
opt = self.copy()

X = []
for i in range(n_points):
x = opt.ask()
X.append(x)
if strategy == "cl_min":
y_lie = np.min(opt.yi) if opt.yi else 0.0  # CL-min lie
elif strategy == "cl_mean":
y_lie = np.mean(opt.yi) if opt.yi else 0.0  # CL-mean lie
else:
y_lie = np.max(opt.yi) if opt.yi else 0.0  # CL-max lie
opt.tell(x, y_lie)  # lie to the optimizer

self.cache_ = {(n_points, strategy): X}  # cache_ the result

return X

def _ask(self):
"""Suggest next point at which to evaluate the objective.

Return a random point while not at least n_initial_points
observations have been telled, after that base_estimator is used
to determine the next point.
"""
if self._n_initial_points > 0 or self.base_estimator_ is None:
# this will not make a copy of self.rng and hence keep advancing
# our random state.
return self.space.rvs(random_state=self.rng)[0]

else:
if not self.models:
raise RuntimeError("Random evaluations exhausted and no "
"model has been fit.")

next_x = self._next_x
min_delta_x = min([self.space.distance(next_x, xi)
for xi in self.Xi])
if abs(min_delta_x) <= 1e-8:
warnings.warn("The objective has been evaluated "
"at this point before.")

# return point computed from last call to tell()
return next_x

def tell(self, x, y, fit=True):
"""Record an observation (or several) of the objective function.

Provide values of the objective function at points suggested by ask()
or other points. By default a new model will be fit to all
observations. The new model is used to suggest the next point at
which to evaluate the objective. This point can be retrieved by calling
ask().

To add observations without fitting a new model set fit to False.

To add multiple observations in a batch pass a list-of-lists for x
and a list of scalars for y.

Parameters
----------
* x [list or list-of-lists]:
Point at which objective was evaluated.

* y [scalar or list]:
Value of objective at x.

* fit [bool, default=True]
Fit a model to observed evaluations of the objective. A model will
only be fitted after n_initial_points points have been told to
the optimizer irrespective of the value of fit.
"""
check_x_in_space(x, self.space)

if "ps" in self.acq_func:
if is_2Dlistlike(x):
if np.ndim(y) == 2 and np.shape(y)[1] == 2:
y = [[val, log(t)] for (val, t) in y]
self.Xi.extend(x)
self.yi.extend(y)
else:
raise TypeError("expcted y to be a list of (func_val, t)")
self._n_initial_points -= len(y)
elif is_listlike(x):
if np.ndim(y) == 1 and len(y) == 2:
y = list(y)
y[1] = log(y[1])
self.Xi.append(x)
self.yi.append(y)
else:
raise TypeError("expected y to be (func_val, t)")
self._n_initial_points -= 1

# if y isn't a scalar it means we have been handed a batch of points
elif is_listlike(y) and is_2Dlistlike(x):
self.Xi.extend(x)
self.yi.extend(y)
self._n_initial_points -= len(y)

elif is_listlike(x):
if isinstance(y, Number):
self.Xi.append(x)
self.yi.append(y)
self._n_initial_points -= 1
else:
raise ValueError("func should return a scalar")

else:
raise ValueError("Type of arguments x (%s) and y (%s) "
"not compatible." % (type(x), type(y)))

# optimizer learned somethnig new - discard cache
self.cache_ = {}

# after being "told" n_initial_points we switch from sampling
# random points to using a surrogate model
if (fit and self._n_initial_points <= 0 and
self.base_estimator_ is not None):
transformed_bounds = np.array(self.space.transformed_bounds)
est = clone(self.base_estimator_)

with warnings.catch_warnings():
warnings.simplefilter("ignore")
est.fit(self.space.transform(self.Xi), self.yi)

if hasattr(self, "next_xs_") and self.acq_func == "gp_hedge":
self.gains_ -= est.predict(np.vstack(self.next_xs_))
self.models.append(est)

# even with BFGS as optimizer we want to sample a large number
# of points and then pick the best ones as starting points
X = self.space.transform(self.space.rvs(
n_samples=self.n_points, random_state=self.rng))

self.next_xs_ = []
for cand_acq_func in self.cand_acq_funcs_:
values = _gaussian_acquisition(
X=X, model=est, y_opt=np.min(self.yi),
acq_func=cand_acq_func,
acq_func_kwargs=self.acq_func_kwargs)
# Find the minimum of the acquisition function by randomly
# sampling points from the space
if self.acq_optimizer == "sampling":
next_x = X[np.argmin(values)]

# Use BFGS to find the mimimum of the acquisition function, the
# minimization starts from n_restarts_optimizer different
# points and the best minimum is used
elif self.acq_optimizer == "lbfgs":
x0 = X[np.argsort(values)[:self.n_restarts_optimizer]]

with warnings.catch_warnings():
warnings.simplefilter("ignore")
results = Parallel(n_jobs=self.n_jobs)(
delayed(fmin_l_bfgs_b)(
gaussian_acquisition_1D, x,
args=(est, np.min(self.yi), cand_acq_func,
self.acq_func_kwargs),
bounds=self.space.transformed_bounds,
approx_grad=False,
maxiter=20)
for x in x0)

cand_xs = np.array([r[0] for r in results])
cand_acqs = np.array([r[1] for r in results])
next_x = cand_xs[np.argmin(cand_acqs)]

# lbfgs should handle this but just in case there are
# precision errors.
if not self.space.is_categorical:
next_x = np.clip(
next_x, transformed_bounds[:, 0],
transformed_bounds[:, 1])
self.next_xs_.append(next_x)

if self.acq_func == "gp_hedge":
logits = np.array(self.gains_)
logits -= np.max(logits)
exp_logits = np.exp(self.eta * logits)
probs = exp_logits / np.sum(exp_logits)
next_x = self.next_xs_[np.argmax(self.rng.multinomial(1,
probs))]
else:
next_x = self.next_xs_[0]

# note the need for [0] at the end
self._next_x = self.space.inverse_transform(
next_x.reshape((1, -1)))[0]

# Pack results
return create_result(self.Xi, self.yi, self.space, self.rng,
models=self.models)

def run(self, func, n_iter=1):
"""Execute ask() + tell() n_iter times"""
for _ in range(n_iter):
x = self.ask()
self.tell(x, func(x))

return create_result(self.Xi, self.yi, self.space, self.rng,
models=self.models)


### Static methods

def __init__(

self, dimensions, base_estimator='gp', n_random_starts=None, n_initial_points=10, acq_func='gp_hedge', acq_optimizer='auto', random_state=None, acq_func_kwargs=None, acq_optimizer_kwargs=None)

Initialize self. See help(type(self)) for accurate signature.

def __init__(self, dimensions, base_estimator="gp",
n_random_starts=None, n_initial_points=10,
acq_func="gp_hedge",
acq_optimizer="auto",
random_state=None, acq_func_kwargs=None,
acq_optimizer_kwargs=None):
# Arguments that are just stored not checked
self.acq_func = acq_func
self.rng = check_random_state(random_state)
self.acq_func_kwargs = acq_func_kwargs
allowed_acq_funcs = ["gp_hedge", "EI", "LCB", "PI", "EIps", "PIps"]
if self.acq_func not in allowed_acq_funcs:
raise ValueError("expected acq_func to be in %s, got %s" %
(",".join(allowed_acq_funcs), self.acq_func))
if self.acq_func == "gp_hedge":
self.cand_acq_funcs_ = ["EI", "LCB", "PI"]
self.gains_ = np.zeros(3)
else:
self.cand_acq_funcs_ = [self.acq_func]
if acq_func_kwargs is None:
acq_func_kwargs = dict()
self.eta = acq_func_kwargs.get("eta", 1.0)
if acq_optimizer_kwargs is None:
acq_optimizer_kwargs = dict()
self.n_points = acq_optimizer_kwargs.get("n_points", 10000)
self.n_restarts_optimizer = acq_optimizer_kwargs.get(
"n_restarts_optimizer", 5)
n_jobs = acq_optimizer_kwargs.get("n_jobs", 1)
self.acq_optimizer_kwargs = acq_optimizer_kwargs
if n_random_starts is not None:
warnings.warn(("n_random_starts will be removed in favour of "
"n_initial_points."),
DeprecationWarning)
n_initial_points = n_random_starts
self._check_arguments(base_estimator, n_initial_points, acq_optimizer,
dimensions)
if isinstance(self.base_estimator_, GaussianProcessRegressor):
dimensions = normalize_dimensions(dimensions)
self.space = Space(dimensions)
self.models = []
self.Xi = []
self.yi = []
self._cat_inds = []
self._non_cat_inds = []
for ind, dim in enumerate(self.space.dimensions):
if isinstance(dim, Categorical):
self._cat_inds.append(ind)
else:
self._non_cat_inds.append(ind)
self.n_jobs = n_jobs
# The cache of responses of ask method for n_points not None.
# This ensures that multiple calls to ask with n_points set
# return same sets of points.
# The cache is reset to {} at every call to tell.
self.cache_ = {}


def ask(

self, n_points=None, strategy='cl_min')

Query point or multiple points at which objective should be evaluated.

• n_points [int or None, default=None]: Number of points returned by the ask method. If the value is None, a single point to evaluate is returned. Otherwise a list of points to evaluate is returned of size n_points. This is useful if you can evaluate your objective in parallel, and thus obtain more objective function evaluations per unit of time.

• strategy [string, default="cl_min"]: Method to use to sample multiple points (see also n_points description). This parameter is ignored if n_points = None. Supported options are "cl_min", "cl_mean" or "cl_max".

• If set to "cl_min", then constant liar strtategy is used with lie objective value being minimum of observed objective values. "cl_mean" and "cl_max" means mean and max of values respectively. For details on this strategy see:

https://hal.archives-ouvertes.fr/hal-00732512/document

With this strategy a copy of optimizer is created, which is then asked for a point, and the point is told to the copy of optimizer with some fake objective (lie), the next point is asked from copy, it is also told to the copy with fake objective and so on. The type of lie defines different flavours of cl_x strategies.

def ask(self, n_points=None, strategy="cl_min"):
"""Query point or multiple points at which objective should be evaluated.
* n_points [int or None, default=None]:
Number of points returned by the ask method.
If the value is None, a single point to evaluate is returned.
Otherwise a list of points to evaluate is returned of size
n_points. This is useful if you can evaluate your objective in
parallel, and thus obtain more objective function evaluations per
unit of time.
* strategy [string, default="cl_min"]:
Method to use to sample multiple points (see also n_points
description). This parameter is ignored if n_points = None.
Supported options are "cl_min", "cl_mean" or "cl_max".
- If set to "cl_min", then constant liar strtategy is used
with lie objective value being minimum of observed objective
values. "cl_mean" and "cl_max" means mean and max of values
respectively. For details on this strategy see:
https://hal.archives-ouvertes.fr/hal-00732512/document
With this strategy a copy of optimizer is created, which is
then asked for a point, and the point is told to the copy of
optimizer with some fake objective (lie), the next point is
asked from copy, it is also told to the copy with fake
objective and so on. The type of lie defines different
flavours of cl_x strategies.
"""
if n_points is None:
return self._ask()
supported_strategies = ["cl_min", "cl_mean", "cl_max"]
if not (isinstance(n_points, int) and n_points > 0):
raise ValueError(
"n_points should be int > 0, got " + str(n_points)
)
if strategy not in supported_strategies:
raise ValueError(
"Expected parallel_strategy to be one of " +
str(supported_strategies) + ", " + "got %s" % strategy
)
# Caching the result with n_points not None. If some new parameters
# are provided to the ask, the cache_ is not used.
if (n_points, strategy) in self.cache_:
return self.cache_[(n_points, strategy)]
# Copy of the optimizer is made in order to manage the
# deletion of points with "lie" objective (the copy of
# oiptimizer is simply discarded)
opt = self.copy()
X = []
for i in range(n_points):
x = opt.ask()
X.append(x)
if strategy == "cl_min":
y_lie = np.min(opt.yi) if opt.yi else 0.0  # CL-min lie
elif strategy == "cl_mean":
y_lie = np.mean(opt.yi) if opt.yi else 0.0  # CL-mean lie
else:
y_lie = np.max(opt.yi) if opt.yi else 0.0  # CL-max lie
opt.tell(x, y_lie)  # lie to the optimizer
self.cache_ = {(n_points, strategy): X}  # cache_ the result
return X


def copy(

self, random_state=None)

Create a shallow copy of an instance of the optimizer.

## Parameters

• random_state [int, RandomState instance, or None (default)]: Set the random state of the copy.
def copy(self, random_state=None):
"""Create a shallow copy of an instance of the optimizer.
Parameters
----------
* random_state [int, RandomState instance, or None (default)]:
Set the random state of the copy.
"""
optimizer = Optimizer(
dimensions=self.space.dimensions,
base_estimator=self.base_estimator_,
n_initial_points=self.n_initial_points_,
acq_func=self.acq_func,
acq_optimizer=self.acq_optimizer,
acq_func_kwargs=self.acq_func_kwargs,
acq_optimizer_kwargs=self.acq_optimizer_kwargs,
random_state=random_state,
)
if hasattr(self, "gains_"):
optimizer.gains_ = np.copy(self.gains_)
if self.Xi:
optimizer.tell(self.Xi, self.yi)
return optimizer


def run(

self, func, n_iter=1)

Execute ask() + tell() n_iter times

def run(self, func, n_iter=1):
"""Execute ask() + tell() n_iter times"""
for _ in range(n_iter):
x = self.ask()
self.tell(x, func(x))
return create_result(self.Xi, self.yi, self.space, self.rng,
models=self.models)


def tell(

self, x, y, fit=True)

Record an observation (or several) of the objective function.

Provide values of the objective function at points suggested by ask() or other points. By default a new model will be fit to all observations. The new model is used to suggest the next point at which to evaluate the objective. This point can be retrieved by calling ask().

To add observations without fitting a new model set fit to False.

To add multiple observations in a batch pass a list-of-lists for x and a list of scalars for y.

## Parameters

• x [list or list-of-lists]: Point at which objective was evaluated.

• y [scalar or list]: Value of objective at x.

• fit [bool, default=True] Fit a model to observed evaluations of the objective. A model will only be fitted after n_initial_points points have been told to the optimizer irrespective of the value of fit.

def tell(self, x, y, fit=True):
"""Record an observation (or several) of the objective function.
Provide values of the objective function at points suggested by ask()
or other points. By default a new model will be fit to all
observations. The new model is used to suggest the next point at
which to evaluate the objective. This point can be retrieved by calling
ask().
To add observations without fitting a new model set fit to False.
To add multiple observations in a batch pass a list-of-lists for x
and a list of scalars for y.
Parameters
----------
* x [list or list-of-lists]:
Point at which objective was evaluated.
* y [scalar or list]:
Value of objective at x.
* fit [bool, default=True]
Fit a model to observed evaluations of the objective. A model will
only be fitted after n_initial_points points have been told to
the optimizer irrespective of the value of fit.
"""
check_x_in_space(x, self.space)
if "ps" in self.acq_func:
if is_2Dlistlike(x):
if np.ndim(y) == 2 and np.shape(y)[1] == 2:
y = [[val, log(t)] for (val, t) in y]
self.Xi.extend(x)
self.yi.extend(y)
else:
raise TypeError("expcted y to be a list of (func_val, t)")
self._n_initial_points -= len(y)
elif is_listlike(x):
if np.ndim(y) == 1 and len(y) == 2:
y = list(y)
y[1] = log(y[1])
self.Xi.append(x)
self.yi.append(y)
else:
raise TypeError("expected y to be (func_val, t)")
self._n_initial_points -= 1
# if y isn't a scalar it means we have been handed a batch of points
elif is_listlike(y) and is_2Dlistlike(x):
self.Xi.extend(x)
self.yi.extend(y)
self._n_initial_points -= len(y)
elif is_listlike(x):
if isinstance(y, Number):
self.Xi.append(x)
self.yi.append(y)
self._n_initial_points -= 1
else:
raise ValueError("func should return a scalar")
else:
raise ValueError("Type of arguments x (%s) and y (%s) "
"not compatible." % (type(x), type(y)))
# optimizer learned somethnig new - discard cache
self.cache_ = {}
# after being "told" n_initial_points we switch from sampling
# random points to using a surrogate model
if (fit and self._n_initial_points <= 0 and
self.base_estimator_ is not None):
transformed_bounds = np.array(self.space.transformed_bounds)
est = clone(self.base_estimator_)
with warnings.catch_warnings():
warnings.simplefilter("ignore")
est.fit(self.space.transform(self.Xi), self.yi)
if hasattr(self, "next_xs_") and self.acq_func == "gp_hedge":
self.gains_ -= est.predict(np.vstack(self.next_xs_))
self.models.append(est)
# even with BFGS as optimizer we want to sample a large number
# of points and then pick the best ones as starting points
X = self.space.transform(self.space.rvs(
n_samples=self.n_points, random_state=self.rng))
self.next_xs_ = []
for cand_acq_func in self.cand_acq_funcs_:
values = _gaussian_acquisition(
X=X, model=est, y_opt=np.min(self.yi),
acq_func=cand_acq_func,
acq_func_kwargs=self.acq_func_kwargs)
# Find the minimum of the acquisition function by randomly
# sampling points from the space
if self.acq_optimizer == "sampling":
next_x = X[np.argmin(values)]
# Use BFGS to find the mimimum of the acquisition function, the
# minimization starts from n_restarts_optimizer different
# points and the best minimum is used
elif self.acq_optimizer == "lbfgs":
x0 = X[np.argsort(values)[:self.n_restarts_optimizer]]
with warnings.catch_warnings():
warnings.simplefilter("ignore")
results = Parallel(n_jobs=self.n_jobs)(
delayed(fmin_l_bfgs_b)(
gaussian_acquisition_1D, x,
args=(est, np.min(self.yi), cand_acq_func,
self.acq_func_kwargs),
bounds=self.space.transformed_bounds,
approx_grad=False,
maxiter=20)
for x in x0)
cand_xs = np.array([r[0] for r in results])
cand_acqs = np.array([r[1] for r in results])
next_x = cand_xs[np.argmin(cand_acqs)]
# lbfgs should handle this but just in case there are
# precision errors.
if not self.space.is_categorical:
next_x = np.clip(
next_x, transformed_bounds[:, 0],
transformed_bounds[:, 1])
self.next_xs_.append(next_x)
if self.acq_func == "gp_hedge":
logits = np.array(self.gains_)
logits -= np.max(logits)
exp_logits = np.exp(self.eta * logits)
probs = exp_logits / np.sum(exp_logits)
next_x = self.next_xs_[np.argmax(self.rng.multinomial(1,
probs))]
else:
next_x = self.next_xs_[0]
# note the need for [0] at the end
self._next_x = self.space.inverse_transform(
next_x.reshape((1, -1)))[0]
# Pack results
return create_result(self.Xi, self.yi, self.space, self.rng,
models=self.models)


### Instance variables

var Xi

var acq_func

var acq_func_kwargs

var acq_optimizer_kwargs

var cache_

var eta

var models

var n_jobs

var n_points

var n_restarts_optimizer

var rng

var space

var yi

class Space

Search space.

class Space(object):
"""Search space."""

def __init__(self, dimensions):
"""Initialize a search space from given specifications.

Parameters
----------
* dimensions [list, shape=(n_dims,)]:
List of search space dimensions.
Each search dimension can be defined either as

- a (lower_bound, upper_bound) tuple (for Real or Integer
dimensions),
- a (lower_bound, upper_bound, "prior") tuple (for Real
dimensions),
- as a list of categories (for Categorical dimensions), or
- an instance of a Dimension object (Real, Integer or
Categorical).

NOTE: The upper and lower bounds are inclusive for Integer
dimensions.
"""
self.dimensions = [check_dimension(dim) for dim in dimensions]

def __eq__(self, other):
return all([a == b for a, b in zip(self.dimensions, other.dimensions)])

def __repr__(self):
if len(self.dimensions) > 31:
dims = self.dimensions[:15] + [_Ellipsis()] + self.dimensions[-15:]
else:
dims = self.dimensions
return "Space([{}])".format(',\n       '.join(map(str, dims)))

def __iter__(self):
return iter(self.dimensions)

@property
def is_real(self):
"""
Returns true if all dimensions are Real
"""
return all([isinstance(dim, Real) for dim in self.dimensions])

def rvs(self, n_samples=1, random_state=None):
"""Draw random samples.

The samples are in the original space. They need to be transformed
before being passed to a model or minimizer by space.transform().

Parameters
----------
* n_samples [int, default=1]:
Number of samples to be drawn from the space.

* random_state [int, RandomState instance, or None (default)]:
Set random state to something other than None for reproducible
results.

Returns
-------
* points: [list of lists, shape=(n_points, n_dims)]
Points sampled from the space.
"""
rng = check_random_state(random_state)

# Draw
columns = []

for dim in self.dimensions:
if sp_version < (0, 16):
columns.append(dim.rvs(n_samples=n_samples))
else:
columns.append(dim.rvs(n_samples=n_samples, random_state=rng))

# Transpose
rows = []

for i in range(n_samples):
r = []
for j in range(self.n_dims):
r.append(columns[j][i])

rows.append(r)

return rows

def transform(self, X):
"""Transform samples from the original space into a warped space.

Note: this transformation is expected to be used to project samples
into a suitable space for numerical optimization.

Parameters
----------
* X [list of lists, shape=(n_samples, n_dims)]:
The samples to transform.

Returns
-------
* Xt [array of floats, shape=(n_samples, transformed_n_dims)]
The transformed samples.
"""
# Pack by dimension
columns = []
for dim in self.dimensions:
columns.append([])

for i in range(len(X)):
for j in range(self.n_dims):
columns[j].append(X[i][j])

# Transform
for j in range(self.n_dims):
columns[j] = self.dimensions[j].transform(columns[j])

# Repack as an array
Xt = np.hstack([np.asarray(c).reshape((len(X), -1)) for c in columns])

return Xt

def inverse_transform(self, Xt):
"""Inverse transform samples from the warped space back to the
original space.

Parameters
----------
* Xt [array of floats, shape=(n_samples, transformed_n_dims)]:
The samples to inverse transform.

Returns
-------
* X [list of lists, shape=(n_samples, n_dims)]
The original samples.
"""
# Inverse transform
columns = []
start = 0

for j in range(self.n_dims):
dim = self.dimensions[j]
offset = dim.transformed_size

if offset == 1:
columns.append(dim.inverse_transform(Xt[:, start]))
else:
columns.append(
dim.inverse_transform(Xt[:, start:start+offset]))

start += offset

# Transpose
rows = []

for i in range(len(Xt)):
r = []
for j in range(self.n_dims):
r.append(columns[j][i])

rows.append(r)

return rows

@property
def n_dims(self):
"""The dimensionality of the original space."""
return len(self.dimensions)

@property
def transformed_n_dims(self):
"""The dimensionality of the warped space."""
return sum([dim.transformed_size for dim in self.dimensions])

@property
def bounds(self):
"""The dimension bounds, in the original space."""
b = []

for dim in self.dimensions:
if dim.size == 1:
b.append(dim.bounds)
else:
b.extend(dim.bounds)

return b

def __contains__(self, point):
"""Check that point is within the bounds of the space."""
for component, dim in zip(point, self.dimensions):
if component not in dim:
return False
return True

@property
def transformed_bounds(self):
"""The dimension bounds, in the warped space."""
b = []

for dim in self.dimensions:
if dim.transformed_size == 1:
b.append(dim.transformed_bounds)
else:
b.extend(dim.transformed_bounds)

return b

@property
def is_categorical(self):
"""Space contains exclusively categorical dimensions"""
return all([isinstance(dim, Categorical) for dim in self.dimensions])

def distance(self, point_a, point_b):
"""Compute distance between two points in this space.

Parameters
----------
* a [array]
First point.

* b [array]
Second point.
"""
distance = 0.
for a, b, dim in zip(point_a, point_b, self.dimensions):
distance += dim.distance(a, b)

return distance


### Static methods

def __init__(

self, dimensions)

Initialize a search space from given specifications.

## Parameters

• dimensions [list, shape=(n_dims,)]: List of search space dimensions. Each search dimension can be defined either as

• a (lower_bound, upper_bound) tuple (for Real or Integer dimensions),
• a (lower_bound, upper_bound, "prior") tuple (for Real dimensions),
• as a list of categories (for Categorical dimensions), or
• an instance of a Dimension object (Real, Integer or Categorical).

NOTE: The upper and lower bounds are inclusive for Integer dimensions.

def __init__(self, dimensions):
"""Initialize a search space from given specifications.
Parameters
----------
* dimensions [list, shape=(n_dims,)]:
List of search space dimensions.
Each search dimension can be defined either as
- a (lower_bound, upper_bound) tuple (for Real or Integer
dimensions),
- a (lower_bound, upper_bound, "prior") tuple (for Real
dimensions),
- as a list of categories (for Categorical dimensions), or
- an instance of a Dimension object (Real, Integer or
Categorical).
NOTE: The upper and lower bounds are inclusive for Integer
dimensions.
"""
self.dimensions = [check_dimension(dim) for dim in dimensions]


def distance(

self, point_a, point_b)

Compute distance between two points in this space.

## Parameters

• a [array] First point.

• b [array] Second point.

def distance(self, point_a, point_b):
"""Compute distance between two points in this space.
Parameters
----------
* a [array]
First point.
* b [array]
Second point.
"""
distance = 0.
for a, b, dim in zip(point_a, point_b, self.dimensions):
distance += dim.distance(a, b)
return distance


def inverse_transform(

self, Xt)

Inverse transform samples from the warped space back to the original space.

## Parameters

• Xt [array of floats, shape=(n_samples, transformed_n_dims)]: The samples to inverse transform.

## Returns

• X [list of lists, shape=(n_samples, n_dims)] The original samples.
def inverse_transform(self, Xt):
"""Inverse transform samples from the warped space back to the
original space.
Parameters
----------
* Xt [array of floats, shape=(n_samples, transformed_n_dims)]:
The samples to inverse transform.
Returns
-------
* X [list of lists, shape=(n_samples, n_dims)]
The original samples.
"""
# Inverse transform
columns = []
start = 0
for j in range(self.n_dims):
dim = self.dimensions[j]
offset = dim.transformed_size
if offset == 1:
columns.append(dim.inverse_transform(Xt[:, start]))
else:
columns.append(
dim.inverse_transform(Xt[:, start:start+offset]))
start += offset
# Transpose
rows = []
for i in range(len(Xt)):
r = []
for j in range(self.n_dims):
r.append(columns[j][i])
rows.append(r)
return rows


def rvs(

self, n_samples=1, random_state=None)

Draw random samples.

The samples are in the original space. They need to be transformed before being passed to a model or minimizer by space.transform().

## Parameters

• n_samples [int, default=1]: Number of samples to be drawn from the space.

• random_state [int, RandomState instance, or None (default)]: Set random state to something other than None for reproducible results.

## Returns

• points: [list of lists, shape=(n_points, n_dims)] Points sampled from the space.
def rvs(self, n_samples=1, random_state=None):
"""Draw random samples.
The samples are in the original space. They need to be transformed
before being passed to a model or minimizer by space.transform().
Parameters
----------
* n_samples [int, default=1]:
Number of samples to be drawn from the space.
* random_state [int, RandomState instance, or None (default)]:
Set random state to something other than None for reproducible
results.
Returns
-------
* points: [list of lists, shape=(n_points, n_dims)]
Points sampled from the space.
"""
rng = check_random_state(random_state)
# Draw
columns = []
for dim in self.dimensions:
if sp_version < (0, 16):
columns.append(dim.rvs(n_samples=n_samples))
else:
columns.append(dim.rvs(n_samples=n_samples, random_state=rng))
# Transpose
rows = []
for i in range(n_samples):
r = []
for j in range(self.n_dims):
r.append(columns[j][i])
rows.append(r)
return rows


def transform(

self, X)

Transform samples from the original space into a warped space.

Note: this transformation is expected to be used to project samples into a suitable space for numerical optimization.

## Parameters

• X [list of lists, shape=(n_samples, n_dims)]: The samples to transform.

## Returns

• Xt [array of floats, shape=(n_samples, transformed_n_dims)] The transformed samples.
def transform(self, X):
"""Transform samples from the original space into a warped space.
Note: this transformation is expected to be used to project samples
into a suitable space for numerical optimization.
Parameters
----------
* X [list of lists, shape=(n_samples, n_dims)]:
The samples to transform.
Returns
-------
* Xt [array of floats, shape=(n_samples, transformed_n_dims)]
The transformed samples.
"""
# Pack by dimension
columns = []
for dim in self.dimensions:
columns.append([])
for i in range(len(X)):
for j in range(self.n_dims):
columns[j].append(X[i][j])
# Transform
for j in range(self.n_dims):
columns[j] = self.dimensions[j].transform(columns[j])
# Repack as an array
Xt = np.hstack([np.asarray(c).reshape((len(X), -1)) for c in columns])
return Xt


### Instance variables

var bounds

The dimension bounds, in the original space.

var dimensions

var is_categorical

Space contains exclusively categorical dimensions

var is_real

Returns true if all dimensions are Real

var n_dims

The dimensionality of the original space.

var transformed_bounds

The dimension bounds, in the warped space.

var transformed_n_dims

The dimensionality of the warped space.