Partial Dependence Plots 2D

Hvass-Labs Dec 2017 Holger Nahrstaedt 2020

Simple example to show the new 2D plots.

print(__doc__)
import numpy as np
from math import exp

from skopt import gp_minimize
from skopt.space import Real, Categorical, Integer
from skopt.plots import plot_histogram, plot_objective_2D, plot_objective
from skopt.utils import point_asdict
np.random.seed(123)
import matplotlib.pyplot as plt

dim_learning_rate = Real(name='learning_rate', low=1e-6, high=1e-2, prior='log-uniform')
dim_num_dense_layers = Integer(name='num_dense_layers', low=1, high=5)
dim_num_dense_nodes = Integer(name='num_dense_nodes', low=5, high=512)
dim_activation = Categorical(name='activation', categories=['relu', 'sigmoid'])

dimensions = [dim_learning_rate,
              dim_num_dense_layers,
              dim_num_dense_nodes,
              dim_activation]

default_parameters = [1e-4, 1, 64, 'relu']

def model_fitness(x):
    learning_rate, num_dense_layers, num_dense_nodes, activation = x

    fitness = ((exp(learning_rate) - 1.0) * 1000) ** 2 + \
               (num_dense_layers) ** 2 + \
               (num_dense_nodes/100) ** 2

    fitness *= 1.0 + 0.1 * np.random.rand()

    if activation == 'sigmoid':
        fitness += 10

    return fitness

print(model_fitness(x=default_parameters))

Out:

1.518471835296799

search_result = gp_minimize(func=model_fitness,
                            dimensions=dimensions,
                            n_calls=30,
                            x0=default_parameters,
                            random_state=123
                            )

print(search_result.x)
print(search_result.fun)

Out:

[2.5683326296760544e-06, 1, 5, 'relu']
1.0117401773345693

for fitness, x in sorted(zip(search_result.func_vals, search_result.x_iters)):
    print(fitness, x)

Out:

1.0117401773345693 [2.5683326296760544e-06, 1, 5, 'relu']
1.02011376627145 [4.9296274178364756e-06, 1, 5, 'relu']
1.0208250164867194 [5.447818995527194e-06, 1, 5, 'relu']
1.0216677303833677 [0.00011447839199199741, 1, 5, 'relu']
1.0319553707990767 [3.1995220781684726e-06, 1, 5, 'relu']
1.035000761229889 [9.696303738529007e-05, 1, 5, 'relu']
1.0387852167773188 [3.917740504174571e-06, 1, 5, 'relu']
1.0558125553699018 [4.826172160300783e-06, 1, 5, 'relu']
1.0657737857823664 [4.163587744230921e-06, 1, 5, 'relu']
1.0660997595359294 [1e-06, 1, 5, 'relu']
1.0669131656352118 [0.00010264491499511595, 1, 5, 'relu']
1.0751293914133275 [1.5998925006763378e-06, 1, 5, 'relu']
1.0876960517563532 [6.11082549910025e-06, 1, 5, 'relu']
1.1301695294147942 [0.0001280379715890307, 1, 19, 'relu']
1.1690663251629732 [0.00010510628672809584, 1, 33, 'relu']
1.4602213686635033 [0.0001, 1, 64, 'relu']
4.174922771740464 [0.00011226065176861382, 2, 5, 'relu']
14.337540595777632 [4.961649309025573e-06, 2, 44, 'sigmoid']
15.811122459303194 [5.768045960755954e-05, 1, 366, 'relu']
20.75714626376416 [4.6648726500116405e-05, 4, 195, 'relu']
20.83105097254721 [3.629134387669892e-06, 3, 323, 'relu']
25.045498550233685 [1.5528231282886148e-05, 3, 380, 'relu']
25.725698564025883 [0.0010034940899532338, 4, 264, 'relu']
26.808790139516606 [1e-06, 5, 5, 'relu']
28.093314338813517 [1e-06, 1, 512, 'relu']
31.67808942295837 [9.214584006695478e-05, 4, 213, 'sigmoid']
32.60979725349034 [0.0007109209001237586, 3, 355, 'sigmoid']
36.436844941374716 [9.52877578124997e-06, 4, 306, 'sigmoid']
108.24130894769868 [0.01, 1, 5, 'relu']
117.22558971730295 [0.008953258961145084, 4, 399, 'relu']

space = search_result.space

print(search_result.x_iters)

search_space = {name: space[name][1] for name in space.dimension_names}

print(point_asdict(search_space, default_parameters))

Out:

[[0.0001, 1, 64, 'relu'], [0.0007109209001237586, 3, 355, 'sigmoid'], [9.214584006695478e-05, 4, 213, 'sigmoid'], [3.629134387669892e-06, 3, 323, 'relu'], [9.52877578124997e-06, 4, 306, 'sigmoid'], [5.768045960755954e-05, 1, 366, 'relu'], [1.5528231282886148e-05, 3, 380, 'relu'], [4.6648726500116405e-05, 4, 195, 'relu'], [0.008953258961145084, 4, 399, 'relu'], [4.961649309025573e-06, 2, 44, 'sigmoid'], [0.0010034940899532338, 4, 264, 'relu'], [0.00010510628672809584, 1, 33, 'relu'], [0.00011447839199199741, 1, 5, 'relu'], [0.00011226065176861382, 2, 5, 'relu'], [0.0001280379715890307, 1, 19, 'relu'], [5.447818995527194e-06, 1, 5, 'relu'], [4.9296274178364756e-06, 1, 5, 'relu'], [4.826172160300783e-06, 1, 5, 'relu'], [0.00010264491499511595, 1, 5, 'relu'], [1e-06, 1, 5, 'relu'], [6.11082549910025e-06, 1, 5, 'relu'], [1.5998925006763378e-06, 1, 5, 'relu'], [0.01, 1, 5, 'relu'], [1e-06, 5, 5, 'relu'], [1e-06, 1, 512, 'relu'], [3.917740504174571e-06, 1, 5, 'relu'], [9.696303738529007e-05, 1, 5, 'relu'], [3.1995220781684726e-06, 1, 5, 'relu'], [4.163587744230921e-06, 1, 5, 'relu'], [2.5683326296760544e-06, 1, 5, 'relu']]
OrderedDict([('activation', 0.0001), ('learning_rate', 1), ('num_dense_layers', 64), ('num_dense_nodes', 'relu')])

print("Plotting now ...")

_ = plot_histogram(result=search_result, dimension_identifier='learning_rate',
                   bins=20)
plt.show()

Out:

Plotting now ...

_ = plot_objective_2D(result=search_result,
                      dimension_identifier1='learning_rate',
                      dimension_identifier2='num_dense_nodes')
plt.show()

_ = plot_objective_2D(result=search_result,
                      dimension_identifier1='num_dense_layers',
                      dimension_identifier2='num_dense_nodes')
plt.show()

_ = plot_objective(result=search_result,
                   plot_dims=['num_dense_layers',
                              'num_dense_nodes'])
plt.show()

Estimated memory usage: 9 MB