.. note::
:class: sphx-glr-download-link-note
Click :ref:`here <sphx_glr_download_auto_examples_applications_plot_model_complexity_influence.py>` to download the full example code or to run this example in your browser via Binder
.. rst-class:: sphx-glr-example-title
.. _sphx_glr_auto_examples_applications_plot_model_complexity_influence.py:
==========================
Model Complexity Influence
==========================
Demonstrate how model complexity influences both prediction accuracy and
computational performance.
The dataset is the Boston Housing dataset (resp. 20 Newsgroups) for
regression (resp. classification).
For each class of models we make the model complexity vary through the choice
of relevant model parameters and measure the influence on both computational
performance (latency) and predictive power (MSE or Hamming Loss).
.. rst-class:: sphx-glr-horizontal
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.. image:: /auto_examples/applications/images/sphx_glr_plot_model_complexity_influence_001.png
:class: sphx-glr-multi-img
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.. image:: /auto_examples/applications/images/sphx_glr_plot_model_complexity_influence_002.png
:class: sphx-glr-multi-img
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.. image:: /auto_examples/applications/images/sphx_glr_plot_model_complexity_influence_003.png
:class: sphx-glr-multi-img
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
Benchmarking SGDClassifier(alpha=0.001, l1_ratio=0.25, loss='modified_huber',
penalty='elasticnet')
Complexity: 4466 | Hamming Loss (Misclassification Ratio): 0.2491 | Pred. Time: 0.020835s
Benchmarking SGDClassifier(alpha=0.001, l1_ratio=0.5, loss='modified_huber',
penalty='elasticnet')
Complexity: 1663 | Hamming Loss (Misclassification Ratio): 0.2915 | Pred. Time: 0.015789s
Benchmarking SGDClassifier(alpha=0.001, l1_ratio=0.75, loss='modified_huber',
penalty='elasticnet')
Complexity: 880 | Hamming Loss (Misclassification Ratio): 0.3180 | Pred. Time: 0.013469s
Benchmarking SGDClassifier(alpha=0.001, l1_ratio=0.9, loss='modified_huber',
penalty='elasticnet')
Complexity: 639 | Hamming Loss (Misclassification Ratio): 0.3337 | Pred. Time: 0.011812s
Benchmarking NuSVR(C=1000.0, gamma=3.0517578125e-05, nu=0.1)
Complexity: 69 | MSE: 31.8139 | Pred. Time: 0.000301s
Benchmarking NuSVR(C=1000.0, gamma=3.0517578125e-05, nu=0.25)
Complexity: 136 | MSE: 25.6140 | Pred. Time: 0.000811s
Benchmarking NuSVR(C=1000.0, gamma=3.0517578125e-05)
Complexity: 244 | MSE: 22.3375 | Pred. Time: 0.000895s
Benchmarking NuSVR(C=1000.0, gamma=3.0517578125e-05, nu=0.75)
Complexity: 351 | MSE: 21.3688 | Pred. Time: 0.001237s
Benchmarking NuSVR(C=1000.0, gamma=3.0517578125e-05, nu=0.9)
Complexity: 404 | MSE: 21.1033 | Pred. Time: 0.001460s
Benchmarking GradientBoostingRegressor(n_estimators=10)
Complexity: 10 | MSE: 29.0148 | Pred. Time: 0.000120s
Benchmarking GradientBoostingRegressor(n_estimators=50)
Complexity: 50 | MSE: 8.6545 | Pred. Time: 0.000302s
Benchmarking GradientBoostingRegressor()
Complexity: 100 | MSE: 7.7179 | Pred. Time: 0.000264s
Benchmarking GradientBoostingRegressor(n_estimators=200)
Complexity: 200 | MSE: 6.7507 | Pred. Time: 0.000425s
Benchmarking GradientBoostingRegressor(n_estimators=500)
Complexity: 500 | MSE: 7.1471 | Pred. Time: 0.000922s
|
.. code-block:: default
print(__doc__)
# Author: Eustache Diemert <eustache@diemert.fr>
# License: BSD 3 clause
import time
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.axes_grid1.parasite_axes import host_subplot
from mpl_toolkits.axisartist.axislines import Axes
from scipy.sparse.csr import csr_matrix
from sklearn import datasets
from sklearn.utils import shuffle
from sklearn.metrics import mean_squared_error
from sklearn.svm import NuSVR
from sklearn.ensemble import GradientBoostingRegressor
from sklearn.linear_model import SGDClassifier
from sklearn.metrics import hamming_loss
# #############################################################################
# Routines
# Initialize random generator
np.random.seed(0)
def generate_data(case, sparse=False):
"""Generate regression/classification data."""
if case == 'regression':
X, y = datasets.load_boston(return_X_y=True)
elif case == 'classification':
X, y = datasets.fetch_20newsgroups_vectorized(subset='all',
return_X_y=True)
X, y = shuffle(X, y)
offset = int(X.shape[0] * 0.8)
X_train, y_train = X[:offset], y[:offset]
X_test, y_test = X[offset:], y[offset:]
if sparse:
X_train = csr_matrix(X_train)
X_test = csr_matrix(X_test)
else:
X_train = np.array(X_train)
X_test = np.array(X_test)
y_test = np.array(y_test)
y_train = np.array(y_train)
data = {'X_train': X_train, 'X_test': X_test, 'y_train': y_train,
'y_test': y_test}
return data
def benchmark_influence(conf):
"""
Benchmark influence of :changing_param: on both MSE and latency.
"""
prediction_times = []
prediction_powers = []
complexities = []
for param_value in conf['changing_param_values']:
conf['tuned_params'][conf['changing_param']] = param_value
estimator = conf['estimator'](**conf['tuned_params'])
print("Benchmarking %s" % estimator)
estimator.fit(conf['data']['X_train'], conf['data']['y_train'])
conf['postfit_hook'](estimator)
complexity = conf['complexity_computer'](estimator)
complexities.append(complexity)
start_time = time.time()
for _ in range(conf['n_samples']):
y_pred = estimator.predict(conf['data']['X_test'])
elapsed_time = (time.time() - start_time) / float(conf['n_samples'])
prediction_times.append(elapsed_time)
pred_score = conf['prediction_performance_computer'](
conf['data']['y_test'], y_pred)
prediction_powers.append(pred_score)
print("Complexity: %d | %s: %.4f | Pred. Time: %fs\n" % (
complexity, conf['prediction_performance_label'], pred_score,
elapsed_time))
return prediction_powers, prediction_times, complexities
def plot_influence(conf, mse_values, prediction_times, complexities):
"""
Plot influence of model complexity on both accuracy and latency.
"""
plt.figure(figsize=(12, 6))
host = host_subplot(111, axes_class=Axes)
plt.subplots_adjust(right=0.75)
par1 = host.twinx()
host.set_xlabel('Model Complexity (%s)' % conf['complexity_label'])
y1_label = conf['prediction_performance_label']
y2_label = "Time (s)"
host.set_ylabel(y1_label)
par1.set_ylabel(y2_label)
p1, = host.plot(complexities, mse_values, 'b-', label="prediction error")
p2, = par1.plot(complexities, prediction_times, 'r-',
label="latency")
host.legend(loc='upper right')
host.axis["left"].label.set_color(p1.get_color())
par1.axis["right"].label.set_color(p2.get_color())
plt.title('Influence of Model Complexity - %s' % conf['estimator'].__name__)
plt.show()
def _count_nonzero_coefficients(estimator):
a = estimator.coef_.toarray()
return np.count_nonzero(a)
# #############################################################################
# Main code
regression_data = generate_data('regression')
classification_data = generate_data('classification', sparse=True)
configurations = [
{'estimator': SGDClassifier,
'tuned_params': {'penalty': 'elasticnet', 'alpha': 0.001, 'loss':
'modified_huber', 'fit_intercept': True, 'tol': 1e-3},
'changing_param': 'l1_ratio',
'changing_param_values': [0.25, 0.5, 0.75, 0.9],
'complexity_label': 'non_zero coefficients',
'complexity_computer': _count_nonzero_coefficients,
'prediction_performance_computer': hamming_loss,
'prediction_performance_label': 'Hamming Loss (Misclassification Ratio)',
'postfit_hook': lambda x: x.sparsify(),
'data': classification_data,
'n_samples': 30},
{'estimator': NuSVR,
'tuned_params': {'C': 1e3, 'gamma': 2 ** -15},
'changing_param': 'nu',
'changing_param_values': [0.1, 0.25, 0.5, 0.75, 0.9],
'complexity_label': 'n_support_vectors',
'complexity_computer': lambda x: len(x.support_vectors_),
'data': regression_data,
'postfit_hook': lambda x: x,
'prediction_performance_computer': mean_squared_error,
'prediction_performance_label': 'MSE',
'n_samples': 30},
{'estimator': GradientBoostingRegressor,
'tuned_params': {'loss': 'ls'},
'changing_param': 'n_estimators',
'changing_param_values': [10, 50, 100, 200, 500],
'complexity_label': 'n_trees',
'complexity_computer': lambda x: x.n_estimators,
'data': regression_data,
'postfit_hook': lambda x: x,
'prediction_performance_computer': mean_squared_error,
'prediction_performance_label': 'MSE',
'n_samples': 30},
]
for conf in configurations:
prediction_performances, prediction_times, complexities = \
benchmark_influence(conf)
plot_influence(conf, prediction_performances, prediction_times,
complexities)
.. rst-class:: sphx-glr-timing
**Total running time of the script:** ( 0 minutes 20.261 seconds)
**Estimated memory usage:** 60 MB
.. _sphx_glr_download_auto_examples_applications_plot_model_complexity_influence.py:
.. only :: html
.. container:: sphx-glr-footer
:class: sphx-glr-footer-example
.. container:: binder-badge
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:width: 150 px
.. container:: sphx-glr-download
:download:`Download Python source code: plot_model_complexity_influence.py <plot_model_complexity_influence.py>`
.. container:: sphx-glr-download
:download:`Download Jupyter notebook: plot_model_complexity_influence.ipynb <plot_model_complexity_influence.ipynb>`
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