.. _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). .. code-block:: python print(__doc__) # Author: Eustache Diemert # 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.classes import NuSVR from sklearn.ensemble.gradient_boosting import GradientBoostingRegressor from sklearn.linear_model.stochastic_gradient import SGDClassifier from sklearn.metrics import hamming_loss Routines .. code-block:: python # initialize random generator np.random.seed(0) def generate_data(case, sparse=False): """Generate regression/classification data.""" bunch = None if case == 'regression': bunch = datasets.load_boston() elif case == 'classification': bunch = datasets.fetch_20newsgroups_vectorized(subset='all') X, y = shuffle(bunch.data, bunch.target) 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 .. code-block:: python 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}, '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-horizontal * .. image:: /auto_examples/applications/images/sphx_glr_plot_model_complexity_influence_001.png :scale: 47 * .. image:: /auto_examples/applications/images/sphx_glr_plot_model_complexity_influence_002.png :scale: 47 * .. image:: /auto_examples/applications/images/sphx_glr_plot_model_complexity_influence_003.png :scale: 47 .. rst-class:: sphx-glr-script-out Out:: Benchmarking SGDClassifier(alpha=0.001, average=False, class_weight=None, epsilon=0.1, eta0=0.0, fit_intercept=True, l1_ratio=0.25, learning_rate='optimal', loss='modified_huber', n_iter=5, n_jobs=1, penalty='elasticnet', power_t=0.5, random_state=None, shuffle=True, verbose=0, warm_start=False) Complexity: 4454 | Hamming Loss (Misclassification Ratio): 0.2501 | Pred. Time: 0.026299s Benchmarking SGDClassifier(alpha=0.001, average=False, class_weight=None, epsilon=0.1, eta0=0.0, fit_intercept=True, l1_ratio=0.5, learning_rate='optimal', loss='modified_huber', n_iter=5, n_jobs=1, penalty='elasticnet', power_t=0.5, random_state=None, shuffle=True, verbose=0, warm_start=False) Complexity: 1624 | Hamming Loss (Misclassification Ratio): 0.2923 | Pred. Time: 0.019267s Benchmarking SGDClassifier(alpha=0.001, average=False, class_weight=None, epsilon=0.1, eta0=0.0, fit_intercept=True, l1_ratio=0.75, learning_rate='optimal', loss='modified_huber', n_iter=5, n_jobs=1, penalty='elasticnet', power_t=0.5, random_state=None, shuffle=True, verbose=0, warm_start=False) Complexity: 873 | Hamming Loss (Misclassification Ratio): 0.3191 | Pred. Time: 0.015463s Benchmarking SGDClassifier(alpha=0.001, average=False, class_weight=None, epsilon=0.1, eta0=0.0, fit_intercept=True, l1_ratio=0.9, learning_rate='optimal', loss='modified_huber', n_iter=5, n_jobs=1, penalty='elasticnet', power_t=0.5, random_state=None, shuffle=True, verbose=0, warm_start=False) Complexity: 655 | Hamming Loss (Misclassification Ratio): 0.3252 | Pred. Time: 0.013982s Benchmarking NuSVR(C=1000.0, cache_size=200, coef0=0.0, degree=3, gamma=3.0517578125e-05, kernel='rbf', max_iter=-1, nu=0.1, shrinking=True, tol=0.001, verbose=False) Complexity: 69 | MSE: 31.8133 | Pred. Time: 0.000363s Benchmarking NuSVR(C=1000.0, cache_size=200, coef0=0.0, degree=3, gamma=3.0517578125e-05, kernel='rbf', max_iter=-1, nu=0.25, shrinking=True, tol=0.001, verbose=False) Complexity: 136 | MSE: 25.6140 | Pred. Time: 0.000647s Benchmarking NuSVR(C=1000.0, cache_size=200, coef0=0.0, degree=3, gamma=3.0517578125e-05, kernel='rbf', max_iter=-1, nu=0.5, shrinking=True, tol=0.001, verbose=False) Complexity: 243 | MSE: 22.3315 | Pred. Time: 0.001103s Benchmarking NuSVR(C=1000.0, cache_size=200, coef0=0.0, degree=3, gamma=3.0517578125e-05, kernel='rbf', max_iter=-1, nu=0.75, shrinking=True, tol=0.001, verbose=False) Complexity: 350 | MSE: 21.3679 | Pred. Time: 0.001559s Benchmarking NuSVR(C=1000.0, cache_size=200, coef0=0.0, degree=3, gamma=3.0517578125e-05, kernel='rbf', max_iter=-1, nu=0.9, shrinking=True, tol=0.001, verbose=False) Complexity: 404 | MSE: 21.0915 | Pred. Time: 0.001788s Benchmarking GradientBoostingRegressor(alpha=0.9, criterion='friedman_mse', init=None, learning_rate=0.1, loss='ls', max_depth=3, max_features=None, max_leaf_nodes=None, min_impurity_split=1e-07, min_samples_leaf=1, min_samples_split=2, min_weight_fraction_leaf=0.0, n_estimators=10, presort='auto', random_state=None, subsample=1.0, verbose=0, warm_start=False) Complexity: 10 | MSE: 28.9793 | Pred. Time: 0.000111s Benchmarking GradientBoostingRegressor(alpha=0.9, criterion='friedman_mse', init=None, learning_rate=0.1, loss='ls', max_depth=3, max_features=None, max_leaf_nodes=None, min_impurity_split=1e-07, min_samples_leaf=1, min_samples_split=2, min_weight_fraction_leaf=0.0, n_estimators=50, presort='auto', random_state=None, subsample=1.0, verbose=0, warm_start=False) Complexity: 50 | MSE: 8.3398 | Pred. Time: 0.000196s Benchmarking GradientBoostingRegressor(alpha=0.9, criterion='friedman_mse', init=None, learning_rate=0.1, loss='ls', max_depth=3, max_features=None, max_leaf_nodes=None, min_impurity_split=1e-07, min_samples_leaf=1, min_samples_split=2, min_weight_fraction_leaf=0.0, n_estimators=100, presort='auto', random_state=None, subsample=1.0, verbose=0, warm_start=False) Complexity: 100 | MSE: 7.0096 | Pred. Time: 0.000274s Benchmarking GradientBoostingRegressor(alpha=0.9, criterion='friedman_mse', init=None, learning_rate=0.1, loss='ls', max_depth=3, max_features=None, max_leaf_nodes=None, min_impurity_split=1e-07, min_samples_leaf=1, min_samples_split=2, min_weight_fraction_leaf=0.0, n_estimators=200, presort='auto', random_state=None, subsample=1.0, verbose=0, warm_start=False) Complexity: 200 | MSE: 6.1836 | Pred. Time: 0.000431s Benchmarking GradientBoostingRegressor(alpha=0.9, criterion='friedman_mse', init=None, learning_rate=0.1, loss='ls', max_depth=3, max_features=None, max_leaf_nodes=None, min_impurity_split=1e-07, min_samples_leaf=1, min_samples_split=2, min_weight_fraction_leaf=0.0, n_estimators=500, presort='auto', random_state=None, subsample=1.0, verbose=0, warm_start=False) Complexity: 500 | MSE: 6.3426 | Pred. Time: 0.000931s **Total running time of the script:** (0 minutes 24.125 seconds) .. container:: sphx-glr-download **Download Python source code:** :download:`plot_model_complexity_influence.py ` .. container:: sphx-glr-download **Download IPython notebook:** :download:`plot_model_complexity_influence.ipynb `