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).
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.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
# 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
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)
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: 0.026183s 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: 0.020048s 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: 0.016268s 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: 0.014223s 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: 0.000362s 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: 0.000640s 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: 0.001110s 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: 0.001546s 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: 0.001786s 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: 0.000110s 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: 0.000190s 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: 0.000271s 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: 0.000425s 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: 0.000921s
Total running time of the script: (0 minutes 23.450 seconds)
Download Python source code:
plot_model_complexity_influence.py
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plot_model_complexity_influence.ipynb
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