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).

  • ../../_images/sphx_glr_plot_model_complexity_influence_001.png
  • ../../_images/sphx_glr_plot_model_complexity_influence_002.png
  • ../../_images/sphx_glr_plot_model_complexity_influence_003.png

Out:

Benchmarking SGDClassifier(alpha=0.001, l1_ratio=0.25, loss='modified_huber',
              penalty='elasticnet')
Complexity: 4466 | Hamming Loss (Misclassification Ratio): 0.2491 | Pred. Time: 0.021127s

Benchmarking SGDClassifier(alpha=0.001, l1_ratio=0.5, loss='modified_huber',
              penalty='elasticnet')
Complexity: 1663 | Hamming Loss (Misclassification Ratio): 0.2915 | Pred. Time: 0.017638s

Benchmarking SGDClassifier(alpha=0.001, l1_ratio=0.75, loss='modified_huber',
              penalty='elasticnet')
Complexity: 880 | Hamming Loss (Misclassification Ratio): 0.3180 | Pred. Time: 0.011905s

Benchmarking SGDClassifier(alpha=0.001, l1_ratio=0.9, loss='modified_huber',
              penalty='elasticnet')
Complexity: 639 | Hamming Loss (Misclassification Ratio): 0.3337 | Pred. Time: 0.010434s

Benchmarking NuSVR(C=1000.0, gamma=3.0517578125e-05, nu=0.1)
Complexity: 69 | MSE: 31.8139 | Pred. Time: 0.000286s

Benchmarking NuSVR(C=1000.0, gamma=3.0517578125e-05, nu=0.25)
Complexity: 136 | MSE: 25.6140 | Pred. Time: 0.000506s

Benchmarking NuSVR(C=1000.0, gamma=3.0517578125e-05)
Complexity: 244 | MSE: 22.3375 | Pred. Time: 0.000871s

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: 0.001399s

Benchmarking GradientBoostingRegressor(n_estimators=10)
Complexity: 10 | MSE: 29.0148 | Pred. Time: 0.000106s

Benchmarking GradientBoostingRegressor(n_estimators=50)
Complexity: 50 | MSE: 8.6545 | Pred. Time: 0.000182s

Benchmarking GradientBoostingRegressor()
Complexity: 100 | MSE: 7.7179 | Pred. Time: 0.000256s

Benchmarking GradientBoostingRegressor(n_estimators=200)
Complexity: 200 | MSE: 6.7507 | Pred. Time: 0.000393s

Benchmarking GradientBoostingRegressor(n_estimators=500)
Complexity: 500 | MSE: 7.1471 | Pred. Time: 0.000835s

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)

Total running time of the script: ( 0 minutes 21.076 seconds)

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