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Click here to download the full example code
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).
Traceback (most recent call last):
File "/usr/lib/python3/dist-packages/sphinx_gallery/gen_gallery.py", line 159, in call_memory
return 0., func()
File "/usr/lib/python3/dist-packages/sphinx_gallery/gen_rst.py", line 466, in __call__
exec(self.code, self.fake_main.__dict__)
File "/build/scikit-learn-ojoSZS/scikit-learn-0.23.2/examples/applications/plot_model_complexity_influence.py", line 128, in <module>
classification_data = generate_data('classification', sparse=True)
File "/build/scikit-learn-ojoSZS/scikit-learn-0.23.2/examples/applications/plot_model_complexity_influence.py", line 50, in generate_data
X, y = datasets.fetch_20newsgroups_vectorized(subset='all',
File "/build/scikit-learn-ojoSZS/scikit-learn-0.23.2/.pybuild/cpython3_3.8/build/sklearn/utils/validation.py", line 72, in inner_f
return f(**kwargs)
File "/build/scikit-learn-ojoSZS/scikit-learn-0.23.2/.pybuild/cpython3_3.8/build/sklearn/datasets/_twenty_newsgroups.py", line 419, in fetch_20newsgroups_vectorized
data_train = fetch_20newsgroups(data_home=data_home,
File "/build/scikit-learn-ojoSZS/scikit-learn-0.23.2/.pybuild/cpython3_3.8/build/sklearn/utils/validation.py", line 72, in inner_f
return f(**kwargs)
File "/build/scikit-learn-ojoSZS/scikit-learn-0.23.2/.pybuild/cpython3_3.8/build/sklearn/datasets/_twenty_newsgroups.py", line 258, in fetch_20newsgroups
cache = _download_20newsgroups(target_dir=twenty_home,
File "/build/scikit-learn-ojoSZS/scikit-learn-0.23.2/.pybuild/cpython3_3.8/build/sklearn/datasets/_twenty_newsgroups.py", line 74, in _download_20newsgroups
archive_path = _fetch_remote(ARCHIVE, dirname=target_dir)
File "/build/scikit-learn-ojoSZS/scikit-learn-0.23.2/.pybuild/cpython3_3.8/build/sklearn/datasets/_base.py", line 1181, in _fetch_remote
urlretrieve(remote.url, file_path)
File "/usr/lib/python3.8/urllib/request.py", line 247, in urlretrieve
with contextlib.closing(urlopen(url, data)) as fp:
File "/usr/lib/python3.8/urllib/request.py", line 222, in urlopen
return opener.open(url, data, timeout)
File "/usr/lib/python3.8/urllib/request.py", line 525, in open
response = self._open(req, data)
File "/usr/lib/python3.8/urllib/request.py", line 542, in _open
result = self._call_chain(self.handle_open, protocol, protocol +
File "/usr/lib/python3.8/urllib/request.py", line 502, in _call_chain
result = func(*args)
File "/usr/lib/python3.8/urllib/request.py", line 1393, in https_open
return self.do_open(http.client.HTTPSConnection, req,
File "/usr/lib/python3.8/urllib/request.py", line 1353, in do_open
raise URLError(err)
urllib.error.URLError: <urlopen error [Errno -2] Name or service not known>
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 0.023 seconds)