Note
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MNIST classfification using multinomial logistic + L1ΒΆ
Here we fit a multinomial logistic regression with L1 penalty on a subset of the MNIST digits classification task. We use the SAGA algorithm for this purpose: this a solver that is fast when the number of samples is significantly larger than the number of features and is able to finely optimize non-smooth objective functions which is the case with the l1-penalty. Test accuracy reaches > 0.8, while weight vectors remains sparse and therefore more easily interpretable.
Note that this accuracy of this l1-penalized linear model is significantly below what can be reached by an l2-penalized linear model or a non-linear multi-layer perceptron model on this dataset.
Traceback (most recent call last):
File "/build/scikit-learn-qZGLk4/scikit-learn-0.20.2+dfsg/examples/linear_model/plot_sparse_logistic_regression_mnist.py", line 39, in <module>
X, y = fetch_openml('mnist_784', version=1, return_X_y=True)
File "/build/scikit-learn-qZGLk4/scikit-learn-0.20.2+dfsg/.pybuild/cpython3_3.7/build/sklearn/datasets/openml.py", line 526, in fetch_openml
data_info = _get_data_info_by_name(name, version, data_home)
File "/build/scikit-learn-qZGLk4/scikit-learn-0.20.2+dfsg/.pybuild/cpython3_3.7/build/sklearn/datasets/openml.py", line 314, in _get_data_info_by_name
data_home)
File "/build/scikit-learn-qZGLk4/scikit-learn-0.20.2+dfsg/.pybuild/cpython3_3.7/build/sklearn/datasets/openml.py", line 164, in _get_json_content_from_openml_api
return _load_json()
File "/build/scikit-learn-qZGLk4/scikit-learn-0.20.2+dfsg/.pybuild/cpython3_3.7/build/sklearn/datasets/openml.py", line 62, in wrapper
return f()
File "/build/scikit-learn-qZGLk4/scikit-learn-0.20.2+dfsg/.pybuild/cpython3_3.7/build/sklearn/datasets/openml.py", line 160, in _load_json
with closing(_open_openml_url(url, data_home)) as response:
File "/build/scikit-learn-qZGLk4/scikit-learn-0.20.2+dfsg/.pybuild/cpython3_3.7/build/sklearn/datasets/openml.py", line 109, in _open_openml_url
with closing(urlopen(req)) as fsrc:
File "/usr/lib/python3.7/urllib/request.py", line 222, in urlopen
return opener.open(url, data, timeout)
File "/usr/lib/python3.7/urllib/request.py", line 525, in open
response = self._open(req, data)
File "/usr/lib/python3.7/urllib/request.py", line 543, in _open
'_open', req)
File "/usr/lib/python3.7/urllib/request.py", line 503, in _call_chain
result = func(*args)
File "/usr/lib/python3.7/urllib/request.py", line 1360, in https_open
context=self._context, check_hostname=self._check_hostname)
File "/usr/lib/python3.7/urllib/request.py", line 1319, in do_open
raise URLError(err)
urllib.error.URLError: <urlopen error [Errno 111] Connection refused>
import time
import matplotlib.pyplot as plt
import numpy as np
from sklearn.datasets import fetch_openml
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.utils import check_random_state
print(__doc__)
# Author: Arthur Mensch <arthur.mensch@m4x.org>
# License: BSD 3 clause
# Turn down for faster convergence
t0 = time.time()
train_samples = 5000
# Load data from https://www.openml.org/d/554
X, y = fetch_openml('mnist_784', version=1, return_X_y=True)
random_state = check_random_state(0)
permutation = random_state.permutation(X.shape[0])
X = X[permutation]
y = y[permutation]
X = X.reshape((X.shape[0], -1))
X_train, X_test, y_train, y_test = train_test_split(
X, y, train_size=train_samples, test_size=10000)
scaler = StandardScaler()
X_train = scaler.fit_transform(X_train)
X_test = scaler.transform(X_test)
# Turn up tolerance for faster convergence
clf = LogisticRegression(C=50. / train_samples,
multi_class='multinomial',
penalty='l1', solver='saga', tol=0.1)
clf.fit(X_train, y_train)
sparsity = np.mean(clf.coef_ == 0) * 100
score = clf.score(X_test, y_test)
# print('Best C % .4f' % clf.C_)
print("Sparsity with L1 penalty: %.2f%%" % sparsity)
print("Test score with L1 penalty: %.4f" % score)
coef = clf.coef_.copy()
plt.figure(figsize=(10, 5))
scale = np.abs(coef).max()
for i in range(10):
l1_plot = plt.subplot(2, 5, i + 1)
l1_plot.imshow(coef[i].reshape(28, 28), interpolation='nearest',
cmap=plt.cm.RdBu, vmin=-scale, vmax=scale)
l1_plot.set_xticks(())
l1_plot.set_yticks(())
l1_plot.set_xlabel('Class %i' % i)
plt.suptitle('Classification vector for...')
run_time = time.time() - t0
print('Example run in %.3f s' % run_time)
plt.show()
Total running time of the script: ( 0 minutes 0.000 seconds)