MNIST classification using multinomial logistic + L1

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-HBxYkq/scikit-learn-1.0.2/examples/linear_model/plot_sparse_logistic_regression_mnist.py", line 38, in <module>
    X, y = fetch_openml("mnist_784", version=1, return_X_y=True, as_frame=False)
  File "/build/scikit-learn-HBxYkq/scikit-learn-1.0.2/.pybuild/cpython3_3.9/build/sklearn/datasets/_openml.py", line 862, in fetch_openml
    data_info = _get_data_info_by_name(name, version, data_home)
  File "/build/scikit-learn-HBxYkq/scikit-learn-1.0.2/.pybuild/cpython3_3.9/build/sklearn/datasets/_openml.py", line 428, in _get_data_info_by_name
    json_data = _get_json_content_from_openml_api(
  File "/build/scikit-learn-HBxYkq/scikit-learn-1.0.2/.pybuild/cpython3_3.9/build/sklearn/datasets/_openml.py", line 175, in _get_json_content_from_openml_api
    return _load_json()
  File "/build/scikit-learn-HBxYkq/scikit-learn-1.0.2/.pybuild/cpython3_3.9/build/sklearn/datasets/_openml.py", line 69, in wrapper
    return f(*args, **kw)
  File "/build/scikit-learn-HBxYkq/scikit-learn-1.0.2/.pybuild/cpython3_3.9/build/sklearn/datasets/_openml.py", line 171, in _load_json
    with closing(_open_openml_url(url, data_home)) as response:
  File "/build/scikit-learn-HBxYkq/scikit-learn-1.0.2/.pybuild/cpython3_3.9/build/sklearn/datasets/_openml.py", line 118, in _open_openml_url
    with closing(urlopen(req)) as fsrc:
  File "/usr/lib/python3.9/urllib/request.py", line 214, in urlopen
    return opener.open(url, data, timeout)
  File "/usr/lib/python3.9/urllib/request.py", line 517, in open
    response = self._open(req, data)
  File "/usr/lib/python3.9/urllib/request.py", line 534, in _open
    result = self._call_chain(self.handle_open, protocol, protocol +
  File "/usr/lib/python3.9/urllib/request.py", line 494, in _call_chain
    result = func(*args)
  File "/usr/lib/python3.9/urllib/request.py", line 1389, in https_open
    return self.do_open(http.client.HTTPSConnection, req,
  File "/usr/lib/python3.9/urllib/request.py", line 1349, in do_open
    raise URLError(err)
urllib.error.URLError: <urlopen error [Errno -2] Name or service not known>

# Author: Arthur Mensch <arthur.mensch@m4x.org>
# License: BSD 3 clause

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

# 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, as_frame=False)

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=50.0 / train_samples, 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 0.006 seconds)

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