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.
Sparsity with L1 penalty: 80.89% Test score with L1 penalty: 0.8309 Example run in 42.213 s
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 <[email protected]> # 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) X = X[permutation] y = y[permutation] X = X.reshape((X.shape, -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 42.214 seconds)
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