demo_adaptive_lasso_lasso_adaptivelasso_DEMO_adaptive_

"""Example of adaptive Lasso to produce event sparser solutions Adaptive lasso consists in computing many Lasso with feature reweighting. It's also known as iterated L1. """ # Authors: Alexandre Gramfort <firstname.lastname@inria.fr> # # License: BSD (3-clause) import numpy as np from sklearn.datasets import make_regression from sklearn.linear_model import Lasso X, y, coef = make_regression(n_samples=306, n_features=8000, n_informative=50, noise=0.1, shuffle=True, coef=True, random_state=42) X /= np.sum(X ** 2, axis=0) # scale features alpha = 0.1 g = lambda w: np.sqrt(np.abs(w)) gprime = lambda w: 1. / (2. * np.sqrt(np.abs(w)) + np.finfo(float).eps) # Or another option: # ll = 0.01 # g = lambda w: np.log(ll + np.abs(w)) # gprime = lambda w: 1. / (ll + np.abs(w)) n_samples, n_features = X.shape p_obj = lambda w: 1. / (2 * n_samples) * np.sum((y - np.dot(X, w)) ** 2) \ + alpha * np.sum(g(w)) weights = np.ones(n_features) n_lasso_iterations = 5 for k in range(n_lasso_iterations): X_w = X / weights[np.newaxis, :] clf = Lasso(alpha=alpha, fit_intercept=False) clf.fit(X_w, y) coef_ = clf.coef_ / weights weights = gprime(coef_) print p_obj(coef_) # should go down print np.mean((clf.coef_ != 0.0) == (coef != 0.0))