def test_tikhonov_regularization_vs_graph_net():
# Test for one of the extreme cases of Graph-Net: That is, with
# l1_ratio = 0 (pure Smooth), we compare Graph-Net's performance
# with the analytical solution for Tikhonov Regularization
# XXX A small dataset here (this test is very lengthy)
G = get_gradient_matrix(w.size, mask)
optimal_model = np.dot(
sp.linalg.pinv(np.dot(X.T, X) + y.size * np.dot(G.T, G)),
np.dot(X.T, y))
graph_net = BaseSpaceNet(mask=mask_,
alphas=1. * X.shape[0],
l1_ratios=0.,
max_iter=400,
fit_intercept=False,
screening_percentile=100.,
standardize=False)
graph_net.fit(X_, y.copy())
coef_ = graph_net.coef_[0]
graph_net_perf = 0.5 / y.size * extmath.norm(
np.dot(X, coef_) - y) ** 2\
+ 0.5 * extmath.norm(np.dot(G, coef_)) ** 2
optimal_model_perf = 0.5 / y.size * extmath.norm(
np.dot(X, optimal_model) - y) ** 2\
+ 0.5 * extmath.norm(np.dot(G, optimal_model)) ** 2
assert_almost_equal(graph_net_perf, optimal_model_perf, decimal=1)
def test_max_alpha__squared_loss():
"""Tests that models with L1 regularization over the theoretical bound
are full of zeros, for logistic regression"""
l1_ratios = np.linspace(0.1, 1, 3)
reg = BaseSpaceNet(mask=mask_, max_iter=10, penalty="graph-net",
is_classif=False)
for l1_ratio in l1_ratios:
reg.l1_ratios = l1_ratio
reg.alphas = np.max(np.dot(X.T, y)) / l1_ratio
reg.fit(X_, y)
assert_almost_equal(reg.coef_, 0.)
def test_max_alpha__squared_loss():
"""Tests that models with L1 regularization over the theoretical bound
are full of zeros, for logistic regression"""
l1_ratios = np.linspace(0.1, 1, 3)
reg = BaseSpaceNet(mask=mask_, max_iter=10, penalty="graph-net",
is_classif=False)
for l1_ratio in l1_ratios:
reg.l1_ratios = l1_ratio
reg.alphas = np.max(np.dot(X.T, y)) / l1_ratio
reg.fit(X_, y)
assert_almost_equal(reg.coef_, 0.)
def test_lasso_vs_graph_net():
# Test for one of the extreme cases of Graph-Net: That is, with
# l1_ratio = 1 (pure Lasso), we compare Graph-Net's performance with
# Scikit-Learn lasso
lasso = Lasso(max_iter=100, tol=1e-8, normalize=False)
graph_net = BaseSpaceNet(mask=mask, alphas=1. * X_.shape[0],
l1_ratios=1, is_classif=False,
penalty="graph-net", max_iter=100)
lasso.fit(X_, y)
graph_net.fit(X, y)
lasso_perf = 0.5 / y.size * extmath.norm(np.dot(
X_, lasso.coef_) - y) ** 2 + np.sum(np.abs(lasso.coef_))
graph_net_perf = 0.5 * ((graph_net.predict(X) - y) ** 2).mean()
np.testing.assert_almost_equal(graph_net_perf, lasso_perf, decimal=3)
def test_tikhonov_regularization_vs_graph_net():
# Test for one of the extreme cases of Graph-Net: That is, with
# l1_ratio = 0 (pure Smooth), we compare Graph-Net's performance
# with the analytical solution for Tikhonov Regularization
# XXX A small dataset here (this test is very lengthy)
G = get_gradient_matrix(w.size, mask)
optimal_model = np.dot(sp.linalg.pinv(
np.dot(X.T, X) + y.size * np.dot(G.T, G)), np.dot(X.T, y))
graph_net = BaseSpaceNet(
mask=mask_, alphas=1. * X.shape[0], l1_ratios=0., max_iter=400,
fit_intercept=False,
screening_percentile=100., standardize=False)
graph_net.fit(X_, y.copy())
coef_ = graph_net.coef_[0]
graph_net_perf = 0.5 / y.size * extmath.norm(
np.dot(X, coef_) - y) ** 2\
+ 0.5 * extmath.norm(np.dot(G, coef_)) ** 2
optimal_model_perf = 0.5 / y.size * extmath.norm(
np.dot(X, optimal_model) - y) ** 2\
+ 0.5 * extmath.norm(np.dot(G, optimal_model)) ** 2
assert_almost_equal(graph_net_perf, optimal_model_perf, decimal=1)