tests for comparison of results for Lasso and LarsLasso added.

Author: michigraber

sklearn/linear_model/tests/test_least_angle.py

@@ -506,3 +506,100 @@ def test_estimatorclasses_positive_constraint():
         estimator = getattr(linear_model, estname)(positive=True, **params)
         estimator.fit(diabetes['data'], diabetes['target'])
         assert_true(min(estimator.coef_) >= 0)
+
+
+def test_lasso_lars_vs_lasso_cd_positive(verbose=False):
+    # Test that LassoLars and Lasso using coordinate descent give the
+    # same results when using the positive option
+
+    # this test is basically a copy of the above plus the positive option
+
+    X = 3 * diabetes.data
+
+    alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso',
+            positive=True)
+    lasso_cd = linear_model.Lasso(fit_intercept=False, tol=1e-8, positive=True)
+    for c, a in zip(lasso_path.T, alphas):
+        if a == 0:
+            continue
+        lasso_cd.alpha = a
+        lasso_cd.fit(X, y)
+        error = linalg.norm(c - lasso_cd.coef_)
+        assert_less(error, 0.01)
+
+    # same test, with normalized data
+    X = diabetes.data
+    alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso',
+            positive=True)
+    lasso_cd = linear_model.Lasso(fit_intercept=False, normalize=True,
+                                  tol=1e-8, positive=True)
+    for c, a in zip(lasso_path.T, alphas):
+        if a == 0:
+            continue
+        lasso_cd.alpha = a
+        lasso_cd.fit(X, y)
+        error = linalg.norm(c - lasso_cd.coef_)
+        assert_less(error, 0.01)
+
+
+
+def evaluate_lasso_lars_vs_lasso_cd_positive_middle_part():
+    # this part of the above tests does not confirm equality of results.
+    # but i'm not entirely sure whether this is necessarily to be expected ..
+    # see comments and results below
+
+    # similar test, with the classifiers
+
+    for alpha in np.linspace(1e-2, 1 - 1e-2, 20):
+        clf1 = linear_model.LassoLars(
+                fit_intercept=False, alpha=alpha, normalize=False,
+                positive=True).fit(X, y)
+        clf2 = linear_model.Lasso(
+                fit_intercept=False, alpha=alpha, tol=1e-8,
+                normalize=False, positive=True).fit(X, y)
+        err = linalg.norm(clf1.coef_ - clf2.coef_)
+        mess = 'alpha={} \t err={} \t num_coeffs=({}/{}) (LassoLars / Lasso)'
+        print(mess.format(
+            alpha,
+            err, 
+            sum(clf1.coef_ > 0),
+            sum(clf2.coef_ > 0),
+            ))
+        #assert_less(err, 1e-3)
+
+
+    '''
+    Results produced:
+
+    In [19]: test_least_angle.evaluate_lasso_lars_vs_lasso_cd_positive_middle_part()
+    alpha=0.01 	                 err=25.7243223179 	 num_coeffs=(5/5) (LassoLars / Lasso)
+    alpha=0.0615789473684 	 err=18.2545548874 	 num_coeffs=(5/5) (LassoLars / Lasso)
+    alpha=0.113157894737 	 err=10.7847873501 	 num_coeffs=(5/5) (LassoLars / Lasso)
+    alpha=0.164736842105 	 err=3.31501982266 	 num_coeffs=(5/5) (LassoLars / Lasso)
+    alpha=0.216315789474 	 err=3.69727628935e-06 	 num_coeffs=(4/4) (LassoLars / Lasso)
+    alpha=0.267894736842 	 err=3.56502617927e-06 	 num_coeffs=(4/4) (LassoLars / Lasso)
+    alpha=0.319473684211 	 err=3.43302342569e-06 	 num_coeffs=(4/4) (LassoLars / Lasso)
+    alpha=0.371052631579 	 err=1.05509699804e-06 	 num_coeffs=(3/3) (LassoLars / Lasso)
+    alpha=0.422631578947 	 err=5.9269674114e-07 	 num_coeffs=(3/3) (LassoLars / Lasso)
+    alpha=0.474210526316 	 err=1.56511823248e-06 	 num_coeffs=(3/3) (LassoLars / Lasso)
+    alpha=0.525789473684 	 err=1.28253471214e-06 	 num_coeffs=(3/3) (LassoLars / Lasso)
+    alpha=0.577368421053 	 err=1.00002954531e-06 	 num_coeffs=(3/3) (LassoLars / Lasso)
+    alpha=0.628947368421 	 err=7.38618104242e-07 	 num_coeffs=(3/3) (LassoLars / Lasso)
+    alpha=0.680526315789 	 err=6.78234533087e-07 	 num_coeffs=(3/3) (LassoLars / Lasso)
+    alpha=0.732105263158 	 err=2.25315273789e-06 	 num_coeffs=(3/3) (LassoLars / Lasso)
+    alpha=0.783684210526 	 err=1.98825668767e-06 	 num_coeffs=(3/3) (LassoLars / Lasso)
+    alpha=0.835263157895 	 err=1.72877180183e-06 	 num_coeffs=(3/3) (LassoLars / Lasso)
+    alpha=0.886842105263 	 err=1.58242049123e-06 	 num_coeffs=(3/3) (LassoLars / Lasso)
+    alpha=0.938421052632 	 err=1.50923193078e-06 	 num_coeffs=(3/3) (LassoLars / Lasso)
+    alpha=0.99 	                 err=1.43604831986e-06 	 num_coeffs=(3/3) (LassoLars / Lasso)
+
+
+    We see that the 'equality of results' is violated for 'small' alphas.
+    This is mentioned in the original paper by Efron et al. 2004:
+
+    `The positive Lasso usually does not converge to the full OLS solution
+    beta_{m}, even fro very large choices of t.`
+
+
+    '''
+