Add projection on l1-ball to FISTA.

Author: mblondel

lightning/impl/fista.py

@@ -19,6 +19,7 @@
 from .penalty import L1L2Penalty
 from .penalty import TracePenalty
 from .penalty import SimplexConstraint
+from .penalty import L1BallConstraint
 from .penalty import TotalVariation1DPenalty
 
 
@@ -32,6 +33,7 @@ def _get_penalty(self):
             "l1/l2": L1L2Penalty(),
             "trace": TracePenalty(),
             "simplex": SimplexConstraint(),
+            "l1-ball": L1BallConstraint(),
             "tv1d": TotalVariation1DPenalty()
         }
         return penalties[self.penalty]

lightning/impl/penalty.py

@@ -77,6 +77,15 @@ def project_l1_ball(v, z=1):
     return np.sign(v) * project_simplex(np.abs(v), z)
 
 
+class L1BallConstraint(object):
+
+    def projection(self, coef, alpha, L):
+        return project_l1_ball(coef[0], alpha).reshape(1,-1)
+
+    def regularization(self, coef):
+        return 0
+
+
 class TotalVariation1DPenalty(object):
     def projection(self, coef, alpha, L):
         tmp = coef.copy()

lightning/impl/tests/test_fista.py

@@ -12,7 +12,7 @@
 from lightning.impl.datasets.samples_generator import make_classification
 from lightning.classification import FistaClassifier
 from lightning.regression import FistaRegressor
-from lightning.impl.penalty import project_simplex, L1Penalty
+from lightning.impl.penalty import project_simplex, project_l1_ball, L1Penalty
 
 bin_dense, bin_target = make_classification(n_samples=200, n_features=100,
                                             n_informative=5,
@@ -142,6 +142,21 @@ def test_fista_regression_simplex():
     assert_almost_equal(np.sum(reg.coef_), 1.0, 3)
 
 
+def test_fista_regression_l1_ball():
+    rng = np.random.RandomState(0)
+    alpha = 5.0
+    w = project_simplex(rng.randn(10), alpha)
+    X = rng.randn(1000, 10)
+    y = np.dot(X, w)
+
+    reg = FistaRegressor(penalty="l1-ball", alpha=alpha, max_iter=100, verbose=0)
+    reg.fit(X, y)
+    y_pred = reg.predict(X)
+    error = np.sqrt(np.mean((y - y_pred) ** 2))
+    assert_almost_equal(error, 0.000, 3)
+    assert_almost_equal(np.sum(np.abs(reg.coef_)), alpha, 3)
+
+
 def test_fista_regression_trace():
     rng = np.random.RandomState(0)
     def _make_data(n_samples, n_features, n_tasks, n_components):