[MRG] Implement fitting intercept with sparse_cg solver in Ridge re…

…gression (scikit-learn#13336)

* add skeleton for fit_intercept with sparse_cg

* fix sparse_cg solver with fit_intercept=True

* fix test

* linting

* add what's new entry

* remove X_scale and X_offset from public interface of ridge_regression

* reformat if clause

* fixed linting issues

* add comments on about the conditions of different code branches

* update warning

* remove whitespace

* add extra checks in the test of ridge with fit_intercept

* remove unused argument

doc/whats_new/v0.21.rst

@@ -230,6 +230,10 @@ Support for Python 3.4 and below has been officially dropped.
   in version 0.21 and will be removed in version 0.23.
   :issue:`12821` by :user:`Nicolas Hug <NicolasHug>`.
 
+- |Enhancement| `sparse_cg` solver in :class:`linear_model.ridge.Ridge`
+  now supports fitting the intercept (i.e. ``fit_intercept=True``) when
+  inputs are sparse . :issue:`13336` by :user:`Bartosz Telenczuk <btel>`
+
 :mod:`sklearn.manifold`
 ............................
 

sklearn/linear_model/ridge.py

@@ -33,9 +33,31 @@
 from ..exceptions import ConvergenceWarning
 
 
-def _solve_sparse_cg(X, y, alpha, max_iter=None, tol=1e-3, verbose=0):
+def _solve_sparse_cg(X, y, alpha, max_iter=None, tol=1e-3, verbose=0,
+                     X_offset=None, X_scale=None):
+
+    def _get_rescaled_operator(X):
+
+        X_offset_scale = X_offset / X_scale
+
+        def matvec(b):
+            return X.dot(b) - b.dot(X_offset_scale)
+
+        def rmatvec(b):
+            return X.T.dot(b) - X_offset_scale * np.sum(b)
+
+        X1 = sparse.linalg.LinearOperator(shape=X.shape,
+                                          matvec=matvec,
+                                          rmatvec=rmatvec)
+        return X1
+
     n_samples, n_features = X.shape
-    X1 = sp_linalg.aslinearoperator(X)
+
+    if X_offset is None or X_scale is None:
+        X1 = sp_linalg.aslinearoperator(X)
+    else:
+        X1 = _get_rescaled_operator(X)
+
     coefs = np.empty((y.shape[1], n_features), dtype=X.dtype)
 
     if n_features > n_samples:
@@ -326,6 +348,25 @@ def ridge_regression(X, y, alpha, sample_weight=None, solver='auto',
     -----
     This function won't compute the intercept.
     """
+
+    return _ridge_regression(X, y, alpha,
+                             sample_weight=sample_weight,
+                             solver=solver,
+                             max_iter=max_iter,
+                             tol=tol,
+                             verbose=verbose,
+                             random_state=random_state,
+                             return_n_iter=return_n_iter,
+                             return_intercept=return_intercept,
+                             X_scale=None,
+                             X_offset=None)
+
+
+def _ridge_regression(X, y, alpha, sample_weight=None, solver='auto',
+                      max_iter=None, tol=1e-3, verbose=0, random_state=None,
+                      return_n_iter=False, return_intercept=False,
+                      X_scale=None, X_offset=None):
+
     if return_intercept and sparse.issparse(X) and solver != 'sag':
         if solver != 'auto':
             warnings.warn("In Ridge, only 'sag' solver can currently fit the "
@@ -395,7 +436,12 @@ def ridge_regression(X, y, alpha, sample_weight=None, solver='auto',
 
     n_iter = None
     if solver == 'sparse_cg':
-        coef = _solve_sparse_cg(X, y, alpha, max_iter, tol, verbose)
+        coef = _solve_sparse_cg(X, y, alpha,
+                                max_iter=max_iter,
+                                tol=tol,
+                                verbose=verbose,
+                                X_offset=X_offset,
+                                X_scale=X_scale)
 
     elif solver == 'lsqr':
         coef, n_iter = _solve_lsqr(X, y, alpha, max_iter, tol)
@@ -492,24 +538,35 @@ def fit(self, X, y, sample_weight=None):
                 np.atleast_1d(sample_weight).ndim > 1):
             raise ValueError("Sample weights must be 1D array or scalar")
 
+        # when X is sparse we only remove offset from y
         X, y, X_offset, y_offset, X_scale = self._preprocess_data(
             X, y, self.fit_intercept, self.normalize, self.copy_X,
-            sample_weight=sample_weight)
+            sample_weight=sample_weight, return_mean=True)
 
         # temporary fix for fitting the intercept with sparse data using 'sag'
-        if sparse.issparse(X) and self.fit_intercept:
-            self.coef_, self.n_iter_, self.intercept_ = ridge_regression(
+        if (sparse.issparse(X) and self.fit_intercept and
+           self.solver != 'sparse_cg'):
+            self.coef_, self.n_iter_, self.intercept_ = _ridge_regression(
                 X, y, alpha=self.alpha, sample_weight=sample_weight,
                 max_iter=self.max_iter, tol=self.tol, solver=self.solver,
                 random_state=self.random_state, return_n_iter=True,
                 return_intercept=True)
+            # add the offset which was subtracted by _preprocess_data
             self.intercept_ += y_offset
         else:
-            self.coef_, self.n_iter_ = ridge_regression(
+            if sparse.issparse(X):
+                # required to fit intercept with sparse_cg solver
+                params = {'X_offset': X_offset, 'X_scale': X_scale}
+            else:
+                # for dense matrices or when intercept is set to 0
+                params = {}
+
+            self.coef_, self.n_iter_ = _ridge_regression(
                 X, y, alpha=self.alpha, sample_weight=sample_weight,
                 max_iter=self.max_iter, tol=self.tol, solver=self.solver,
                 random_state=self.random_state, return_n_iter=True,
-                return_intercept=False)
+                return_intercept=False, **params)
+
             self._set_intercept(X_offset, y_offset, X_scale)
 
         return self

sklearn/linear_model/tests/test_ridge.py

@@ -815,21 +815,25 @@ def test_n_iter():
 def test_ridge_fit_intercept_sparse():
     X, y = make_regression(n_samples=1000, n_features=2, n_informative=2,
                            bias=10., random_state=42)
+
     X_csr = sp.csr_matrix(X)
 
-    for solver in ['saga', 'sag']:
+    for solver in ['sag', 'sparse_cg']:
         dense = Ridge(alpha=1., tol=1.e-15, solver=solver, fit_intercept=True)
         sparse = Ridge(alpha=1., tol=1.e-15, solver=solver, fit_intercept=True)
         dense.fit(X, y)
-        sparse.fit(X_csr, y)
+        with pytest.warns(None) as record:
+            sparse.fit(X_csr, y)
+        assert len(record) == 0
         assert_almost_equal(dense.intercept_, sparse.intercept_)
         assert_array_almost_equal(dense.coef_, sparse.coef_)
 
     # test the solver switch and the corresponding warning
-    sparse = Ridge(alpha=1., tol=1.e-15, solver='lsqr', fit_intercept=True)
-    assert_warns(UserWarning, sparse.fit, X_csr, y)
-    assert_almost_equal(dense.intercept_, sparse.intercept_)
-    assert_array_almost_equal(dense.coef_, sparse.coef_)
+    for solver in ['saga', 'lsqr']:
+        sparse = Ridge(alpha=1., tol=1.e-15, solver=solver, fit_intercept=True)
+        assert_warns(UserWarning, sparse.fit, X_csr, y)
+        assert_almost_equal(dense.intercept_, sparse.intercept_)
+        assert_array_almost_equal(dense.coef_, sparse.coef_)
 
 
 def test_errors_and_values_helper():