Merge pull request scikit-learn#3656 from dougalsutherland/fix-rbf-samp

FIX RBFSampler's incorrect bandwidth

Author: larsmans

doc/whats_new.rst

@@ -91,6 +91,13 @@ Bug fixes
       appropriate error message and suggests a work around.
       By `Danny Sullivan`_.
 
+    - :class:`RBFSampler <kernel_approximation.RBFSampler>` with ``gamma=g``
+      formerly approximated :func:`rbf_kernel <metrics.pairwise.rbf_kernel>`
+      with ``gamma=g/2.``; the definition of ``gamma`` is now consistent,
+      which may substantially change your results if you use a fixed value.
+      (If you cross-validated over ``gamma``, it probably doesn't matter
+      too much.) By `Dougal Sutherland`_.
+
 
 API changes summary
 -------------------
@@ -2969,3 +2976,5 @@ David Huard, Dave Morrill, Ed Schofield, Travis Oliphant, Pearu Peterson.
 .. _Nikolay Mayorov: https://github.com/nmayorov
 
 .. _Jatin Shah: http://jatinshah.org/
+
+.. _Dougal Sutherland: https://github.com/dougalsutherland

sklearn/kernel_approximation.py

@@ -69,7 +69,7 @@ def fit(self, X, y=None):
         random_state = check_random_state(self.random_state)
         n_features = X.shape[1]
 
-        self.random_weights_ = (np.sqrt(self.gamma) * random_state.normal(
+        self.random_weights_ = (np.sqrt(2 * self.gamma) * random_state.normal(
             size=(n_features, self.n_components)))
 
         self.random_offset_ = random_state.uniform(0, 2 * np.pi,

sklearn/tests/test_kernel_approximation.py

@@ -4,6 +4,7 @@
 from sklearn.utils.testing import assert_array_equal, assert_equal
 from sklearn.utils.testing import assert_not_equal
 from sklearn.utils.testing import assert_array_almost_equal, assert_raises
+from sklearn.utils.testing import assert_less_equal
 
 from sklearn.metrics.pairwise import kernel_metrics
 from sklearn.kernel_approximation import RBFSampler
@@ -121,7 +122,11 @@ def test_rbf_sampler():
     Y_trans = rbf_transform.transform(Y)
     kernel_approx = np.dot(X_trans, Y_trans.T)
 
-    assert_array_almost_equal(kernel, kernel_approx, 1)
+    error = kernel - kernel_approx
+    assert_less_equal(np.abs(np.mean(error)), 0.01)  # close to unbiased
+    np.abs(error, out=error)
+    assert_less_equal(np.max(error), 0.1)  # nothing too far off
+    assert_less_equal(np.mean(error), 0.05)  # mean is fairly close
 
 
 def test_input_validation():