scikit-learn
diff --git a/‎doc/whats_new/v1.2.rst
Lines changed: 4 additions & 0 deletions b/‎doc/whats_new/v1.2.rst
Lines changed: 4 additions & 0 deletions
diff --git a/‎sklearn/kernel_approximation.py
Lines changed: 19 additions & 5 deletions b/‎sklearn/kernel_approximation.py
Lines changed: 19 additions & 5 deletions
diff --git a/‎sklearn/tests/test_kernel_approximation.py
Lines changed: 8 additions & 0 deletions b/‎sklearn/tests/test_kernel_approximation.py
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@@ -350,6 +350,10 @@ Changelog
 - |Enhancement| :class:`kernel_approximation.SkewedChi2Sampler` now preserves
   dtype for `numpy.float32` inputs. :pr:`24350` by :user:`Rahil Parikh <rprkh>`.
 
+- |Enhancement| :class:`kernel_approximation.RBFSampler` now accepts
+  `'scale'` option for parameter `gamma`.
+  :pr:`24755` by :user:`Gleb Levitski <GLevV>`
+
 :mod:`sklearn.linear_model`
 ...........................
 
 
@@ -249,8 +249,13 @@ class RBFSampler(ClassNamePrefixFeaturesOutMixin, TransformerMixin, BaseEstimato
 
     Parameters
     ----------
-    gamma : float, default=1.0
+    gamma : 'scale' or float, default=1.0
         Parameter of RBF kernel: exp(-gamma * x^2).
+        If ``gamma='scale'`` is passed then it uses
+        1 / (n_features * X.var()) as value of gamma.
+
+        .. versionadded:: 1.2
+           The option `"scale"` was added in 1.2.
 
     n_components : int, default=100
         Number of Monte Carlo samples per original feature.
@@ -319,7 +324,10 @@ class RBFSampler(ClassNamePrefixFeaturesOutMixin, TransformerMixin, BaseEstimato
     """
 
     _parameter_constraints: dict = {
-        "gamma": [Interval(Real, 0, None, closed="left")],
+        "gamma": [
+            StrOptions({"scale"}),
+            Interval(Real, 0.0, None, closed="left"),
+        ],
         "n_components": [Interval(Integral, 1, None, closed="left")],
         "random_state": ["random_state"],
     }
@@ -354,8 +362,14 @@ def fit(self, X, y=None):
         X = self._validate_data(X, accept_sparse="csr")
         random_state = check_random_state(self.random_state)
         n_features = X.shape[1]
-
-        self.random_weights_ = np.sqrt(2 * self.gamma) * random_state.normal(
+        sparse = sp.isspmatrix(X)
+        if self.gamma == "scale":
+            # var = E[X^2] - E[X]^2 if sparse
+            X_var = (X.multiply(X)).mean() - (X.mean()) ** 2 if sparse else X.var()
+            self._gamma = 1.0 / (n_features * X_var) if X_var != 0 else 1.0
+        else:
+            self._gamma = self.gamma
+        self.random_weights_ = (2.0 * self._gamma) ** 0.5 * random_state.normal(
             size=(n_features, self.n_components)
         )
 
@@ -390,7 +404,7 @@ def transform(self, X):
         projection = safe_sparse_dot(X, self.random_weights_)
         projection += self.random_offset_
         np.cos(projection, projection)
-        projection *= np.sqrt(2.0) / np.sqrt(self.n_components)
+        projection *= (2.0 / self.n_components) ** 0.5
         return projection
 
     def _more_tags(self):
 
@@ -242,6 +242,14 @@ def test_rbf_sampler_dtype_equivalence():
     assert_allclose(rbf32.random_weights_, rbf64.random_weights_)
 
 
+def test_rbf_sampler_gamma_scale():
+    """Check the inner value computed when `gamma='scale'`."""
+    X, y = [[0.0], [1.0]], [0, 1]
+    rbf = RBFSampler(gamma="scale")
+    rbf.fit(X, y)
+    assert rbf._gamma == pytest.approx(4)
+
+
 def test_skewed_chi2_sampler_fitted_attributes_dtype(global_dtype):
     """Check that the fitted attributes are stored accordingly to the
     data type of X."""