MNT: trees/forests/GBT: deprecate `"friedman_mse"` criterion

#### [NAME_REDACTED]/PRs

Towards #32700 (deprecation before complete removal).

Fixes:
- #32707
- #32718

#### What does this implement/fix? Explain your changes.

- Remove class `FriedmanMSE(MSE)` in `sklearn/tree/_criterion.pyx`
- Deprecate `"friedman_mse"` for trees & forests (`if criterion="friedman_mse": criterion="squared_error"` + deprecation warning)
- Deprecate `criterion` param for gradient boosting
- Adapt the doc/docstrings/tests/... accordingly

@@ -2987,7 +2987,7 @@ quantile regressor via cross-validation:
   ...     random_state=0,
   ... )
   >>> cross_val_score(estimator, X, y, cv=5, scoring=mean_pinball_loss_95p)
-  array([13.6, 9.7, 23.3, 9.5, 10.4])
+  array([14.3,  9.8, 23.9,  9.4, 10.8])

 It is also possible to build scorer objects for hyper-parameter tuning. The
 sign of the loss must be switched to ensure that greater means better as

@@ -649,7 +649,7 @@ non-missing values, see the :ref:`Forest section <forest>`.

 The criterion supported when there are missing values are
 `'gini'`, `'entropy'`, or `'log_loss'`, for classification or
-`'squared_error'`, `'friedman_mse'`, or `'poisson'` for regression.
+`'squared_error'` or `'poisson'` for regression.

 First we will describe how :class:`DecisionTreeClassifier`, :class:`DecisionTreeRegressor`
 handle missing-values in the data.

@@ -0,0 +1,6 @@
+- The `criterion` parameter is now deprecated for classes
+  :class:`ensemble.GradientBoostingRegressor`
+  and :class:`ensemble.GradientBoostingClassifier`, as both options
+  (`"friedman_mse"` and `"squared_error"`) were producing the same results,
+  up to floating-point rounding discrepancies and a bug in `"friedman_mse"`.
+  By :user:`[NAME_REDACTED] <cakedev0>`

@@ -0,0 +1,7 @@
+- Both :class:`ensemble.GradientBoostingRegressor` and
+  :class:`ensemble.GradientBoostingClassifier` with the default
+  `"friedman_mse"` criterion were computing impurity values with an incorrect scaling,
+  leading to unexpected trees in some cases. The implementation now uses
+  `"squared_error"`, which is exactly equivalent to `"friedman_mse"` up to
+  floating-point error discrepancies but computes correct impurity values.
+  By :user:`[NAME_REDACTED] <cakedev0>`.

@@ -0,0 +1,9 @@
+- `criterion="friedman_mse"` is now deprecated. This criterion was intended for
+  gradient boosting but was incorrectly implemented in scikit-learn's trees and
+  was actually behaving identically to `criterion="squared_error"`. Use
+  `criterion="squared_error"` instead. This affects:
+  - :class:`tree.DecisionTreeRegressor`
+  - :class:`tree.ExtraTreeRegressor`
+  - :class:`ensemble.RandomForestRegressor`
+  - :class:`ensemble.ExtraTreesRegressor`
+  By :user:`[NAME_REDACTED] <cakedev0>`

@@ -52,13 +52,13 @@ def f(x):
 # Fitting non-linear quantile and least squares regressors
 # --------------------------------------------------------
 #
-# Fit gradient boosting models trained with the quantile loss and
-# alpha=0.05, 0.5, 0.95.
+# Fit gradient boosting models trained with the quantile loss and `alpha=0.05`,
+# `alpha=0.5`, `alpha=0.95`.
 #
-# The models obtained for alpha=0.05 and alpha=0.95 produce a 90% confidence
-# interval (95% - 5% = 90%).
+# The models obtained for `alpha=0.05` and `alpha=0.95` produce a 90%
+# confidence interval (95% - 5% = 90%).
 #
-# The model trained with alpha=0.5 produces a regression of the median: on
+# The model trained with `alpha=0.5` produces a regression of the median: on
 # average, there should be the same number of target observations above and
 # below the predicted values.
 from sklearn.ensemble import GradientBoostingRegressor

@@ -1603,25 +1603,24 @@ class RandomForestRegressor(ForestRegressor):
            The default value of ``n_estimators`` changed from 10 to 100
            in 0.22.

-    criterion : {"squared_error", "absolute_error", "friedman_mse", "poisson"}, \
-            default="squared_error"
+    criterion : {"squared_error", "absolute_error", "poisson"}, default="squared_error"
         The function to measure the quality of a split. Supported criteria
         are "squared_error" for the mean squared error, which is equal to
         variance reduction as feature selection criterion and minimizes the L2
-        loss using the mean of each terminal node, "friedman_mse", which uses
-        mean squared error with Friedman's improvement score for potential
-        splits, "absolute_error" for the mean absolute error, which minimizes
-        the L1 loss using the median of each terminal node, and "poisson" which
-        uses reduction in Poisson deviance to find splits.
-        Training using "absolute_error" is significantly slower
-        than when using "squared_error".
+        loss using the mean of each terminal node, "absolute_error" for the mean
+        absolute error, which minimizes the L1 loss using the median of each terminal
+        node, and "poisson" which uses reduction in Poisson deviance to find splits,
+        also using the mean of each terminal node.

         .. versionadded:: 0.18
            [NAME_REDACTED] (MAE) criterion.

         .. versionadded:: 1.0
            Poisson criterion.

+        .. versionchanged:: 1.9
+            Criterion `"friedman_mse"` was deprecated.
+
     max_depth : int, default=None
         The maximum depth of the tree. If None, then nodes are expanded until
         all leaves are pure or until all leaves contain less than
@@ -2353,22 +2352,21 @@ class ExtraTreesRegressor(ForestRegressor):
            The default value of ``n_estimators`` changed from 10 to 100
            in 0.22.

-    criterion : {"squared_error", "absolute_error", "friedman_mse", "poisson"}, \
-            default="squared_error"
+    criterion : {"squared_error", "absolute_error", "poisson"}, default="squared_error"
         The function to measure the quality of a split. Supported criteria
         are "squared_error" for the mean squared error, which is equal to
         variance reduction as feature selection criterion and minimizes the L2
-        loss using the mean of each terminal node, "friedman_mse", which uses
-        mean squared error with Friedman's improvement score for potential
-        splits, "absolute_error" for the mean absolute error, which minimizes
-        the L1 loss using the median of each terminal node, and "poisson" which
-        uses reduction in Poisson deviance to find splits.
-        Training using "absolute_error" is significantly slower
-        than when using "squared_error".
+        loss using the mean of each terminal node, "absolute_error" for the mean
+        absolute error, which minimizes the L1 loss using the median of each terminal
+        node, and "poisson" which uses reduction in Poisson deviance to find splits,
+        also using the mean of each terminal node.

         .. versionadded:: 0.18
            [NAME_REDACTED] (MAE) criterion.

+        .. versionchanged:: 1.9
+            Criterion `"friedman_mse"` was deprecated.
+
     max_depth : int, default=None
         The maximum depth of the tree. If None, then nodes are expanded until
         all leaves are pure or until all leaves contain less than

@@ -52,7 +52,7 @@
 from sklearn.tree import DecisionTreeRegressor
 from sklearn.tree._tree import DOUBLE, DTYPE, TREE_LEAF
 from sklearn.utils import check_array, check_random_state, column_or_1d
-from sklearn.utils._param_validation import HasMethods, Interval, StrOptions
+from sklearn.utils._param_validation import HasMethods, Hidden, Interval, StrOptions
 from sklearn.utils.multiclass import check_classification_targets
 from sklearn.utils.stats import _weighted_percentile
 from sklearn.utils.validation import (
@@ -365,7 +365,10 @@ class BaseGradientBoosting(BaseEnsemble, metaclass=ABCMeta):
         **DecisionTreeRegressor._parameter_constraints,
         "learning_rate": [Interval(Real, 0.0, None, closed="left")],
         "n_estimators": [Interval(Integral, 1, None, closed="left")],
-        "criterion": [StrOptions({"friedman_mse", "squared_error"})],
+        "criterion": [
+            StrOptions({"squared_error"}),
+            Hidden(StrOptions({"deprecated", "friedman_mse"})),
+        ],
         "subsample": [Interval(Real, 0.0, 1.0, closed="right")],
         "verbose": ["verbose"],
         "warm_start": ["boolean"],
@@ -383,7 +386,6 @@ def __init__(
         loss,
         learning_rate,
         n_estimators,
-        criterion,
         min_samples_split,
         min_samples_leaf,
         min_weight_fraction_leaf,
@@ -401,6 +403,7 @@ def __init__(
         validation_fraction=0.1,
         n_iter_no_change=None,
         tol=1e-4,
+        criterion="deprecated",
     ):
         self.n_estimators = n_estimators
         self.learning_rate = learning_rate
@@ -476,7 +479,7 @@ def _fit_stage(

             # induce regression tree on the negative gradient
             tree = DecisionTreeRegressor(
-                criterion=self.criterion,
+                criterion="squared_error",
                 splitter="best",
                 max_depth=self.max_depth,
                 min_samples_split=self.min_samples_split,
@@ -659,6 +662,14 @@ def fit(self, X, y, sample_weight=None, monitor=None):
         if not self.warm_start:
             self._clear_state()

+        if self.criterion != "deprecated":
+            warnings.warn(
+                "The parameter `criterion` is deprecated and will be "
+                "removed in 1.11. It has no effect. Leave it to its default value to "
+                "avoid this warning.",
+                FutureWarning,
+            )
+
         # Check input
         # Since check_array converts both X and y to the same dtype, but the
         # trees use different types for X and y, checking them separately.
@@ -1013,7 +1024,7 @@ def feature_importances_(self):

         The higher, the more important the feature.
         The importance of a feature is computed as the (normalized)
-        total reduction of the criterion brought by [NAME_REDACTED] also
+        total reduction of the MSE brought by [NAME_REDACTED] also
         known as the Gini importance.

         Warning: impurity-based feature importances can be misleading for
@@ -1179,14 +1190,13 @@ class GradientBoostingClassifier(ClassifierMixin, BaseGradientBoosting):
         Values must be in the range `(0.0, 1.0]`.

     criterion : {'friedman_mse', 'squared_error'}, default='friedman_mse'
-        The function to measure the quality of a split. Supported criteria are
-        'friedman_mse' for the mean squared error with improvement score by
-        Friedman, 'squared_error' for mean squared error. The default value of
-        'friedman_mse' is generally the best as it can provide a better
-        approximation in some cases.
+        This parameter has no effect.

         .. versionadded:: 0.18

+        .. deprecated:: 1.9
+           `criterion` is deprecated and will be removed in 1.11.
+
     min_samples_split : int or float, default=2
         The minimum number of samples required to split an internal node:

@@ -1354,7 +1364,7 @@ class GradientBoostingClassifier(ClassifierMixin, BaseGradientBoosting):
         The impurity-based feature importances.
         The higher, the more important the feature.
         The importance of a feature is computed as the (normalized)
-        total reduction of the criterion brought by [NAME_REDACTED] also
+        total reduction of the MSE brought by [NAME_REDACTED] also
         known as the Gini importance.

         Warning: impurity-based feature importances can be misleading for
@@ -1432,7 +1442,7 @@ class GradientBoostingClassifier(ClassifierMixin, BaseGradientBoosting):
     -----
     The features are always randomly permuted at each split. Therefore,
     the best found split may vary, even with the same training data and
-    ``max_features=n_features``, if the improvement of the criterion is
+    ``max_features=n_features``, if the improvement of the MSE is
     identical for several splits enumerated during the search of the best
     split. To obtain a deterministic behaviour during fitting,
     ``random_state`` has to be fixed.
@@ -1478,7 +1488,7 @@ def __init__(
         learning_rate=0.1,
         n_estimators=100,
         subsample=1.0,
-        criterion="friedman_mse",
+        criterion="deprecated",
         min_samples_split=2,
         min_samples_leaf=1,
         min_weight_fraction_leaf=0.0,
@@ -1791,14 +1801,13 @@ class GradientBoostingRegressor(RegressorMixin, BaseGradientBoosting):
         Values must be in the range `(0.0, 1.0]`.

     criterion : {'friedman_mse', 'squared_error'}, default='friedman_mse'
-        The function to measure the quality of a split. Supported criteria are
-        "friedman_mse" for the mean squared error with improvement score by
-        Friedman, "squared_error" for mean squared error. The default value of
-        "friedman_mse" is generally the best as it can provide a better
-        approximation in some cases.
+        This parameter has no effect.

         .. versionadded:: 0.18

+        .. deprecated:: 1.9
+           `criterion` is deprecated and will be removed in 1.11.
+
     min_samples_split : int or float, default=2
         The minimum number of samples required to split an internal node:

@@ -1970,7 +1979,7 @@ class GradientBoostingRegressor(RegressorMixin, BaseGradientBoosting):
         The impurity-based feature importances.
         The higher, the more important the feature.
         The importance of a feature is computed as the (normalized)
-        total reduction of the criterion brought by [NAME_REDACTED] also
+        total reduction of the MSE brought by [NAME_REDACTED] also
         known as the Gini importance.

         Warning: impurity-based feature importances can be misleading for
@@ -2033,7 +2042,7 @@ class GradientBoostingRegressor(RegressorMixin, BaseGradientBoosting):
     -----
     The features are always randomly permuted at each split. Therefore,
     the best found split may vary, even with the same training data and
-    ``max_features=n_features``, if the improvement of the criterion is
+    ``max_features=n_features``, if the improvement of the MSE is
     identical for several splits enumerated during the search of the best
     split. To obtain a deterministic behaviour during fitting,
     ``random_state`` has to be fixed.
@@ -2084,7 +2093,7 @@ def __init__(
         learning_rate=0.1,
         n_estimators=100,
         subsample=1.0,
-        criterion="friedman_mse",
+        criterion="deprecated",
         min_samples_split=2,
         min_samples_leaf=1,
         min_weight_fraction_leaf=0.0,

@@ -158,9 +158,7 @@ def test_iris_criterion(name, criterion):

 [USER_REDACTED].mark.parametrize("name", FOREST_REGRESSORS)
-[USER_REDACTED].mark.parametrize(
-    "criterion", ("squared_error", "absolute_error", "friedman_mse")
-)
+[USER_REDACTED].mark.parametrize("criterion", ("squared_error", "absolute_error"))
 def test_regression_criterion(name, criterion):
     # Check consistency on regression dataset.
     ForestRegressor = FOREST_REGRESSORS[name]
@@ -294,7 +292,7 @@ def test_probability(name):
     "name, criterion",
     itertools.chain(
         product(FOREST_CLASSIFIERS, ["gini", "log_loss"]),
-        product(FOREST_REGRESSORS, ["squared_error", "friedman_mse", "absolute_error"]),
+        product(FOREST_REGRESSORS, ["squared_error", "absolute_error"]),
     ),
 )
 def test_importances(dtype, name, criterion):

@@ -1551,52 +1551,18 @@ def test_squared_error_exact_backward_compat():
     assert_allclose(gbt.train_score_[-10:], train_score, rtol=1e-3, atol=1e-11)

-[USER_REDACTED]_if_32bit
-def test_huber_exact_backward_compat():
-    """Test huber GBT backward compat on a simple dataset.
-
-    The results to compare against are taken from scikit-learn v1.2.0.
-    """
+def test_huber_overfit():
+    """Test huber GBT can completely overfit"""
     n_samples = 10
     y = np.arange(n_samples)
     x1 = np.minimum(y, n_samples / 2)
     x2 = np.minimum(-y, -n_samples / 2)
     X = np.c_[x1, x2]
     gbt = GradientBoostingRegressor(loss="huber", n_estimators=100, alpha=0.8).fit(X, y)

-    assert_allclose(gbt._loss.closs.delta, 0.0001655688041282133)
-
-    pred_result = np.array(
-        [
-            1.48120765e-04,
-            9.99949174e-01,
-            2.00116957e00,
-            2.99986716e00,
-            4.00012064e00,
-            5.00002462e00,
-            5.99998898e00,
-            6.99692549e00,
-            8.00006356e00,
-            8.99985099e00,
-        ]
-    )
-    assert_allclose(gbt.predict(X), pred_result, rtol=1e-8)
-
-    train_score = np.array(
-        [
-            2.59484709e-07,
-            2.19165900e-07,
-            1.89644782e-07,
-            1.64556454e-07,
-            1.38705110e-07,
-            1.20373736e-07,
-            1.04746082e-07,
-            9.13835687e-08,
-            8.20245756e-08,
-            7.17122188e-08,
-        ]
-    )
-    assert_allclose(gbt.train_score_[-10:], train_score, rtol=1e-8)
+    assert gbt._loss.closs.delta < 2e-4
+    assert_allclose(gbt.predict(X), y, atol=0.01)
+    assert np.all(gbt.train_score_[-10:] < 3e-7)

 def test_binomial_error_exact_backward_compat():
@@ -1715,3 +1681,10 @@ def test_gb_denominator_zero(global_random_seed):
     with warnings.catch_warnings():
         warnings.simplefilter("error")
         clf.fit(X, y)
+
+
+[USER_REDACTED].mark.parametrize("GradientBoosting", GRADIENT_BOOSTING_ESTIMATORS)
+def test_criterion_param_deprecation(GradientBoosting):
+    with pytest.warns(FutureWarning, match="criterion"):
+        reg = GradientBoosting(criterion="friedman_mse")
+        reg.fit(X, y)

@@ -411,7 +411,6 @@ def test_recursion_decision_tree_vs_forest_and_gbdt(seed):
     gbdt = GradientBoostingRegressor(
         n_estimators=1,
         learning_rate=1,
-        criterion="squared_error",
         max_depth=max_depth,
         random_state=equiv_random_state,
     )

@@ -8,6 +8,7 @@

 import copy
 import numbers
+import warnings
 from abc import ABCMeta, abstractmethod
 from math import ceil
 from numbers import Integral, Real
@@ -74,7 +75,6 @@
 }
 CRITERIA_REG = {
     "squared_error": _criterion.MSE,
-    "friedman_mse": _criterion.FriedmanMSE,
     "absolute_error": _criterion.MAE,
     "poisson": _criterion.Poisson,
 }
@@ -1118,23 +1118,24 @@ class DecisionTreeRegressor(RegressorMixin, BaseDecisionTree):

     Parameters
     ----------
-    criterion : {"squared_error", "friedman_mse", "absolute_error", \
-            "poisson"}, default="squared_error"
+    criterion : {"squared_error", "absolute_error", "poisson"}, default="squared_error"
         The function to measure the quality of a split. Supported criteria
         are "squared_error" for the mean squared error, which is equal to
         variance reduction as feature selection criterion and minimizes the L2
-        loss using the mean of each terminal node, "friedman_mse", which uses
-        mean squared error with Friedman's improvement score for potential
-        splits, "absolute_error" for the mean absolute error, which minimizes
-        the L1 loss using the median of each terminal node, and "poisson" which
-        uses reduction in the half mean Poisson deviance to find splits.
+        loss using the mean of each terminal node, "absolute_error" for the mean
+        absolute error, which minimizes the L1 loss using the median of each terminal
+        node, and "poisson" which uses reduction in Poisson deviance to find splits,
+        also using the mean of each terminal node.

         .. versionadded:: 0.18
            [NAME_REDACTED] (MAE) criterion.

         .. versionadded:: 0.24
             Poisson deviance criterion.

+        .. versionchanged:: 1.9
+            Criterion `"friedman_mse"` was deprecated.
+
     splitter : {"best", "random"}, default="best"
         The strategy used to choose the split at each node. Supported
         strategies are "best" to choose the best split and "random" to choose
@@ -1338,7 +1339,7 @@ class DecisionTreeRegressor(RegressorMixin, BaseDecisionTree):
     _parameter_constraints: dict = {
         **BaseDecisionTree._parameter_constraints,
         "criterion": [
-            StrOptions({"squared_error", "friedman_mse", "absolute_error", "poisson"}),
+            StrOptions({"squared_error", "absolute_error", "poisson"}),
             Hidden(Criterion),
         ],
     }
@@ -1359,6 +1360,16 @@ def __init__(
         ccp_alpha=0.0,
         monotonic_cst=None,
     ):
+        if isinstance(criterion, str) and criterion == "friedman_mse":
+            # TODO(1.11): remove support of "friedman_mse" criterion.
+            criterion = "squared_error"
+            warnings.warn(
+                'Value `"friedman_mse"` for `criterion` is deprecated and will be '
+                'removed in 1.11. It maps to `"squared_error"` as both '
+                'were always equivalent. Use `criterion="squared_error"` '
+                "to remove this warning.",
+                FutureWarning,
+            )
         super().__init__(
             criterion=criterion,
             splitter=splitter,
@@ -1446,7 +1457,6 @@ def __sklearn_tags__(self):
         # common test to pass, specifically: check_estimators_nan_inf
         allow_nan = self.splitter in ("best", "random") and self.criterion in {
             "squared_error",
-            "friedman_mse",
             "poisson",
         }
         tags.input_tags.allow_nan = allow_nan
@@ -1758,23 +1768,24 @@ class ExtraTreeRegressor(DecisionTreeRegressor):

     Parameters
     ----------
-    criterion : {"squared_error", "friedman_mse", "absolute_error", "poisson"}, \
-            default="squared_error"
+    criterion : {"squared_error", "absolute_error", "poisson"}, default="squared_error"
         The function to measure the quality of a split. Supported criteria
         are "squared_error" for the mean squared error, which is equal to
         variance reduction as feature selection criterion and minimizes the L2
-        loss using the mean of each terminal node, "friedman_mse", which uses
-        mean squared error with Friedman's improvement score for potential
-        splits, "absolute_error" for the mean absolute error, which minimizes
-        the L1 loss using the median of each terminal node, and "poisson" which
-        uses reduction in Poisson deviance to find splits.
+        loss using the mean of each terminal node, "absolute_error" for the mean
+        absolute error, which minimizes the L1 loss using the median of each terminal
+        node, and "poisson" which uses reduction in Poisson deviance to find splits,
+        also using the mean of each terminal node.

         .. versionadded:: 0.18
            [NAME_REDACTED] (MAE) criterion.

         .. versionadded:: 0.24
             Poisson deviance criterion.

+        .. versionchanged:: 1.9
+            Criterion `"friedman_mse"` was deprecated.
+
     splitter : {"random", "best"}, default="random"
         The strategy used to choose the split at each node. Supported
         strategies are "best" to choose the best split and "random" to choose
@@ -1993,7 +2004,6 @@ def __sklearn_tags__(self):
         # common test to pass, specifically: check_estimators_nan_inf
         allow_nan = self.splitter == "random" and self.criterion in {
             "squared_error",
-            "friedman_mse",
             "poisson",
         }
         tags.input_tags.allow_nan = allow_nan

@@ -1687,61 +1687,6 @@ cdef class MAE(Criterion):
             dest[0] = upper_bound

-cdef class FriedmanMSE(MSE):
-    """Mean squared error impurity criterion with improvement score by Friedman.
-
-    Uses the formula (35) in Friedman's original [NAME_REDACTED] paper:
-
-        diff = mean_left - mean_right
-        improvement = n_left * n_right * diff^2 / (n_left + n_right)
-    """
-
-    cdef float64_t proxy_impurity_improvement(self) noexcept nogil:
-        """Compute a proxy of the impurity reduction.
-
-        This method is used to speed up the search for the best split.
-        It is a proxy quantity such that the split that maximizes this value
-        also maximizes the impurity improvement. It neglects all constant terms
-        of the impurity decrease for a given split.
-
-        The absolute impurity improvement is only computed by the
-        impurity_improvement method once the best split has been found.
-        """
-        cdef float64_t total_sum_left = 0.0
-        cdef float64_t total_sum_right = 0.0
-
-        cdef intp_t k
-        cdef float64_t diff = 0.0
-
-        for k in range(self.n_outputs):
-            total_sum_left += self.sum_left[k]
-            total_sum_right += self.sum_right[k]
-
-        diff = (self.weighted_n_right * total_sum_left -
-                self.weighted_n_left * total_sum_right)
-
-        return diff * diff / (self.weighted_n_left * self.weighted_n_right)
-
-    cdef float64_t impurity_improvement(self, float64_t impurity_parent, float64_t
-                                        impurity_left, float64_t impurity_right) noexcept nogil:
-        # Note: none of the arguments are used here
-        cdef float64_t total_sum_left = 0.0
-        cdef float64_t total_sum_right = 0.0
-
-        cdef intp_t k
-        cdef float64_t diff = 0.0
-
-        for k in range(self.n_outputs):
-            total_sum_left += self.sum_left[k]
-            total_sum_right += self.sum_right[k]
-
-        diff = (self.weighted_n_right * total_sum_left -
-                self.weighted_n_left * total_sum_right) / self.n_outputs
-
-        return (diff * diff / (self.weighted_n_left * self.weighted_n_right *
-                               self.weighted_n_node_samples))
-
-
 cdef class Poisson(RegressionCriterion):
     """[NAME_REDACTED] deviance as impurity criterion.

@@ -334,9 +334,7 @@ def node_to_str(self, tree, node_id, criterion):

         # Write impurity
         if self.impurity:
-            if isinstance(criterion, _criterion.FriedmanMSE):
-                criterion = "friedman_mse"
-            elif isinstance(criterion, _criterion.MSE) or criterion == "squared_error":
+            if isinstance(criterion, _criterion.MSE) or criterion == "squared_error":
                 criterion = "squared_error"
             elif not isinstance(criterion, str):
                 criterion = "impurity"

@@ -11,7 +11,6 @@
 from numpy.random import RandomState

 from sklearn.base import is_classifier
-from sklearn.ensemble import GradientBoostingClassifier
 from sklearn.exceptions import NotFittedError
 from sklearn.tree import (
     DecisionTreeClassifier,
@@ -21,6 +20,9 @@
     plot_tree,
 )

+CLF_CRITERIONS = ("gini", "log_loss")
+REG_CRITERIONS = ("squared_error", "absolute_error", "poisson")
+
 # toy sample
 X = [[-2, -1], [-1, -1], [-1, -2], [1, 1], [1, 2], [2, 1]]
 y = [-1, -1, -1, 1, 1, 1]
@@ -389,19 +391,20 @@ def test_graphviz_errors():
         export_graphviz(clf, out, class_names=[])

-def test_friedman_mse_in_graphviz():
-    clf = DecisionTreeRegressor(criterion="friedman_mse", random_state=0)
-    clf.fit(X, y)
+[USER_REDACTED].mark.parametrize("criterion", CLF_CRITERIONS + REG_CRITERIONS)
+def test_criterion_in_gradient_boosting_graphviz(criterion):
     dot_data = StringIO()
-    export_graphviz(clf, out_file=dot_data)

-    clf = GradientBoostingClassifier(n_estimators=2, random_state=0)
-    clf.fit(X, y)
-    for estimator in clf.estimators_:
-        export_graphviz(estimator[0], out_file=dot_data)
+    is_reg = criterion in REG_CRITERIONS
+    Tree = DecisionTreeRegressor if is_reg else DecisionTreeClassifier
+    clf = Tree(random_state=0, criterion=criterion)
+    # positive values for poisson criterion:
+    y_ = [yi + 2 for yi in y] if is_reg else y
+    clf.fit(X, y_)
+    export_graphviz(clf, out_file=dot_data)

     for finding in finditer(r"\[.*?samples.*?\]", dot_data.getvalue()):
-        assert "friedman_mse" in finding.group()
+        assert criterion in finding.group()

 def test_precision():
@@ -411,9 +414,7 @@ def test_precision():
         (rng_reg.random_sample((5, 2)), rng_clf.random_sample((1000, 4))),
         (rng_reg.random_sample((5,)), rng_clf.randint(2, size=(1000,))),
         (
-            DecisionTreeRegressor(
-                criterion="friedman_mse", random_state=0, max_depth=1
-            ),
+            DecisionTreeRegressor(random_state=0, max_depth=1),
             DecisionTreeClassifier(max_depth=1, random_state=0),
         ),
     ):
@@ -436,7 +437,7 @@ def test_precision():
             if is_classifier(clf):
                 pattern = r"gini = \d+\.\d+"
             else:
-                pattern = r"friedman_mse = \d+\.\d+"
+                pattern = r"squared_error = \d+\.\d+"

             # check impurity
             for finding in finditer(pattern, dot_data):

@@ -267,6 +267,8 @@ def test_weighted_classification_toy():
         assert_array_equal(clf.predict(T), true_result, "Failed with {0}".format(name))

+# TODO(1.11): remove the deprecated friedman_mse criterion parametrization
+[USER_REDACTED].mark.filterwarnings("ignore:.*friedman_mse.*:FutureWarning")
 [USER_REDACTED].mark.parametrize("Tree", REG_TREES.values())
 [USER_REDACTED].mark.parametrize("criterion", REG_CRITERIONS)
 def test_regression_toy(Tree, criterion):
@@ -329,6 +331,8 @@ def test_iris():
         )

+# TODO(1.11): remove the deprecated friedman_mse criterion parametrization
+[USER_REDACTED].mark.filterwarnings("ignore:.*friedman_mse.*:FutureWarning")
 [USER_REDACTED].mark.parametrize("name, Tree", REG_TREES.items())
 [USER_REDACTED].mark.parametrize("criterion", REG_CRITERIONS)
 def test_diabetes_overfit(name, Tree, criterion):
@@ -342,6 +346,8 @@ def test_diabetes_overfit(name, Tree, criterion):
     )

+# TODO(1.11): remove the deprecated friedman_mse criterion parametrization
+[USER_REDACTED].mark.filterwarnings("ignore:.*friedman_mse.*:FutureWarning")
 [USER_REDACTED].mark.parametrize("Tree", REG_TREES.values())
 [USER_REDACTED].mark.parametrize(
     "criterion, metric",
@@ -946,6 +952,8 @@ def test_pickle():
             )

+# TODO(1.11): remove the deprecated friedman_mse criterion parametrization
+[USER_REDACTED].mark.filterwarnings("ignore:.*friedman_mse.*:FutureWarning")
 [USER_REDACTED].mark.parametrize(
     "Tree, criterion",
     [
@@ -1490,6 +1498,8 @@ def test_sparse_parameters(tree_type, dataset, csc_container):
     assert_array_almost_equal(s.predict(X), d.predict(X))

+# TODO(1.11): remove the deprecated friedman_mse criterion parametrization
+[USER_REDACTED].mark.filterwarnings("ignore:.*friedman_mse.*:FutureWarning")
 [USER_REDACTED].mark.parametrize(
     "tree_type, criterion",
     list(product([tree for tree in SPARSE_TREES if tree in REG_TREES], REG_CRITERIONS))
@@ -2034,6 +2044,8 @@ def test_apply_path_readonly_all_trees(name, splitter, sparse_container):
     )

+# TODO(1.11): remove the deprecated friedman_mse criterion parametrization
+[USER_REDACTED].mark.filterwarnings("ignore:.*friedman_mse.*:FutureWarning")
 [USER_REDACTED].mark.parametrize("criterion", ["squared_error", "friedman_mse", "poisson"])
 [USER_REDACTED].mark.parametrize("Tree", REG_TREES.values())
 def test_balance_property(criterion, Tree):
@@ -2456,6 +2468,8 @@ def test_min_sample_split_1_error(Tree):
         tree.fit(X, y)

+# TODO(1.11): remove the deprecated friedman_mse criterion parametrization
+[USER_REDACTED].mark.filterwarnings("ignore:.*friedman_mse.*:FutureWarning")
 [USER_REDACTED].mark.parametrize("criterion", ["squared_error", "friedman_mse"])
 def test_missing_values_best_splitter_on_equal_nodes_no_missing(criterion):
     """Check missing values goes to correct node during predictions."""
@@ -2482,6 +2496,8 @@ def test_missing_values_best_splitter_on_equal_nodes_no_missing(criterion):
     assert_allclose(y_pred, [np.mean(y_equal[-4:])])

+# TODO(1.11): remove the deprecated friedman_mse criterion parametrization
+[USER_REDACTED].mark.filterwarnings("ignore:.*friedman_mse.*:FutureWarning")
 [USER_REDACTED].mark.parametrize("seed", range(3))
 [USER_REDACTED].mark.parametrize("criterion", ["squared_error", "friedman_mse"])
 def test_missing_values_random_splitter_on_equal_nodes_no_missing(criterion, seed):
@@ -2757,6 +2773,8 @@ def test_deterministic_pickle():
     assert pickle1 == pickle2

+# TODO(1.11): remove the deprecated friedman_mse criterion parametrization
+[USER_REDACTED].mark.filterwarnings("ignore:.*friedman_mse.*:FutureWarning")
 [USER_REDACTED].mark.parametrize("Tree", [DecisionTreeRegressor, ExtraTreeRegressor])
 [USER_REDACTED].mark.parametrize(
     "X",
@@ -3047,3 +3065,8 @@ def test_missing_values_and_constant_toy():
     assert_array_equal(tree.predict(X), y)
     # with just one split (-> three nodes: the root + 2 leaves)
     assert tree.tree_.node_count == 3
+
+
+def test_friedman_mse_deprecation():
+    with pytest.warns(FutureWarning, match="friedman_mse"):
+        _ = DecisionTreeRegressor(criterion="friedman_mse")

@@ -515,13 +515,11 @@
         "check_sample_weight_equivalence_on_dense_data": [
             dict(criterion="squared_error"),
             dict(criterion="absolute_error"),
-            dict(criterion="friedman_mse"),
             dict(criterion="poisson"),
         ],
         "check_sample_weight_equivalence_on_sparse_data": [
             dict(criterion="squared_error"),
             dict(criterion="absolute_error"),
-            dict(criterion="friedman_mse"),
             dict(criterion="poisson"),
         ],
     },

Otherwise LGTM

LGTM. Maybe [USER_REDACTED] would like to have a look.

Since, the concerns raised by https://github.com/[USER_REDACTED]n/scikit-learn/issues/32700#issuecomment-3554494044 have been addressed in the follow-up discussion, I think we can finalize the review and merge of this PR.

Besides the following points, it looks good to me.

Bumping version numbers everywhere because 1.8 has already been released.

Otherwise LGTM.

Missing feedback I intended to include in the review above.

Unrelated to this PR, but now that MAE criterion is at much 10x slower than the MSE, and usually more like 5x slower. Is it really significantly slower? It will still fit fairly fast for most tabular datasets (less than let's say 10M points).

I propose to delete this test, as the changes proposed by [NAME_REDACTED] **exactly** backward compatible, given that the criterion calculations now use a different but equivalent formula.

Another option would be to update it with the current values, but I feel that a such test prevents legitimate changes/improvements that slightly affect any calculation.

not sure if we should remove them, we can keep them with only one value, and add more in the future.

`"friedman_mse"` could also be `Hidden`

I wouldn't skip. What's the difference after the change in this test? What should be the tolerance for it to pass?

> What should be the tolerance for it to pass?

`rtol=0.1`, which doesn't make much sense for a test named `test_huber_exact_backward_compat`

In this test, the model 100% overfits, so the values checked in the asserts are mostly 0 + some float precision noise I think :sweat_smile: , at least the one for which `rtol=0.1` would be needed.

So I propose to transform this test into `test_huber_overfit`, see my commit https://github.com/[USER_REDACTED]n/scikit-learn/pull/32708/commits/4009fd3791ef7e9a6caaeb1029b1deb488ecd3a6

Hum... I prefer removing it because:
- HGBT has no `criterion` param, so it's a step towards unifying those two models (#27873)
- it's surely a bit confusing for users to have both the `loss` and the `criterion` parameter.
- I think it's unlikely we'll add more in the future: poisson criterion can't work on gradients (requires positive y), MAE is still quite slower than MSE, which isn't great for fitting trees sequentially...

indeed 👍

Is this change cause by [NAME_REDACTED] switching from `criterion="friedman_mse"` to `criterion="squared_error"`? Or is this a consequence of #32707?

I think we should rather document this a fix and rephrase this entry accordingly, since this PR changes the default behavior of the estimators by [NAME_REDACTED] from the buggy `"friedman_mse"` implementation to the correct `"squared_error"` implementation (#32707).

It's caused by [NAME_REDACTED] #32707 only affects the scale of the impurity I think, see the fix I made temporarily in PR https://github.com/[USER_REDACTED]n/scikit-learn/pull/32699, and here the scale of impurity shouldn't impact the results (trees are controlled by `max_depth` only).

 But the calculation of impurity (`criterion.impurity_improvement`) being implemented differently, the rounding errors differ, and when you have several features with very similar (or the same) splits, the selected split might differ.

This happens for all the losses, except for `loss="absolute_error"`: I think the gradient being -1 or 1 for this loss, there are no rounding errors (integers everywhere, and integers small enough to fit in the mantissa of a float64).

Please rephrase. "Friedman MSE" (the name was, I guess, invented by scikit-learn) only makes sense for gradient boosting and in fact is different than SE and is less about the criterion more about weights, scikit-learn just implemented it wrongly.
I want to make clear that Friedman is not to blame for this mistake, scikit-learn is.

Please undo the changes of this test. I should still pass. If not, this PR introduces a regression.

```suggestion
        node, and "poisson" which uses reduction in Poisson deviance to find splits, also using the mean of each terminal node.
```

Can this test be modified instead of removed? Or is it tested elsewhere?

```suggestion
                "to remove this warning.",
```

I am inclined to remove this sentence. The reason for choosing either squared error or absolute error should not be fit time, but use case / statistically driven.

Codecov says this is not tested.

Codecov says this is not tested.

This test doesn't pass after the changes in this PR because of round errors. As mentioned above, in this test (`test_huber_exact_backward_compat`) the model 100% overfits, so the values checked in the asserts are mostly 0/<some_int> + some float precision noise. Checking the exact values means checking the exact float precision noise, preventing almost any change, even meaningful and valid, from passing it.

> If not, this PR introduces a regression

No. This test was just not a meaningful test (as I already found and fixed many since I started working on scikit-learn...).

I rephrased.

> I want to make clear that Friedman is not to blame for this mistake, scikit-learn is.

+1, good point. I tried to make it clear.

Hum... I wrote both a `.fix.rst` and a `.api.rst`, each one focuses on a different aspect. Let me know what you think.

This test was mostly testing that the string "friedman_mse" was present in appropriate places in the output. We have some much more complete tests in this file (for the squared error criterion). So I think it's fine removing it.

Alternatively, I can keep this test and just ignore the deprecation warnings. And we'll remove it when we remove "friedman_mse" completely.

Tested it

Fixed.

Typically, this test fails when you change:

`median = _weighted_percentile(y_true, sample_weight, 50)` to `median = _weighted_percentile(y_true, sample_weight, 50, average=True)` in `HuberLoss.fit_intercept_only`. Even though I think we consider that `average=True` is a better option for computing the weighted median. At least that's what I assumed when I wrote the PR #32100 and was, in a sense, confirmed by [USER_REDACTED] who asked me to test my logic against `_weighted_percentile(..., average=True)`.

I would rename the test to `test_criterion_in_gradient_boosting_graphviz` and check that the name of the new criterion (`"squared_error"`) is present in the nodes.

Let's remove.

I agree that we will need to open another PR for to use `average=True` in. `HuberLoss.fit_intercept_only` and check that optimizing the `HuberLoss` on a dataset with symmetrically distributed target data and constant features returns the same as `np.median`, whether the sum of integer sample weights is even or odd and remove this arbitrary bias.

```suggestion
- The `criterion` parameter is now deprecated for classes
```

```suggestion
- Both :class:`ensemble.GradientBoostingRegressor` and
  :class:`ensemble.GradientBoostingClassifier` with the default
  `"friedman_mse"` criterion were incorrectly computing scaled impurity values,
  leading to unexpected trees in some cases. The implementation now uses
```

I think this would be redundant with `test_graphviz_toy` where we compare with exact outputs (including examples including `"squared_error"`.

Edit: ah no, this test fits `GradientBoostingClassifier`, ok let's do what you suggest.

Though TBH, I don't think this test makes a lot of sense: why testing the export of `GB.estimators_[0]` and not `RF.estimators_[0]`, `ET.estimators_[0]`, etc.?

I would rather suggest a test (parametrized by [NAME_REDACTED]) that fits a decision tree, and tests the presence of the criterion name in the exported string. So we test all criteria. And we avoid importing from `sklearn.ensemble` in a test from `sklearn.tree` which looks like a bad pattern in most cases.

Happy to :smile:

I'd be happy to do that :smile: We have the same thing for the losses `AbsoluteError` and `PinballLoss`.

I agree with the above, but I wouldn't make it a requirement to have this PR merged. The current state is good enough.

Usually, for deprecated features, we keep the existing tests unchanged and add a decorator to silence the deprecation warning and a TODO comment with the scikit-learn version number that explains how the tests will have to change once the deprecation period is over.

Ah yes, that makes sense. I can do that if needed.

I prefer not merging a piece of code I touched but I'm not too happy with (if changes to make it better are small enough). So I went for the parameterized test.

(I committed & pushed by error a change to this test where I use `pytest.mark.filterwarnings`. I can either generalize the same pattern to other tests, or revert.)

Let's make it easier to `git grep` TODOs before the 1.10 release.

```suggestion
# TODO(1.11): remove the deprecated friedman_mse criterion parametrization and
# use the default instead.
[USER_REDACTED].mark.filterwarnings("ignore:.*friedman_mse.*:FutureWarning")
```

```suggestion
        .. versionchanged:: 1.9
```

```suggestion
        .. deprecated:: 1.9
           `criterion` is deprecated and will be removed in 1.11.
```

```suggestion
                'removed in 1.11. It maps to `"squared_error"` as both '
```

```suggestion
                "removed in 1.11. It has no effect. Leave it to its default value to "
```

```suggestion
        .. versionchanged:: 1.9
            Criterion `"friedman_mse"` was deprecated.
```

Actually, this test should rather stay unchanged but annotated with `[USER_REDACTED].mark.filterwarnings("ignore:.*friedman_mse.*:FutureWarning")` and a `TODO(1.11)` comment.

Should I do that for all tests where I removed "friedman_mse" from a `parametrize`? It should not take me too long.

```suggestion
def test_missing_values_random_splitter_on_equal_nodes_no_missing(criterion, seed):
```

Did that for all the applicable tests, and verified all warnings were indeed filtered :white_check_mark:

What does „incorrect scaling“ mean?

I answered here, in the issue about this bug:
https://github.com/[USER_REDACTED]n/scikit-learn/issues/32707#issuecomment-3730689152


Return `'cpu'` for `device(numpy_array)` when dispatch is enabled

This PR will check using the CI whether we can change the current behavior for `device` to return `"cpu"` on numpy inputs when `array_api_dispatch is True`.

Context: https://github.com/[USER_REDACTED]n/scikit-learn/pull/31829#issuecomment-3523758213

@@ -153,8 +153,7 @@ def _check_array_api_dispatch(array_api_dispatch):
 def _single_array_device(array):
     """Hardware device where the array data resides on."""
     if (
-        isinstance(array, (numpy.ndarray, numpy.generic))
-        or not hasattr(array, "device")
+        not hasattr(array, "device")
         # When array API dispatch is disabled, we expect the scikit-learn code
         # to use np.asarray so that the resulting NumPy array will implicitly use the
         # CPU. In this case, scikit-learn should stay as device neutral as possible,

@@ -687,14 +687,17 @@ def test_add_to_diagonal(array_namespace, device_, dtype_name):
 [USER_REDACTED].mark.parametrize("csr_container", CSR_CONTAINERS)
 [USER_REDACTED].mark.parametrize("dispatch", [True, False])
 def test_sparse_device(csr_container, dispatch):
+    np_arr = numpy.array([1])
+    # For numpy < 2, the device attribute is not available on numpy arrays
+    expected_numpy_array_device = getattr(np_arr, "device", None) if dispatch else None
     a, b = csr_container(numpy.array([[1]])), csr_container(numpy.array([[2]]))
     if dispatch and os.environ.get("SCIPY_ARRAY_API") is None:
         raise SkipTest("SCIPY_ARRAY_API is not set: not checking array_api input")
     with config_context(array_api_dispatch=dispatch):
         assert device(a, b) is None
-        assert device(a, numpy.array([1])) is None
+        assert device(a, np_arr) == expected_numpy_array_device
         assert get_namespace_and_device(a, b)[2] is None
-        assert get_namespace_and_device(a, numpy.array([1]))[2] is None
+        assert get_namespace_and_device(a, np_arr)[2] == expected_numpy_array_device

 [USER_REDACTED].mark.parametrize(

I vote for this change. No opinion about including it in #31829 or merging this PR separately. Maybe separately makes it easier to understand why we made this change (for people from the future)?

[USER_REDACTED] any opinions on this and where to include this change?

That will fail for numpy<2, right? In this case the numpy array has no `.device` so even when `dispatch is True`, the device will be `None`.

To be honest, the simplest may be to decide you need numpy>=2 for array API.

Right now we have scipy 1.14.0 as the minimum version (released 2024-06-24) for array API and numpy 2.0 was released around the same time (2024-06-16).

> To be honest, the simplest may be to decide you need numpy>=2 for array API.

I agree. I doubt that anybody will enable array API dispatch with old versions of the dependencies.

Let me update this test to take the numpy version into account to set our expectations straight.

I updated the test in 384e4bd so that the assertions won't fail even if we decide to move array API support out of the experimental phase before we drop numpy <2 support.

The code of the `device` itself stays the same.

Good point about `numpy<2`. I'd also vote that we can make it a requirement for array API support - I think before v2 Numpy did not have (complete) array API support.

Two things that I'm wondering/for my education:
1. the CI didn't fail because we only test Numpy>=2 with `dispatch=True`? My first thought when reading the comment about numpy<2 was "ah, we should see a CI failure". After thinking for a bit I came up with the explanation that we don't test dispatch=True with old Numpy, but wondering if that is right.
2. how does using `array_api_compat` effect things? The goal is to paper over (small) incompatibilities. But I think it can't change the array class/instances themselves. And I think that is part of why there is `array_api_compat.device()`? I think because the ndarray class and instances aren't modified it basically doesn't matter that we are using `array_api_compat` (if the attribute is missing in older numpy, it is missing)

Maybe using https://github.com/data-apis/array-api-compat/blob/main/array_api_compat/common/_helpers.py#L711 in our `device()` could be something to do in the future.

> the CI didn't fail because we only test Numpy>=2 with dispatch=True?

Yep, as far as I know the only CI builds we have with array API use recent versions for numpy, scipy etc ... grepping the CI lock-files for array-api-strict and numpy scipy is the 100% certain way to know.

Yes, and I think this is fine as it is.


TST: trees: run `test_min_impurity_decrease` for all criteria

Since I started working on the tree module (in September 2025), I found 3 bugs related to impurity calculation, so I think it's worth trying to extend a bit the coverage around impurity.

#### [NAME_REDACTED]/PRs

The three impurity related bugs:
- https://github.com/[USER_REDACTED]n/scikit-learn/issues/32178
- https://github.com/[USER_REDACTED]n/scikit-learn/issues/32707
- https://github.com/[USER_REDACTED]n/scikit-learn/issues/32870

Note: I opened this PR a while ago, but I was waiting for #32708 to be merged before opening it.

#### What does this implement/fix? Explain your changes.

- Parameterize `test_min_impurity_decrease` to test all criteria.
- Greatly simplify the test.

=> better coverage with less loc.

@@ -829,76 +829,49 @@ def test_min_weight_fraction_leaf_with_min_samples_leaf_on_sparse_input(
     )

-def test_min_impurity_decrease(global_random_seed):
+# TODO(1.11): remove the deprecated friedman_mse criterion parametrization
+[USER_REDACTED].mark.filterwarnings("ignore:.*friedman_mse.*:FutureWarning")
+[USER_REDACTED].mark.parametrize(
+    "TreeEstimator, criterion",
+    [
+        *product(REG_TREES.values(), REG_CRITERIONS),
+        *product(CLF_TREES.values(), CLF_CRITERIONS),
+    ],
+)
+def test_min_impurity_decrease(TreeEstimator, criterion, global_random_seed):
     # test if min_impurity_decrease ensure that a split is made only if
     # if the impurity decrease is at least that value
     X, y = datasets.make_classification(n_samples=100, random_state=global_random_seed)

     # test both DepthFirstTreeBuilder and BestFirstTreeBuilder
     # by [NAME_REDACTED]_leaf_nodes
-    for max_leaf_nodes, name in product((None, 1000), ALL_TREES.keys()):
-        TreeEstimator = ALL_TREES[name]
-
-        # Check default value of min_impurity_decrease, 1e-7
-        est1 = TreeEstimator(max_leaf_nodes=max_leaf_nodes, random_state=0)
-        # Check with explicit value of 0.05
-        est2 = TreeEstimator(
-            max_leaf_nodes=max_leaf_nodes, min_impurity_decrease=0.05, random_state=0
-        )
-        # Check with a much lower value of 0.0001
-        est3 = TreeEstimator(
-            max_leaf_nodes=max_leaf_nodes, min_impurity_decrease=0.0001, random_state=0
-        )
-        # Check with a much lower value of 0.1
-        est4 = TreeEstimator(
-            max_leaf_nodes=max_leaf_nodes, min_impurity_decrease=0.1, random_state=0
-        )
-
-        for est, expected_decrease in (
-            (est1, 1e-7),
-            (est2, 0.05),
-            (est3, 0.0001),
-            (est4, 0.1),
-        ):
-            assert est.min_impurity_decrease <= expected_decrease, (
-                "Failed, min_impurity_decrease = {0} > {1}".format(
-                    est.min_impurity_decrease, expected_decrease
-                )
+    for max_leaf_nodes in [None, 1000]:
+        for expected_decrease in [0.05, 0.0001, 0.1]:
+            est = TreeEstimator(
+                criterion=criterion,
+                max_leaf_nodes=max_leaf_nodes,
+                min_impurity_decrease=expected_decrease,
+                random_state=global_random_seed,
             )
             est.fit(X, y)
-            for node in range(est.tree_.node_count):
+            tree = est.tree_
+            weighted_impurity = (
+                tree.impurity * tree.weighted_n_node_samples / X.shape[0]
+            )
+
+            for node in range(tree.node_count):
                 # If current node is a not leaf node, check if the split was
                 # justified w.r.t the min_impurity_decrease
-                if est.tree_.children_left[node] != TREE_LEAF:
-                    imp_parent = est.tree_.impurity[node]
-                    wtd_n_node = est.tree_.weighted_n_node_samples[node]
+                if tree.children_left[node] != TREE_LEAF:
+                    left = tree.children_left[node]
+                    right = tree.children_right[node]

-                    left = est.tree_.children_left[node]
-                    wtd_n_left = est.tree_.weighted_n_node_samples[left]
-                    imp_left = est.tree_.impurity[left]
-                    wtd_imp_left = wtd_n_left * imp_left
-
-                    right = est.tree_.children_right[node]
-                    wtd_n_right = est.tree_.weighted_n_node_samples[right]
-                    imp_right = est.tree_.impurity[right]
-                    wtd_imp_right = wtd_n_right * imp_right
-
-                    wtd_avg_left_right_imp = wtd_imp_right + wtd_imp_left
-                    wtd_avg_left_right_imp /= wtd_n_node
-
-                    fractional_node_weight = (
-                        est.tree_.weighted_n_node_samples[node] / X.shape[0]
+                    actual_decrease = weighted_impurity[node] - (
+                        weighted_impurity[left] + weighted_impurity[right]
                     )

-                    actual_decrease = fractional_node_weight * (
-                        imp_parent - wtd_avg_left_right_imp
-                    )
-
-                    assert actual_decrease >= expected_decrease, (
-                        "Failed with {0} expected min_impurity_decrease={1}".format(
-                            actual_decrease, expected_decrease
-                        )
-                    )
+                    # Allow a tiny slack to account for floating-point rounding errors:
+                    assert actual_decrease > expected_decrease - 1e-10

 def test_pickle():

Thanks for the PR, this is indeed cleaner and more comprehensive.

```suggestion
            weighted_impurity = tree.impurity * tree.weighted_n_node_samples / X.shape[0]
```

nit:

```suggestion
                    # Allow a tiny slack to account for floating-point rounding errors:
```


FEA Add array API support to `davies_bouldin_score`

#### [NAME_REDACTED]/PRs
Towards #26024

#### What does this implement/fix? Explain your changes.
Add array API support to `davies_bouldin_score`

#### Any other comments?

@@ -0,0 +1,2 @@
+- :func:`sklearn.metrics.cluster.davies_bouldin_score` now supports Array API compliant inputs.
+  By :user:`[NAME_REDACTED] <jaffourt>`.

@@ -18,6 +18,7 @@
 from sklearn.preprocessing import LabelEncoder
 from sklearn.utils import _safe_indexing, check_random_state, check_X_y
 from sklearn.utils._array_api import (
+    _average,
     _convert_to_numpy,
     _is_numpy_namespace,
     _max_precision_float_dtype,
@@ -453,27 +454,34 @@ def davies_bouldin_score(X, labels):
     >>> davies_bouldin_score(X, labels)
     0.12...
     """
+    xp, _, device_ = get_namespace_and_device(X, labels)
     X, labels = check_X_y(X, labels)
     le = LabelEncoder()
     labels = le.fit_transform(labels)
     n_samples, _ = X.shape
-    n_labels = len(le.classes_)
+    n_labels = le.classes_.shape[0]
     check_number_of_labels(n_labels, n_samples)

-    intra_dists = np.zeros(n_labels)
-    centroids = np.zeros((n_labels, len(X[0])), dtype=float)
+    dtype = _max_precision_float_dtype(xp, device_)
+    intra_dists = xp.zeros(n_labels, dtype=dtype, device=device_)
+    centroids = xp.zeros((n_labels, X.shape[1]), dtype=dtype, device=device_)
     for k in range(n_labels):
-        cluster_k = _safe_indexing(X, labels == k)
-        centroid = cluster_k.mean(axis=0)
-        centroids[k] = centroid
-        intra_dists[k] = np.average(pairwise_distances(cluster_k, [centroid]))
+        cluster_k = _safe_indexing(X, xp.nonzero(labels == k)[0])
+        centroid = _average(cluster_k, axis=0, xp=xp)
+        centroids[k, ...] = centroid
+        intra_dists[k] = _average(
+            pairwise_distances(cluster_k, xp.stack([centroid])), xp=xp
+        )

     centroid_distances = pairwise_distances(centroids)

-    if np.allclose(intra_dists, 0) or np.allclose(centroid_distances, 0):
+    zero = xp.asarray(0.0, device=device_, dtype=dtype)
+    if xp.all(xpx.isclose(intra_dists, zero)) or xp.all(
+        xpx.isclose(centroid_distances, zero)
+    ):
         return 0.0

-    centroid_distances[centroid_distances == 0] = np.inf
+    centroid_distances[centroid_distances == 0] = xp.inf
     combined_intra_dists = intra_dists[:, None] + intra_dists
-    scores = np.max(combined_intra_dists / centroid_distances, axis=1)
-    return float(np.mean(scores))
+    scores = xp.max(combined_intra_dists / centroid_distances, axis=1)
+    return float(_average(scores, xp=xp))

@@ -256,7 +256,10 @@ def check_array_api_unsupervised_metric(metric, array_namespace, device, dtype_n
 array_api_metric_checkers = {
     calinski_harabasz_score: [
         check_array_api_unsupervised_metric,
-    ]
+    ],
+    davies_bouldin_score: [
+        check_array_api_unsupervised_metric,
+    ],
 }

LGTM! Thanks, [USER_REDACTED]!

CUDA CI is green as well. [USER_REDACTED], [USER_REDACTED], friendly ping, would you like to have a look?

LGTM. Thanks [USER_REDACTED]

Just a quick question, why `_max_precision_float_dtype` and not `_find_matching_floating_dtype` here?

Its a good question and I don't have a solid answer. I have seen a number of different approaches for finding a common floating dtype in `array_api` compliant calculations, and it would be nice to have a more defined heuristic if needed :)

In this case, my reasoning for `_max_precision_float_dtype` was that `_find_matching_floating_dtype` finds a common float type between several arrays, but in this implementation we are building new floating arrays for intermediate calculations.

I.e., does it make sense to use the floating dtype returned from `_find_matching_floating_dtype(x, labels)`?

Yes, we could have better consistency around the use of these two.

From my understanding, `_max_precision_float_dtype` is used when we require the highest precision e.g. here:

https://github.com/[USER_REDACTED]n/scikit-learn/blob/de3816631818fa905ba14a26c2fa721aa91ffa09/sklearn/metrics/_ranking.py#L969-L974

`cumulative_sum` is notorious for floating point precision error, so it's best to use the highest precision.

I was just wondering if `intra_dists` had a particular requirement for higher precision.

Probably not worth worrying about here (I think?)


DOC: [NAME_REDACTED] to SpectralBiclustering and SpectralCoclustering

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#### What does this implement/fix? Explain your changes.

[NAME_REDACTED] to SpectralBiclustering and SpectralCoclustering

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@@ -200,7 +200,7 @@ def __sklearn_tags__(self):

 class SpectralCoclustering(BaseSpectral):
-    """[NAME_REDACTED] algorithm (Dhillon, 2001).
+    """[NAME_REDACTED] algorithm (Dhillon, 2001) [1]_.

     Clusters rows and columns of an array `X` to solve the relaxed
     normalized cut of the bipartite graph created from `X` as follows:
@@ -290,9 +290,9 @@ class SpectralCoclustering(BaseSpectral):

     References
     ----------
-    * :doi:`Dhillon, Inderjit S, 2001. Co-clustering documents and words using
-      bipartite spectral graph partitioning.
-      <10.1145/502512.502550>`
+    .. [1] :doi:`Dhillon, Inderjit S, 2001. Co-clustering documents and words using
+           bipartite spectral graph partitioning.
+           <10.1145/502512.502550>`

     Examples
     --------
@@ -358,7 +358,7 @@ def _fit(self, X):

 class SpectralBiclustering(BaseSpectral):
-    """Spectral biclustering (Kluger, 2003).
+    """Spectral biclustering (Kluger, 2003) [1]_.

     Partitions rows and columns under the assumption that the data has
     an underlying checkerboard structure. For instance, if there are
@@ -458,14 +458,15 @@ class SpectralBiclustering(BaseSpectral):

     See Also
     --------
-    SpectralCoclustering : [NAME_REDACTED] algorithm (Dhillon, 2001).
+    SpectralCoclustering : Clusters rows and columns of an array `X` to solve the
+        relaxed normalized cut of the bipartite graph created from `X`.

     References
     ----------

-    * :doi:`Kluger, Yuval, et. al., 2003. Spectral biclustering of microarray
-      data: coclustering genes and conditions.
-      <10.1101/gr.648603>`
+    .. [1] :doi:`Kluger, Yuval, et. al., 2003. Spectral biclustering of microarray
+           data: coclustering genes and conditions.
+           <10.1101/gr.648603>`

     Examples
     --------

sphinx fails on this line

[USER_REDACTED] Thanks for catching this. I have fixed the indentation, and now the compilation works.


CI Pin pytest<9 in wheels

Work-around for https://github.com/[USER_REDACTED]n/scikit-learn/issues/32393#issuecomment-3509587108.

See https://github.com/pytest-dev/pytest/issues/13895 for the pytest issue, `raise unittest.SkipTest` raises in pytest 9.0 released on November 8.

Could be a temporary work-around depending how fast pytest merges https://github.com/pytest-dev/pytest/pull/13912 and do a new release.

@@ -231,7 +231,7 @@ jobs:
           # TODO Remove scipy<1.16.2 when hang on macOS_x86_64 has been fixed.
           # See https://github.com/[USER_REDACTED]n/scikit-learn/issues/32279 for
           # more details.
-          CIBW_TEST_REQUIRES: ${{ contains(matrix.python, '314') && 'pytest' || 'pytest pandas' }} scipy<1.16.2
+          CIBW_TEST_REQUIRES: ${{ contains(matrix.python, '314') && 'pytest<9' || 'pytest<9 pandas' }} scipy<1.16.2
           # On Windows, we use a custom Docker image and CIBW_TEST_REQUIRES_WINDOWS
           # does not make sense because it would install dependencies in the host
           # rather than inside the Docker image

@@ -22,11 +22,6 @@ if [[ $FREE_THREADED_BUILD == "False" && "$PLATFORM_ID" != "win_arm64" ]]; then
     # Dot the Python version for identifying the base Docker image
     PYTHON_DOCKER_IMAGE_PART=$(echo ${PYTHON_VERSION:0:1}.${PYTHON_VERSION:1:2})

-    # TODO Remove this when Python 3.14 is released and there is a Docker image
-    if [[ "$PYTHON_DOCKER_IMAGE_PART" == "3.14" ]]; then
-        PYTHON_DOCKER_IMAGE_PART="3.14-rc"
-    fi
-
     # We could have all of the following logic in a Dockerfile but it's a lot
     # easier to do it in bash rather than figure out how to do it in Powershell
     # inside the Dockerfile ...
@@ -50,5 +45,5 @@ else
     # TODO When pandas has a release with a Windows free-threaded wheel we can
     # replace the next line with
     # python -m pip install CIBW_TEST_REQUIRES
-    python -m pip install pytest
+    python -m pip install 'pytest<9'
 fi

@@ -9,7 +9,7 @@ python -m venv test_env
 source test_env/bin/activate

 python -m pip install scikit-learn/scikit-learn/dist/*.tar.gz
-python -m pip install pytest pandas
+python -m pip install 'pytest<9' pandas

 # Run the tests on the installed source distribution
 mkdir tmp_for_test

Not really related to pytest<9 ... I can move it to a separate PR if someone insists :roll_eyes:.


MNT Clean-up old scipy version mentions and code

Towards https://github.com/orgs/scikit-learn/projects/16?query=sort%3Aupdated-desc+is%3Aopen&pane=issue&itemId=137126112

@@ -18,13 +18,7 @@
 # a couple of information regarding the image, such as the shape and data type used
 # to store the image.
 #
-# Note that depending of the SciPy version, we have to adapt the import since the
-# function returning the image is not located in the same module. Also, SciPy >= 1.10
-# requires the package `pooch` to be installed.
-try:  # Scipy >= 1.10
-    from scipy.datasets import face
-except ImportError:
-    from scipy.misc import face
+from scipy.datasets import face

 raccoon_face = face(gray=True)

@@ -39,11 +39,7 @@
 # Generate distorted image
 # ------------------------
 import numpy as np
-
-try:  # Scipy >= 1.10
-    from scipy.datasets import face
-except ImportError:
-    from scipy.misc import face
+from scipy.datasets import face

 raccoon_face = face(gray=True)

@@ -244,12 +244,7 @@ def test_isotonic_regression_auto_decreasing():

     # Create model and fit_transform
     ir = IsotonicRegression(increasing="auto")
-    with warnings.catch_warnings(record=True) as w:
-        warnings.simplefilter("always")
-        y_ = ir.fit_transform(x, y)
-        # work-around for pearson divide warnings in scipy <= 0.17.0
-        assert all(["invalid value encountered in " in str(warn.message) for warn in w])
-
+    y_ = ir.fit_transform(x, y)
     # Check that relationship decreases
     is_increasing = y_[0] < y_[-1]
     assert not is_increasing
@@ -262,11 +257,7 @@ def test_isotonic_regression_auto_increasing():

     # Create model and fit_transform
     ir = IsotonicRegression(increasing="auto")
-    with warnings.catch_warnings(record=True) as w:
-        warnings.simplefilter("always")
-        y_ = ir.fit_transform(x, y)
-        # work-around for pearson divide warnings in scipy <= 0.17.0
-        assert all(["invalid value encountered in " in str(warn.message) for warn in w])
+    y_ = ir.fit_transform(x, y)

     # Check that relationship increases
     is_increasing = y_[0] < y_[-1]

Thanks for the PR! A few comments below

LGTM, thanks!

I enabled auto-merge.

I think you can remove the full comment between "Note that depending on the Scipy version" until "requires the package pooch to be installed"

I guess this one is the same as https://github.com/[USER_REDACTED]n/scikit-learn/pull/32654. I guess don't touch it in this PR and leave it for later.

same comment, no need to modify this in this PR

Ops...
Done.

Ok

Ok again.


DOC: Improve formatting of `sklearn.mixture` API documentation

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Improve formatting of `sklearn.mixture` API documentation

#### What does this implement/fix? Explain your changes.

#### Any other comments?

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@@ -203,7 +203,7 @@ def fit(self, X, y=None):
     def fit_predict(self, X, y=None):
         """Estimate model parameters using X and predict the labels for X.

-        The method fits the model n_init times and sets the parameters with
+        The method fits the model ``n_init`` times and sets the parameters with
         which the model has the largest likelihood or lower bound. Within each
         trial, the method iterates between E-step and M-step for `max_iter`
         times until the change of likelihood or lower bound is less than

@@ -230,7 +230,7 @@ class BayesianGaussianMixture(BaseMixture):
             (n_components, n_features, n_features) if 'full'

     precisions_cholesky_ : array-like
-        The cholesky decomposition of the precision matrices of each mixture
+        The Cholesky decomposition of the precision matrices of each mixture
         component. A precision matrix is the inverse of a covariance matrix.
         A covariance matrix is symmetric positive definite so the mixture of
         Gaussian can be equivalently parameterized by [NAME_REDACTED]
@@ -329,7 +329,7 @@ class BayesianGaussianMixture(BaseMixture):
     .. [2] `[NAME_REDACTED]. (2000). "A [NAME_REDACTED] for
        [NAME_REDACTED]". In Advances in [NAME_REDACTED]
        Systems 12.
-       <https://citeseerx.ist.psu.edu/doc_view/pid/ee844fd96db7041a9681b5a18bff008912052c7e>`_
+       <https://proceedings.neurips.cc/paper_files/paper/1999/file/74563ba21a90da13dacf2a73e3ddefa7-Paper.pdf>`_

     .. [3] `Blei, David M. and Michael I. Jordan. (2006). "Variational
        inference for Dirichlet process mixtures". Bayesian analysis 1.1

@@ -335,7 +335,7 @@ def _compute_precision_cholesky(covariances, covariance_type, xp=None):
     Returns
     -------
     precisions_cholesky : array-like
-        The cholesky decomposition of sample precisions of the current
+        The Cholesky decomposition of sample precisions of the current
         components. The shape depends of the covariance_type.
     """
     xp, _, device_ = get_namespace_and_device(covariances, xp=xp)
@@ -422,7 +422,7 @@ def _compute_precision_cholesky_from_precisions(precisions, covariance_type, xp=
     Returns
     -------
     precisions_cholesky : array-like
-        The cholesky decomposition of sample precisions of the current
+        The Cholesky decomposition of sample precisions of the current
         components. The shape depends on the covariance_type.
     """
     if covariance_type == "full":
@@ -446,7 +446,7 @@ def _compute_precision_cholesky_from_precisions(precisions, covariance_type, xp=
 ###############################################################################
 # Gaussian mixture probability estimators
 def _compute_log_det_cholesky(matrix_chol, covariance_type, n_features, xp=None):
-    """Compute the log-det of the cholesky decomposition of matrices.
+    """Compute the log-det of the Cholesky decomposition of matrices.

     Parameters
     ----------
@@ -690,7 +690,7 @@ class GaussianMixture(BaseMixture):
             (n_components, n_features, n_features) if 'full'

     precisions_cholesky_ : array-like
-        The cholesky decomposition of the precision matrices of each mixture
+        The Cholesky decomposition of the precision matrices of each mixture
         component. A precision matrix is the inverse of a covariance matrix.
         A covariance matrix is symmetric positive definite so the mixture of
         Gaussian can be equivalently parameterized by [NAME_REDACTED]

LGTM, I've re-run the CI just to be safe.

FYI for future, single backtick would work, because we have set a default role for our docs to be 'code'.


DOC Add info on 'array-like' array API inputs when `array_api_dispatch=False`

#### [NAME_REDACTED]/PRs
Related #30454
Found out in https://github.com/[USER_REDACTED]n/scikit-learn/pull/32600#discussion_r2505943104

#### What does this implement/fix? Explain your changes.
Adds info on what happens when non-NumPy array input occurs with `array_api_dispatch=False`
I only realised that we do this and I think it would be nice if it was mentioned in the docs.

I thought I'd add a section on the `array_api_dispatch` as it no longer seemed to fit under the 'Example usage' section

#### Any other comments?
cc [USER_REDACTED] [USER_REDACTED]

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@@ -63,6 +63,12 @@ [NAME_REDACTED]
         * a :class:`pandas.DataFrame` with all columns numeric
         * a numeric :class:`pandas.Series`

+        Other array API inputs, but see :ref:`array_api` for the preferred way of
+        using these:
+
+        * a `PyTorch <https://pytorch.org/>`_ tensor on 'cpu' device
+        * a `JAX <https://docs.jax.dev/en/latest/index.html>`_ array
+
         It excludes:

         * a :term:`sparse matrix`

@@ -42,15 +42,26 @@ and how it facilitates interoperability between array libraries:
 - `Scikit-learn on GPUs with Array API <https://www.youtube.com/watch?v=c_s8tr1AizA>`_
   by :user:`[NAME_REDACTED] <thomasjpfan>` at PyData NYC 2023.

-Example usage
-=============
+Enabling array API support
+==========================

 The configuration `array_api_dispatch=True` needs to be set to `True` to enable array
 API support. We recommend setting this configuration globally to ensure consistent
 behaviour and prevent accidental mixing of array namespaces.
-Note that we set it with :func:`config_context` below to avoid having to call
-:func:`set_config(array_api_dispatch=False)` at the end of every code snippet
-that uses the array API.
+Note that in the examples below, we use a context manager (:func:`config_context`)
+to avoid having to reset it to `False` at the end of every code snippet, so as to
+not affect the rest of the documentation.
+
+Scikit-learn accepts :term:`array-like` inputs for all :mod:`metrics`
+and some estimators. When `array_api_dispatch=False`, these inputs are converted
+into NumPy arrays using :func:`numpy.asarray` (or :func:`numpy.array`).
+While this will successfully convert some array API inputs (e.g., JAX array),
+we generally recommend setting `array_api_dispatch=True` when using array API inputs.
+This is because NumPy conversion can often fail, e.g., torch tensor allocated on GPU.
+
+Example usage
+=============
+
 The example code snippet below demonstrates how to use `CuPy
 <https://cupy.dev/>`_ to run
 :class:`~discriminant_analysis.LinearDiscriminantAnalysis` on a GPU::

I've realised that we (probably) do `np.array` or `np.asarray` on all inputs that we specify as `array-like`. Thus I amended the glossary entry for `array-like` to include pytorch tensors on cpu and JAX arrays as examples. Also amended working in the array API user guide.

I couldn't find another suitable place in the user guide to add this info, so I think I will leave for now and hope the glossary is adequate for now.

More than super good enough!

Not sure 'for historical reasons' is the best phrase. I just meant that as some inputs can be lists, we always did `asarray`, which will also convert non-numpy arrays to numpy arrays.

> all :mod:`~sklearn.metrics`

Is this true..?

This last line is probably redundant, I am happy to remove.

How about joining the two lists?

```suggestion
Note that in the examples below, we use a context manager (:func:`config_context`)
```

```suggestion
to avoid having to reset it to `False` at the end of every code snippet, so as to
```

I think it's better to keep the lists separated because the latter is only expected to work when array API dispatch is enabled, which is not the case by default.

I think it's important to somehow highlight that when `array_api_dispatch=False`, NumPy conversion can fail, for instance, calling `fit` on a torch tensor allocated on a GPU will raise an error.

I thought the reason for listing them here is that these inputs already work/are used in the wild. See the linked issue in the discussion of this PR (and I think the same person created another one like it earlier)

I originally had them as one list, but I changed to two lists mostly so I could add a link to array API docs - so that we can recommend not using array API inputs with dispatch set to False.

So I'm 50/50 on it (2 lists vs 1 list).

> I thought the reason for listing them here is that these inputs already work/are used

I think it is partly that, and partly to be complete and document all behaviours.

Added a sentence, not 100% happy with it so let me know what you think.

I've also removed the last line, which was redundant, I think thats what [USER_REDACTED] 's thumbs up meant 😄

```suggestion
        Other array inputs, but see :ref:`array_api` for the preferred way of using these :
```

What do you think of this rewording? My goal was to try and make it more obvious that the reader should go read the doc

Fine for me to keep the two lists, just wondering if we can improve the in between text.

Changed - I agree this conveys the message better.


DOC move pre-commit instructions to development setup and make them mandatory

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#### [NAME_REDACTED]/PRs
Follow up from #32509, specifically [this comment](https://github.com/[USER_REDACTED]n/scikit-learn/pull/32509#discussion_r2454649769)
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#### What does this implement/fix? Explain your changes.
Move the installation and set up instructions for `pre-commit` to the development setup and remove the (**Optional**) marker. I also made it a sub-heading, so the linting message can point directly to it.

#### Any other comments?
I moved it to the section just before installing scikit-learn, because `pre-commit` is also already installed in Codespaces, so the instructions on using that (#32474) can then jump over everything up to this point.

[USER_REDACTED] [USER_REDACTED]

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@@ -213,7 +213,7 @@ def get_message(log_file, repo, pr_number, sha, run_id, details, versions):
         + "This PR is introducing linting issues. Here's a summary of the issues. "
         + "Note that you can avoid having linting issues by enabling `pre-commit` "
         + "hooks. Instructions to enable them can be found [here]("
-        + "https://scikit-learn.org/dev/developers/contributing.html#how-to-contribute)"
+        + "https://scikit-learn.org/dev/developers/development_setup.html#set-up-pre-commit)"
         + ".\n\n"
         + "You can see the details of the linting issues under the `lint` job [here]"
         + f"(https://github.com/{repo}/actions/runs/{run_id})\n\n"

@@ -269,28 +269,24 @@ The next steps describe the process of modifying code and submitting a PR:
    and start making changes. Always use a feature branch. It's good
    practice to never work on the ``main`` branch!

-#. (**Optional**) Install `pre-commit <https://pre-commit.com/#install>`_ to
-   run code style checks before each commit:
-
-   .. prompt:: bash
-
-      pip install pre-commit
-      pre-commit install
-
-    pre-commit checks can be disabled for a particular commit with
-    `git commit -n`.
-
 #. Develop the feature on your feature branch on your computer, using Git to
    do the version control. When you're done editing, add changed files using
    ``git add`` and then ``git commit``:

-    .. prompt:: bash
+   .. prompt:: bash

       git add modified_files
       git commit

-   to record your changes in Git, then push the changes to your GitHub
-   account with:
+   .. note::
+
+     :ref:`pre-commit <pre_commit>` may reformat your code automatically when
+     you do `git commit`. When this happens, you need to do `git add` followed
+     by `git commit` again. In some rarer cases, you may need to fix things
+     manually, use the error message to figure out what needs to be changed,
+     and use `git add` followed by `git commit` until the commit is successful.
+
+   Then push the changes to your GitHub account with:

    .. prompt:: bash

@@ -130,7 +130,7 @@ the required packages.
             conda create -n sklearn-dev -c conda-forge ^
               python numpy scipy cython meson-python ninja ^
               pytest pytest-cov ruff==0.11.2 mypy numpydoc ^
-              joblib threadpoolctl
+              joblib threadpoolctl pre-commit

           Activate the newly created conda environment:

@@ -168,7 +168,7 @@ the required packages.

             pip install wheel numpy scipy cython meson-python ninja ^
               pytest pytest-cov ruff==0.11.2 mypy numpydoc ^
-              joblib threadpoolctl
+              joblib threadpoolctl pre-commit

     .. tab-item:: MacOS
@@ -200,7 +200,7 @@ the required packages.
             conda create -n sklearn-dev -c conda-forge python \
               numpy scipy cython meson-python ninja \
               pytest pytest-cov ruff==0.11.2 mypy numpydoc \
-              joblib threadpoolctl compilers llvm-openmp
+              joblib threadpoolctl compilers llvm-openmp pre-commit

           and activate the newly created conda environment:

@@ -245,7 +245,7 @@ the required packages.

             pip install wheel numpy scipy cython meson-python ninja \
               pytest pytest-cov ruff==0.11.2 mypy numpydoc \
-              joblib threadpoolctl
+              joblib threadpoolctl pre-commit

     .. tab-item:: Linux
       :class-label: tab-4
@@ -268,7 +268,7 @@ the required packages.
             conda create -n sklearn-dev -c conda-forge python \
               numpy scipy cython meson-python ninja \
               pytest pytest-cov ruff==0.11.2 mypy numpydoc \
-              joblib threadpoolctl compilers
+              joblib threadpoolctl compilers pre-commit

           and activate the newly created environment:

@@ -328,7 +328,8 @@ the required packages.

             pip install wheel numpy scipy cython meson-python ninja \
               pytest pytest-cov ruff==0.11.2 mypy numpydoc \
-              joblib threadpoolctl
+              joblib threadpoolctl pre-commit
+

 .. _install_from_source:

@@ -377,6 +378,19 @@ related to you contribution:
 For more information on testing, see also the :ref:`pr_checklist`
 and :ref:`pytest_tips`.

+.. _pre_commit:
+
+Set up pre-commit
+^^^^^^^^^^^^^^^^^
+
+Additionally, install the `pre-commit hooks <https://pre-commit.com>`__, which will
+automatically check your code for linting problems before each commit in the
+:ref:`development_workflow`:
+
+.. prompt::
+
+  pre-commit install
+
 .. _OpenMP: https://en.wikipedia.org/wiki/OpenMP
 .. _meson-python: https://mesonbuild.com/meson-python
 .. _Ninja: https://ninja-build.org/

Small nit but LGTM! Thanks!

Thanks for the PR, a few comments

One small nit otherwise LGTM, thank you!

LGTM, thanks for the PR!

Maybe this last line is also too much information at this stage?

I moved it to the development workflow note.

Maybe we should mention that sometimes the error is not fixable by pre-commit, and the user will need to manually fix the error. Pre-commit will tell you where and which rule was broken - not sure if it is useful to link to doc of ruff rules (https://docs.astral.sh/ruff/rules/) - the message does describe the rule.

```suggestion
     performed and you will be notified. You have to review the changes and possibly
```
personal nit, feel free to ignore

```suggestion
     executed and you will be notified. Some fixes will be automatically performed
     by pre-commit (e.g., whitespace clean up) while others will require you to
     manually fix them. Pre-commit will specify where the lint error is and which
     lint rule was broken.
     Please review any changes before adding and committing the changed files again.
```

Sorry, I didn't see that the details about dealing with pre-commit were already made above in the text. I have a small preference for 'single source of truth' (i.e. writing things once and referencing them) but for documentation I know 'WET' (write everything twice) also has support.

I'll remove the explanation here. People don't have to worry about this during the installation (and if they want to know more, there is still the link above), and more detailed information is given in the note in the development workflow.

Maybe add `pre-commit` in the `conda` / `pip` command creating the dev environment (instead of doing a separate `pip install`)?

I would move this after the build (i.e. install in editable mode) since this is only useful for committing not building.

I would describe the happy path first. In most cases: `pre-commit` will change your files and you need to `git add` + `git commit` again (which can be a bit confusing ...)

Not so often, you may need to fix the problem yourself.

I moved it to the section just before installing scikit-learn because pre-commit is also already installed in Codespaces, so the instructions on using that (https://github.com/[USER_REDACTED]n/scikit-learn/pull/32474) can then jump over everything up to this point. But I can also move it to the end and add a note there later that this is not required on Codespaces.

I guess it's not really a big deal, if you do `pre-commit install` again in Codespace everything should still work.

```suggestion
automatically check your code for linting problems before each commit in the
:ref:`development_workflow`:
```