_search.py

"""
The :mod:`sklearn.model_selection._search` includes utilities to fine-tune the
parameters of an estimator.
"""

# Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>,
#         Gael Varoquaux <gael.varoquaux@normalesup.org>
#         Andreas Mueller <amueller@ais.uni-bonn.de>
#         Olivier Grisel <olivier.grisel@ensta.org>
#         Raghav RV <rvraghav93@gmail.com>
# License: BSD 3 clause

from abc import ABCMeta, abstractmethod
from collections import defaultdict
from collections.abc import Mapping, Sequence, Iterable
from functools import partial, reduce
from itertools import product
import numbers
import operator
import time
import warnings

import numpy as np
from numpy.ma import MaskedArray
from scipy.stats import rankdata

from ..base import BaseEstimator, is_classifier, clone
from ..base import MetaEstimatorMixin
from ._split import check_cv
from ._validation import _fit_and_score
from ._validation import _aggregate_score_dicts
from ._validation import _insert_error_scores
from ._validation import _normalize_score_results
from ..exceptions import NotFittedError
from joblib import Parallel
from ..utils import check_random_state
from ..utils.random import sample_without_replacement
from ..utils._tags import _safe_tags
from ..utils.validation import indexable, check_is_fitted, _check_fit_params
from ..utils.validation import _deprecate_positional_args
from ..utils.metaestimators import if_delegate_has_method
from ..utils.fixes import delayed
from ..metrics._scorer import _check_multimetric_scoring
from ..metrics import check_scoring
from ..utils import deprecated

__all__ = ['GridSearchCV', 'ParameterGrid', 'fit_grid_point',
           'ParameterSampler', 'RandomizedSearchCV']


class ParameterGrid:
    """Grid of parameters with a discrete number of values for each.

    Can be used to iterate over parameter value combinations with the
    Python built-in function iter.
    The order of the generated parameter combinations is deterministic.

    Read more in the :ref:`User Guide <grid_search>`.

    Parameters
    ----------
    param_grid : dict of str to sequence, or sequence of such
        The parameter grid to explore, as a dictionary mapping estimator
        parameters to sequences of allowed values.

        An empty dict signifies default parameters.

        A sequence of dicts signifies a sequence of grids to search, and is
        useful to avoid exploring parameter combinations that make no sense
        or have no effect. See the examples below.

    Examples
    --------
    >>> from sklearn.model_selection import ParameterGrid
    >>> param_grid = {'a': [1, 2], 'b': [True, False]}
    >>> list(ParameterGrid(param_grid)) == (
    ...    [{'a': 1, 'b': True}, {'a': 1, 'b': False},
    ...     {'a': 2, 'b': True}, {'a': 2, 'b': False}])
    True

    >>> grid = [{'kernel': ['linear']}, {'kernel': ['rbf'], 'gamma': [1, 10]}]
    >>> list(ParameterGrid(grid)) == [{'kernel': 'linear'},
    ...                               {'kernel': 'rbf', 'gamma': 1},
    ...                               {'kernel': 'rbf', 'gamma': 10}]
    True
    >>> ParameterGrid(grid)[1] == {'kernel': 'rbf', 'gamma': 1}
    True

    See Also
    --------
    GridSearchCV : Uses :class:`ParameterGrid` to perform a full parallelized
        parameter search.
    """

    def __init__(self, param_grid):
        if not isinstance(param_grid, (Mapping, Iterable)):
            raise TypeError('Parameter grid is not a dict or '
                            'a list ({!r})'.format(param_grid))

        if isinstance(param_grid, Mapping):
            # wrap dictionary in a singleton list to support either dict
            # or list of dicts
            param_grid = [param_grid]

        # check if all entries are dictionaries of lists
        for grid in param_grid:
            if not isinstance(grid, dict):
                raise TypeError('Parameter grid is not a '
                                'dict ({!r})'.format(grid))
            for key in grid:
                if not isinstance(grid[key], Iterable):
                    raise TypeError('Parameter grid value is not iterable '
                                    '(key={!r}, value={!r})'
                                    .format(key, grid[key]))

        self.param_grid = param_grid

    def __iter__(self):
        """Iterate over the points in the grid.

        Returns
        -------
        params : iterator over dict of str to any
            Yields dictionaries mapping each estimator parameter to one of its
            allowed values.
        """
        for p in self.param_grid:
            # Always sort the keys of a dictionary, for reproducibility
            items = sorted(p.items())
            if not items:
                yield {}
            else:
                keys, values = zip(*items)
                for v in product(*values):
                    params = dict(zip(keys, v))
                    yield params

    def __len__(self):
        """Number of points on the grid."""
        # Product function that can handle iterables (np.product can't).
        product = partial(reduce, operator.mul)
        return sum(product(len(v) for v in p.values()) if p else 1
                   for p in self.param_grid)

    def __getitem__(self, ind):
        """Get the parameters that would be ``ind``th in iteration

        Parameters
        ----------
        ind : int
            The iteration index

        Returns
        -------
        params : dict of str to any
            Equal to list(self)[ind]
        """
        # This is used to make discrete sampling without replacement memory
        # efficient.
        for sub_grid in self.param_grid:
            # XXX: could memoize information used here
            if not sub_grid:
                if ind == 0:
                    return {}
                else:
                    ind -= 1
                    continue

            # Reverse so most frequent cycling parameter comes first
            keys, values_lists = zip(*sorted(sub_grid.items())[::-1])
            sizes = [len(v_list) for v_list in values_lists]
            total = np.product(sizes)

            if ind >= total:
                # Try the next grid
                ind -= total
            else:
                out = {}
                for key, v_list, n in zip(keys, values_lists, sizes):
                    ind, offset = divmod(ind, n)
                    out[key] = v_list[offset]
                return out

        raise IndexError('ParameterGrid index out of range')


class ParameterSampler:
    """Generator on parameters sampled from given distributions.

    Non-deterministic iterable over random candidate combinations for hyper-
    parameter search. If all parameters are presented as a list,
    sampling without replacement is performed. If at least one parameter
    is given as a distribution, sampling with replacement is used.
    It is highly recommended to use continuous distributions for continuous
    parameters.

    Read more in the :ref:`User Guide <grid_search>`.

    Parameters
    ----------
    param_distributions : dict
        Dictionary with parameters names (`str`) as keys and distributions
        or lists of parameters to try. Distributions must provide a ``rvs``
        method for sampling (such as those from scipy.stats.distributions).
        If a list is given, it is sampled uniformly.
        If a list of dicts is given, first a dict is sampled uniformly, and
        then a parameter is sampled using that dict as above.

    n_iter : int
        Number of parameter settings that are produced.

    random_state : int, RandomState instance or None, default=None
        Pseudo random number generator state used for random uniform sampling
        from lists of possible values instead of scipy.stats distributions.
        Pass an int for reproducible output across multiple
        function calls.
        See :term:`Glossary <random_state>`.

    Returns
    -------
    params : dict of str to any
        **Yields** dictionaries mapping each estimator parameter to
        as sampled value.

    Examples
    --------
    >>> from sklearn.model_selection import ParameterSampler
    >>> from scipy.stats.distributions import expon
    >>> import numpy as np
    >>> rng = np.random.RandomState(0)
    >>> param_grid = {'a':[1, 2], 'b': expon()}
    >>> param_list = list(ParameterSampler(param_grid, n_iter=4,
    ...                                    random_state=rng))
    >>> rounded_list = [dict((k, round(v, 6)) for (k, v) in d.items())
    ...                 for d in param_list]
    >>> rounded_list == [{'b': 0.89856, 'a': 1},
    ...                  {'b': 0.923223, 'a': 1},
    ...                  {'b': 1.878964, 'a': 2},
    ...                  {'b': 1.038159, 'a': 2}]
    True
    """
    @_deprecate_positional_args
    def __init__(self, param_distributions, n_iter, *, random_state=None):
        if not isinstance(param_distributions, (Mapping, Iterable)):
            raise TypeError('Parameter distribution is not a dict or '
                            'a list ({!r})'.format(param_distributions))

        if isinstance(param_distributions, Mapping):
            # wrap dictionary in a singleton list to support either dict
            # or list of dicts
            param_distributions = [param_distributions]

        for dist in param_distributions:
            if not isinstance(dist, dict):
                raise TypeError('Parameter distribution is not a '
                                'dict ({!r})'.format(dist))
            for key in dist:
                if (not isinstance(dist[key], Iterable)
                        and not hasattr(dist[key], 'rvs')):
                    raise TypeError('Parameter value is not iterable '
                                    'or distribution (key={!r}, value={!r})'
                                    .format(key, dist[key]))
        self.n_iter = n_iter
        self.random_state = random_state
        self.param_distributions = param_distributions

    def _is_all_lists(self):
        return all(
            all(not hasattr(v, "rvs") for v in dist.values())
            for dist in self.param_distributions
        )

    def __iter__(self):
        rng = check_random_state(self.random_state)

        # if all distributions are given as lists, we want to sample without
        # replacement
        if self._is_all_lists():
            # look up sampled parameter settings in parameter grid
            param_grid = ParameterGrid(self.param_distributions)
            grid_size = len(param_grid)
            n_iter = self.n_iter

            if grid_size < n_iter:
                warnings.warn(
                    'The total space of parameters %d is smaller '
                    'than n_iter=%d. Running %d iterations. For exhaustive '
                    'searches, use GridSearchCV.'
                    % (grid_size, self.n_iter, grid_size), UserWarning)
                n_iter = grid_size
            for i in sample_without_replacement(grid_size, n_iter,
                                                random_state=rng):
                yield param_grid[i]

        else:
            for _ in range(self.n_iter):
                dist = rng.choice(self.param_distributions)
                # Always sort the keys of a dictionary, for reproducibility
                items = sorted(dist.items())
                params = dict()
                for k, v in items:
                    if hasattr(v, "rvs"):
                        params[k] = v.rvs(random_state=rng)
                    else:
                        params[k] = v[rng.randint(len(v))]
                yield params

    def __len__(self):
        """Number of points that will be sampled."""
        if self._is_all_lists():
            grid_size = len(ParameterGrid(self.param_distributions))
            return min(self.n_iter, grid_size)
        else:
            return self.n_iter


# FIXME Remove fit_grid_point in 1.0
@deprecated(
    "fit_grid_point is deprecated in version 0.23 "
    "and will be removed in version 1.0 (renaming of 0.25)"
)
def fit_grid_point(X, y, estimator, parameters, train, test, scorer,
                   verbose, error_score=np.nan, **fit_params):
    """Run fit on one set of parameters.

    Parameters
    ----------
    X : array-like, sparse matrix or list
        Input data.

    y : array-like or None
        Targets for input data.

    estimator : estimator object
        A object of that type is instantiated for each grid point.
        This is assumed to implement the scikit-learn estimator interface.
        Either estimator needs to provide a ``score`` function,
        or ``scoring`` must be passed.

    parameters : dict
        Parameters to be set on estimator for this grid point.

    train : ndarray, dtype int or bool
        Boolean mask or indices for training set.

    test : ndarray, dtype int or bool
        Boolean mask or indices for test set.

    scorer : callable or None
        The scorer callable object / function must have its signature as
        ``scorer(estimator, X, y)``.

        If ``None`` the estimator's score method is used.

    verbose : int
        Verbosity level.

    **fit_params : kwargs
        Additional parameter passed to the fit function of the estimator.

    error_score : 'raise' or numeric, default=np.nan
        Value to assign to the score if an error occurs in estimator fitting.
        If set to 'raise', the error is raised. If a numeric value is given,
        FitFailedWarning is raised. This parameter does not affect the refit
        step, which will always raise the error.

    Returns
    -------
    score : float
         Score of this parameter setting on given test split.

    parameters : dict
        The parameters that have been evaluated.

    n_samples_test : int
        Number of test samples in this split.
    """
    # NOTE we are not using the return value as the scorer by itself should be
    # validated before. We use check_scoring only to reject multimetric scorer
    check_scoring(estimator, scorer)
    results = _fit_and_score(estimator, X, y, scorer, train,
                             test, verbose, parameters,
                             fit_params=fit_params,
                             return_n_test_samples=True,
                             error_score=error_score)
    return results["test_scores"], parameters, results["n_test_samples"]


def _check_param_grid(param_grid):
    if hasattr(param_grid, 'items'):
        param_grid = [param_grid]

    for p in param_grid:
        for name, v in p.items():
            if isinstance(v, np.ndarray) and v.ndim > 1:
                raise ValueError("Parameter array should be one-dimensional.")

            if (isinstance(v, str) or
                    not isinstance(v, (np.ndarray, Sequence))):
                raise ValueError("Parameter grid for parameter ({0}) needs to"
                                 " be a list or numpy array, but got ({1})."
                                 " Single values need to be wrapped in a list"
                                 " with one element.".format(name, type(v)))

            if len(v) == 0:
                raise ValueError("Parameter values for parameter ({0}) need "
                                 "to be a non-empty sequence.".format(name))


class BaseSearchCV(MetaEstimatorMixin, BaseEstimator, metaclass=ABCMeta):
    """Abstract base class for hyper parameter search with cross-validation.
    """

    @abstractmethod
    @_deprecate_positional_args
    def __init__(self, estimator, *, scoring=None, n_jobs=None,
                 refit=True, cv=None, verbose=0,
                 pre_dispatch='2*n_jobs', error_score=np.nan,
                 return_train_score=True):

        self.scoring = scoring
        self.estimator = estimator
        self.n_jobs = n_jobs
        self.refit = refit
        self.cv = cv
        self.verbose = verbose
        self.pre_dispatch = pre_dispatch
        self.error_score = error_score
        self.return_train_score = return_train_score

    @property
    def _estimator_type(self):
        return self.estimator._estimator_type

    def _more_tags(self):
        # allows cross-validation to see 'precomputed' metrics
        return {
            'pairwise': _safe_tags(self.estimator, "pairwise"),
            "_xfail_checks": {"check_supervised_y_2d":
                              "DataConversionWarning not caught"},
        }

    # TODO: Remove in 1.1
    # mypy error: Decorated property not supported
    @deprecated("Attribute _pairwise was deprecated in "  # type: ignore
                "version 0.24 and will be removed in 1.1 (renaming of 0.26).")
    @property
    def _pairwise(self):
        # allows cross-validation to see 'precomputed' metrics
        return getattr(self.estimator, '_pairwise', False)

    def score(self, X, y=None):
        """Returns the score on the given data, if the estimator has been refit.

        This uses the score defined by ``scoring`` where provided, and the
        ``best_estimator_.score`` method otherwise.

        Parameters
        ----------
        X : array-like of shape (n_samples, n_features)
            Input data, where n_samples is the number of samples and
            n_features is the number of features.

        y : array-like of shape (n_samples, n_output) \
            or (n_samples,), default=None
            Target relative to X for classification or regression;
            None for unsupervised learning.

        Returns
        -------
        score : float
        """
        self._check_is_fitted('score')
        if self.scorer_ is None:
            raise ValueError("No score function explicitly defined, "
                             "and the estimator doesn't provide one %s"
                             % self.best_estimator_)
        if isinstance(self.scorer_, dict):
            if self.multimetric_:
                scorer = self.scorer_[self.refit]
            else:
                scorer = self.scorer_
            return scorer(self.best_estimator_, X, y)

        # callable
        score = self.scorer_(self.best_estimator_, X, y)
        if self.multimetric_:
            score = score[self.refit]
        return score

    @if_delegate_has_method(delegate=('best_estimator_', 'estimator'))
    def score_samples(self, X):
        """Call score_samples on the estimator with the best found parameters.

        Only available if ``refit=True`` and the underlying estimator supports
        ``score_samples``.

        .. versionadded:: 0.24

        Parameters
        ----------
        X : iterable
            Data to predict on. Must fulfill input requirements
            of the underlying estimator.

        Returns
        -------
        y_score : ndarray of shape (n_samples,)
        """
        self._check_is_fitted('score_samples')
        return self.best_estimator_.score_samples(X)

    def _check_is_fitted(self, method_name):
        if not self.refit:
            raise NotFittedError('This %s instance was initialized '
                                 'with refit=False. %s is '
                                 'available only after refitting on the best '
                                 'parameters. You can refit an estimator '
                                 'manually using the ``best_params_`` '
                                 'attribute'
                                 % (type(self).__name__, method_name))
        else:
            check_is_fitted(self)

    @if_delegate_has_method(delegate=('best_estimator_', 'estimator'))
    def predict(self, X):
        """Call predict on the estimator with the best found parameters.

        Only available if ``refit=True`` and the underlying estimator supports
        ``predict``.

        Parameters
        ----------
        X : indexable, length n_samples
            Must fulfill the input assumptions of the
            underlying estimator.

        """
        self._check_is_fitted('predict')
        return self.best_estimator_.predict(X)

    @if_delegate_has_method(delegate=('best_estimator_', 'estimator'))
    def predict_proba(self, X):
        """Call predict_proba on the estimator with the best found parameters.

        Only available if ``refit=True`` and the underlying estimator supports
        ``predict_proba``.

        Parameters
        ----------
        X : indexable, length n_samples
            Must fulfill the input assumptions of the
            underlying estimator.

        """
        self._check_is_fitted('predict_proba')
        return self.best_estimator_.predict_proba(X)

    @if_delegate_has_method(delegate=('best_estimator_', 'estimator'))
    def predict_log_proba(self, X):
        """Call predict_log_proba on the estimator with the best found parameters.

        Only available if ``refit=True`` and the underlying estimator supports
        ``predict_log_proba``.

        Parameters
        ----------
        X : indexable, length n_samples
            Must fulfill the input assumptions of the
            underlying estimator.

        """
        self._check_is_fitted('predict_log_proba')
        return self.best_estimator_.predict_log_proba(X)

    @if_delegate_has_method(delegate=('best_estimator_', 'estimator'))
    def decision_function(self, X):
        """Call decision_function on the estimator with the best found parameters.

        Only available if ``refit=True`` and the underlying estimator supports
        ``decision_function``.

        Parameters
        ----------
        X : indexable, length n_samples
            Must fulfill the input assumptions of the
            underlying estimator.

        """
        self._check_is_fitted('decision_function')
        return self.best_estimator_.decision_function(X)

    @if_delegate_has_method(delegate=('best_estimator_', 'estimator'))
    def transform(self, X):
        """Call transform on the estimator with the best found parameters.

        Only available if the underlying estimator supports ``transform`` and
        ``refit=True``.

        Parameters
        ----------
        X : indexable, length n_samples
            Must fulfill the input assumptions of the
            underlying estimator.

        """
        self._check_is_fitted('transform')
        return self.best_estimator_.transform(X)

    @if_delegate_has_method(delegate=('best_estimator_', 'estimator'))
    def inverse_transform(self, Xt):
        """Call inverse_transform on the estimator with the best found params.

        Only available if the underlying estimator implements
        ``inverse_transform`` and ``refit=True``.

        Parameters
        ----------
        Xt : indexable, length n_samples
            Must fulfill the input assumptions of the
            underlying estimator.

        """
        self._check_is_fitted('inverse_transform')
        return self.best_estimator_.inverse_transform(Xt)

    @property
    def n_features_in_(self):
        # For consistency with other estimators we raise a AttributeError so
        # that hasattr() fails if the search estimator isn't fitted.
        try:
            check_is_fitted(self)
        except NotFittedError as nfe:
            raise AttributeError(
                "{} object has no n_features_in_ attribute."
                .format(self.__class__.__name__)
            ) from nfe

        return self.best_estimator_.n_features_in_

    @property
    def classes_(self):
        self._check_is_fitted("classes_")
        return self.best_estimator_.classes_

    def _run_search(self, evaluate_candidates):
        """Repeatedly calls `evaluate_candidates` to conduct a search.

        This method, implemented in sub-classes, makes it possible to
        customize the the scheduling of evaluations: GridSearchCV and
        RandomizedSearchCV schedule evaluations for their whole parameter
        search space at once but other more sequential approaches are also
        possible: for instance is possible to iteratively schedule evaluations
        for new regions of the parameter search space based on previously
        collected evaluation results. This makes it possible to implement
        Bayesian optimization or more generally sequential model-based
        optimization by deriving from the BaseSearchCV abstract base class.
        For example, Successive Halving is implemented by calling
        `evaluate_candidates` multiples times (once per iteration of the SH
        process), each time passing a different set of candidates with `X`
        and `y` of increasing sizes.

        Parameters
        ----------
        evaluate_candidates : callable
            This callback accepts:
                - a list of candidates, where each candidate is a dict of
                  parameter settings.
                - an optional `cv` parameter which can be used to e.g.
                  evaluate candidates on different dataset splits, or
                  evaluate candidates on subsampled data (as done in the
                  SucessiveHaling estimators). By default, the original `cv`
                  parameter is used, and it is available as a private
                  `_checked_cv_orig` attribute.
                - an optional `more_results` dict. Each key will be added to
                  the `cv_results_` attribute. Values should be lists of
                  length `n_candidates`

            It returns a dict of all results so far, formatted like
            ``cv_results_``.

            Important note (relevant whether the default cv is used or not):
            in randomized splitters, and unless the random_state parameter of
            cv was set to an int, calling cv.split() multiple times will
            yield different splits. Since cv.split() is called in
            evaluate_candidates, this means that candidates will be evaluated
            on different splits each time evaluate_candidates is called. This
            might be a methodological issue depending on the search strategy
            that you're implementing. To prevent randomized splitters from
            being used, you may use _split._yields_constant_splits()

        Examples
        --------

        ::

            def _run_search(self, evaluate_candidates):
                'Try C=0.1 only if C=1 is better than C=10'
                all_results = evaluate_candidates([{'C': 1}, {'C': 10}])
                score = all_results['mean_test_score']
                if score[0] < score[1]:
                    evaluate_candidates([{'C': 0.1}])
        """
        raise NotImplementedError("_run_search not implemented.")

    def _check_refit_for_multimetric(self, scores):
        """Check `refit` is compatible with `scores` is valid"""
        multimetric_refit_msg = (
            "For multi-metric scoring, the parameter refit must be set to a "
            "scorer key or a callable to refit an estimator with the best "
            "parameter setting on the whole data and make the best_* "
            "attributes available for that metric. If this is not needed, "
            f"refit should be set to False explicitly. {self.refit!r} was "
            "passed.")

        valid_refit_dict = (isinstance(self.refit, str) and
                            self.refit in scores)

        if (self.refit is not False and not valid_refit_dict
                and not callable(self.refit)):
            raise ValueError(multimetric_refit_msg)

    @_deprecate_positional_args
    def fit(self, X, y=None, *, groups=None, **fit_params):
        """Run fit with all sets of parameters.

        Parameters
        ----------

        X : array-like of shape (n_samples, n_features)
            Training vector, where n_samples is the number of samples and
            n_features is the number of features.

        y : array-like of shape (n_samples, n_output) \
            or (n_samples,), default=None
            Target relative to X for classification or regression;
            None for unsupervised learning.

        groups : array-like of shape (n_samples,), default=None
            Group labels for the samples used while splitting the dataset into
            train/test set. Only used in conjunction with a "Group" :term:`cv`
            instance (e.g., :class:`~sklearn.model_selection.GroupKFold`).

        **fit_params : dict of str -> object
            Parameters passed to the ``fit`` method of the estimator
        """
        estimator = self.estimator
        refit_metric = "score"

        if callable(self.scoring):
            scorers = self.scoring
        elif self.scoring is None or isinstance(self.scoring, str):
            scorers = check_scoring(self.estimator, self.scoring)
        else:
            scorers = _check_multimetric_scoring(self.estimator, self.scoring)
            self._check_refit_for_multimetric(scorers)
            refit_metric = self.refit

        X, y, groups = indexable(X, y, groups)
        fit_params = _check_fit_params(X, fit_params)

        cv_orig = check_cv(self.cv, y, classifier=is_classifier(estimator))
        n_splits = cv_orig.get_n_splits(X, y, groups)

        base_estimator = clone(self.estimator)

        parallel = Parallel(n_jobs=self.n_jobs,
                            pre_dispatch=self.pre_dispatch)

        fit_and_score_kwargs = dict(scorer=scorers,
                                    fit_params=fit_params,
                                    return_train_score=self.return_train_score,
                                    return_n_test_samples=True,
                                    return_times=True,
                                    return_parameters=False,
                                    error_score=self.error_score,
                                    verbose=self.verbose)
        results = {}
        with parallel:
            all_candidate_params = []
            all_out = []
            all_more_results = defaultdict(list)

            def evaluate_candidates(candidate_params, cv=None,
                                    more_results=None):
                cv = cv or cv_orig
                candidate_params = list(candidate_params)
                n_candidates = len(candidate_params)

                if self.verbose > 0:
                    print("Fitting {0} folds for each of {1} candidates,"
                          " totalling {2} fits".format(
                              n_splits, n_candidates, n_candidates * n_splits))

                out = parallel(delayed(_fit_and_score)(clone(base_estimator),
                                                       X, y,
                                                       train=train, test=test,
                                                       parameters=parameters,
                                                       split_progress=(
                                                           split_idx,
                                                           n_splits),
                                                       candidate_progress=(
                                                           cand_idx,
                                                           n_candidates),
                                                       **fit_and_score_kwargs)
                               for (cand_idx, parameters),
                                   (split_idx, (train, test)) in product(
                                   enumerate(candidate_params),
                                   enumerate(cv.split(X, y, groups))))

                if len(out) < 1:
                    raise ValueError('No fits were performed. '
                                     'Was the CV iterator empty? '
                                     'Were there no candidates?')
                elif len(out) != n_candidates * n_splits:
                    raise ValueError('cv.split and cv.get_n_splits returned '
                                     'inconsistent results. Expected {} '
                                     'splits, got {}'
                                     .format(n_splits,
                                             len(out) // n_candidates))

                # For callable self.scoring, the return type is only know after
                # calling. If the return type is a dictionary, the error scores
                # can now be inserted with the correct key. The type checking
                # of out will be done in `_insert_error_scores`.
                if callable(self.scoring):
                    _insert_error_scores(out, self.error_score)
                all_candidate_params.extend(candidate_params)
                all_out.extend(out)
                if more_results is not None:
                    for key, value in more_results.items():
                        all_more_results[key].extend(value)

                nonlocal results
                results = self._format_results(
                    all_candidate_params, n_splits, all_out,
                    all_more_results)

                return results

            self._run_search(evaluate_candidates)

            # multimetric is determined here because in the case of a callable
            # self.scoring the return type is only known after calling
            first_test_score = all_out[0]['test_scores']
            self.multimetric_ = isinstance(first_test_score, dict)

            # check refit_metric now for a callabe scorer that is multimetric
            if callable(self.scoring) and self.multimetric_:
                self._check_refit_for_multimetric(first_test_score)
                refit_metric = self.refit

        # For multi-metric evaluation, store the best_index_, best_params_ and
        # best_score_ iff refit is one of the scorer names
        # In single metric evaluation, refit_metric is "score"
        if self.refit or not self.multimetric_:
            # If callable, refit is expected to return the index of the best
            # parameter set.
            if callable(self.refit):
                self.best_index_ = self.refit(results)
                if not isinstance(self.best_index_, numbers.Integral):
                    raise TypeError('best_index_ returned is not an integer')
                if (self.best_index_ < 0 or
                   self.best_index_ >= len(results["params"])):
                    raise IndexError('best_index_ index out of range')
            else:
                self.best_index_ = results["rank_test_%s"
                                           % refit_metric].argmin()
                self.best_score_ = results["mean_test_%s" % refit_metric][
                                           self.best_index_]
            self.best_params_ = results["params"][self.best_index_]

        if self.refit:
            # we clone again after setting params in case some
            # of the params are estimators as well.
            self.best_estimator_ = clone(clone(base_estimator).set_params(
                **self.best_params_))
            refit_start_time = time.time()
            if y is not None:
                self.best_estimator_.fit(X, y, **fit_params)
            else:
                self.best_estimator_.fit(X, **fit_params)
            refit_end_time = time.time()
            self.refit_time_ = refit_end_time - refit_start_time

        # Store the only scorer not as a dict for single metric evaluation
        self.scorer_ = scorers

        self.cv_results_ = results
        self.n_splits_ = n_splits

        return self

    def _format_results(self, candidate_params, n_splits, out,
                        more_results=None):
        n_candidates = len(candidate_params)
        out = _aggregate_score_dicts(out)

        results = dict(more_results or {})

        def _store(key_name, array, weights=None, splits=False, rank=False):
            """A small helper to store the scores/times to the cv_results_"""
            # When iterated first by splits, then by parameters
            # We want `array` to have `n_candidates` rows and `n_splits` cols.
            array = np.array(array, dtype=np.float64).reshape(n_candidates,
                                                              n_splits)
            if splits:
                for split_idx in range(n_splits):
                    # Uses closure to alter the results
                    results["split%d_%s"
                            % (split_idx, key_name)] = array[:, split_idx]

            array_means = np.average(array, axis=1, weights=weights)
            results['mean_%s' % key_name] = array_means

            if (key_name.startswith(("train_", "test_")) and
                    np.any(~np.isfinite(array_means))):
                warnings.warn(
                    f"One or more of the {key_name.split('_')[0]} scores "
                    f"are non-finite: {array_means}",
                    category=UserWarning
                )

            # Weighted std is not directly available in numpy
            array_stds = np.sqrt(np.average((array -
                                             array_means[:, np.newaxis]) ** 2,
                                            axis=1, weights=weights))
            results['std_%s' % key_name] = array_stds

            if rank:
                results["rank_%s" % key_name] = np.asarray(
                    rankdata(-array_means, method='min'), dtype=np.int32)

        _store('fit_time', out["fit_time"])
        _store('score_time', out["score_time"])
        # Use one MaskedArray and mask all the places where the param is not
        # applicable for that candidate. Use defaultdict as each candidate may
        # not contain all the params
        param_results = defaultdict(partial(MaskedArray,
                                            np.empty(n_candidates,),
                                            mask=True,
                                            dtype=object))
        for cand_idx, params in enumerate(candidate_params):
            for name, value in params.items():
                # An all masked empty array gets created for the key
                # `"param_%s" % name` at the first occurrence of `name`.
                # Setting the value at an index also unmasks that index
                param_results["param_%s" % name][cand_idx] = value

        results.update(param_results)
        # Store a list of param dicts at the key 'params'
        results['params'] = candidate_params

        test_scores_dict = _normalize_score_results(out["test_scores"])
        if self.return_train_score:
            train_scores_dict = _normalize_score_results(out["train_scores"])

        for scorer_name in test_scores_dict:
            # Computed the (weighted) mean and std for test scores alone
            _store('test_%s' % scorer_name, test_scores_dict[scorer_name],
                   splits=True, rank=True,
                   weights=None)
            if self.return_train_score:
                _store('train_%s' % scorer_name,
                       train_scores_dict[scorer_name],
                       splits=True)

        return results


class GridSearchCV(BaseSearchCV):
    """Exhaustive search over specified parameter values for an estimator.

    Important members are fit, predict.

    GridSearchCV implements a "fit" and a "score" method.
    It also implements "score_samples", "predict", "predict_proba",
    "decision_function", "transform" and "inverse_transform" if they are
    implemented in the estimator used.

    The parameters of the estimator used to apply these methods are optimized
    by cross-validated grid-search over a parameter grid.

    Read more in the :ref:`User Guide <grid_search>`.

    Parameters
    ----------
    estimator : estimator object.
        This is assumed to implement the scikit-learn estimator interface.
        Either estimator needs to provide a ``score`` function,
        or ``scoring`` must be passed.

    param_grid : dict or list of dictionaries
        Dictionary with parameters names (`str`) as keys and lists of
        parameter settings to try as values, or a list of such
        dictionaries, in which case the grids spanned by each dictionary
        in the list are explored. This enables searching over any sequence
        of parameter settings.

    scoring : str, callable, list, tuple or dict, default=None
        Strategy to evaluate the performance of the cross-validated model on
        the test set.

        If `scoring` represents a single score, one can use:

        - a single string (see :ref:`scoring_parameter`);
        - a callable (see :ref:`scoring`) that returns a single value.

        If `scoring` represents multiple scores, one can use:

        - a list or tuple of unique strings;
        - a callable returning a dictionary where the keys are the metric
          names and the values are the metric scores;
        - a dictionary with metric names as keys and callables a values.

        See :ref:`multimetric_grid_search` for an example.

    n_jobs : int, default=None
        Number of jobs to run in parallel.
        ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
        ``-1`` means using all processors. See :term:`Glossary <n_jobs>`
        for more details.

        .. versionchanged:: v0.20
           `n_jobs` default changed from 1 to None

    refit : bool, str, or callable, default=True
        Refit an estimator using the best found parameters on the whole
        dataset.

        For multiple metric evaluation, this needs to be a `str` denoting the
        scorer that would be used to find the best parameters for refitting
        the estimator at the end.

        Where there are considerations other than maximum score in
        choosing a best estimator, ``refit`` can be set to a function which
        returns the selected ``best_index_`` given ``cv_results_``. In that
        case, the ``best_estimator_`` and ``best_params_`` will be set
        according to the returned ``best_index_`` while the ``best_score_``
        attribute will not be available.

        The refitted estimator is made available at the ``best_estimator_``
        attribute and permits using ``predict`` directly on this
        ``GridSearchCV`` instance.

        Also for multiple metric evaluation, the attributes ``best_index_``,
        ``best_score_`` and ``best_params_`` will only be available if
        ``refit`` is set and all of them will be determined w.r.t this specific
        scorer.

        See ``scoring`` parameter to know more about multiple metric
        evaluation.

        .. versionchanged:: 0.20
            Support for callable added.

    cv : int, cross-validation generator or an iterable, default=None
        Determines the cross-validation splitting strategy.
        Possible inputs for cv are:

        - None, to use the default 5-fold cross validation,
        - integer, to specify the number of folds in a `(Stratified)KFold`,
        - :term:`CV splitter`,
        - An iterable yielding (train, test) splits as arrays of indices.

        For integer/None inputs, if the estimator is a classifier and ``y`` is
        either binary or multiclass, :class:`StratifiedKFold` is used. In all
        other cases, :class:`KFold` is used.

        Refer :ref:`User Guide <cross_validation>` for the various
        cross-validation strategies that can be used here.

        .. versionchanged:: 0.22
            ``cv`` default value if None changed from 3-fold to 5-fold.

    verbose : int
        Controls the verbosity: the higher, the more messages.

        - >1 : the computation time for each fold and parameter candidate is
          displayed;
        - >2 : the score is also displayed;
        - >3 : the fold and candidate parameter indexes are also displayed
          together with the starting time of the computation.

    pre_dispatch : int, or str, default=n_jobs
        Controls the number of jobs that get dispatched during parallel
        execution. Reducing this number can be useful to avoid an
        explosion of memory consumption when more jobs get dispatched
        than CPUs can process. This parameter can be:

            - None, in which case all the jobs are immediately
              created and spawned. Use this for lightweight and
              fast-running jobs, to avoid delays due to on-demand
              spawning of the jobs

            - An int, giving the exact number of total jobs that are
              spawned

            - A str, giving an expression as a function of n_jobs,
              as in '2*n_jobs'

    error_score : 'raise' or numeric, default=np.nan
        Value to assign to the score if an error occurs in estimator fitting.
        If set to 'raise', the error is raised. If a numeric value is given,
        FitFailedWarning is raised. This parameter does not affect the refit
        step, which will always raise the error.

    return_train_score : bool, default=False
        If ``False``, the ``cv_results_`` attribute will not include training
        scores.
        Computing training scores is used to get insights on how different
        parameter settings impact the overfitting/underfitting trade-off.
        However computing the scores on the training set can be computationally
        expensive and is not strictly required to select the parameters that
        yield the best generalization performance.

        .. versionadded:: 0.19

        .. versionchanged:: 0.21
            Default value was changed from ``True`` to ``False``


    Examples
    --------
    >>> from sklearn import svm, datasets
    >>> from sklearn.model_selection import GridSearchCV
    >>> iris = datasets.load_iris()
    >>> parameters = {'kernel':('linear', 'rbf'), 'C':[1, 10]}
    >>> svc = svm.SVC()
    >>> clf = GridSearchCV(svc, parameters)
    >>> clf.fit(iris.data, iris.target)
    GridSearchCV(estimator=SVC(),
                 param_grid={'C': [1, 10], 'kernel': ('linear', 'rbf')})
    >>> sorted(clf.cv_results_.keys())
    ['mean_fit_time', 'mean_score_time', 'mean_test_score',...
     'param_C', 'param_kernel', 'params',...
     'rank_test_score', 'split0_test_score',...
     'split2_test_score', ...
     'std_fit_time', 'std_score_time', 'std_test_score']

    Attributes
    ----------
    cv_results_ : dict of numpy (masked) ndarrays
        A dict with keys as column headers and values as columns, that can be
        imported into a pandas ``DataFrame``.

        For instance the below given table

        +------------+-----------+------------+-----------------+---+---------+
        |param_kernel|param_gamma|param_degree|split0_test_score|...|rank_t...|
        +============+===========+============+=================+===+=========+
        |  'poly'    |     --    |      2     |       0.80      |...|    2    |
        +------------+-----------+------------+-----------------+---+---------+
        |  'poly'    |     --    |      3     |       0.70      |...|    4    |
        +------------+-----------+------------+-----------------+---+---------+
        |  'rbf'     |     0.1   |     --     |       0.80      |...|    3    |
        +------------+-----------+------------+-----------------+---+---------+
        |  'rbf'     |     0.2   |     --     |       0.93      |...|    1    |
        +------------+-----------+------------+-----------------+---+---------+

        will be represented by a ``cv_results_`` dict of::

            {
            'param_kernel': masked_array(data = ['poly', 'poly', 'rbf', 'rbf'],
                                         mask = [False False False False]...)
            'param_gamma': masked_array(data = [-- -- 0.1 0.2],
                                        mask = [ True  True False False]...),
            'param_degree': masked_array(data = [2.0 3.0 -- --],
                                         mask = [False False  True  True]...),
            'split0_test_score'  : [0.80, 0.70, 0.80, 0.93],
            'split1_test_score'  : [0.82, 0.50, 0.70, 0.78],
            'mean_test_score'    : [0.81, 0.60, 0.75, 0.85],
            'std_test_score'     : [0.01, 0.10, 0.05, 0.08],
            'rank_test_score'    : [2, 4, 3, 1],
            'split0_train_score' : [0.80, 0.92, 0.70, 0.93],
            'split1_train_score' : [0.82, 0.55, 0.70, 0.87],
            'mean_train_score'   : [0.81, 0.74, 0.70, 0.90],
            'std_train_score'    : [0.01, 0.19, 0.00, 0.03],
            'mean_fit_time'      : [0.73, 0.63, 0.43, 0.49],
            'std_fit_time'       : [0.01, 0.02, 0.01, 0.01],
            'mean_score_time'    : [0.01, 0.06, 0.04, 0.04],
            'std_score_time'     : [0.00, 0.00, 0.00, 0.01],
            'params'             : [{'kernel': 'poly', 'degree': 2}, ...],
            }

        NOTE

        The key ``'params'`` is used to store a list of parameter
        settings dicts for all the parameter candidates.

        The ``mean_fit_time``, ``std_fit_time``, ``mean_score_time`` and
        ``std_score_time`` are all in seconds.

        For multi-metric evaluation, the scores for all the scorers are
        available in the ``cv_results_`` dict at the keys ending with that
        scorer's name (``'_<scorer_name>'``) instead of ``'_score'`` shown
        above. ('split0_test_precision', 'mean_train_precision' etc.)

    best_estimator_ : estimator
        Estimator that was chosen by the search, i.e. estimator
        which gave highest score (or smallest loss if specified)
        on the left out data. Not available if ``refit=False``.

        See ``refit`` parameter for more information on allowed values.

    best_score_ : float
        Mean cross-validated score of the best_estimator

        For multi-metric evaluation, this is present only if ``refit`` is
        specified.

        This attribute is not available if ``refit`` is a function.

    best_params_ : dict
        Parameter setting that gave the best results on the hold out data.

        For multi-metric evaluation, this is present only if ``refit`` is
        specified.

    best_index_ : int
        The index (of the ``cv_results_`` arrays) which corresponds to the best
        candidate parameter setting.

        The dict at ``search.cv_results_['params'][search.best_index_]`` gives
        the parameter setting for the best model, that gives the highest
        mean score (``search.best_score_``).

        For multi-metric evaluation, this is present only if ``refit`` is
        specified.

    scorer_ : function or a dict
        Scorer function used on the held out data to choose the best
        parameters for the model.

        For multi-metric evaluation, this attribute holds the validated
        ``scoring`` dict which maps the scorer key to the scorer callable.

    n_splits_ : int
        The number of cross-validation splits (folds/iterations).

    refit_time_ : float
        Seconds used for refitting the best model on the whole dataset.

        This is present only if ``refit`` is not False.

        .. versionadded:: 0.20

    multimetric_ : bool
        Whether or not the scorers compute several metrics.

    Notes
    -----
    The parameters selected are those that maximize the score of the left out
    data, unless an explicit score is passed in which case it is used instead.

    If `n_jobs` was set to a value higher than one, the data is copied for each
    point in the grid (and not `n_jobs` times). This is done for efficiency
    reasons if individual jobs take very little time, but may raise errors if
    the dataset is large and not enough memory is available.  A workaround in
    this case is to set `pre_dispatch`. Then, the memory is copied only
    `pre_dispatch` many times. A reasonable value for `pre_dispatch` is `2 *
    n_jobs`.

    See Also
    ---------
    ParameterGrid : Generates all the combinations of a hyperparameter grid.
    train_test_split : Utility function to split the data into a development
        set usable for fitting a GridSearchCV instance and an evaluation set
        for its final evaluation.
    sklearn.metrics.make_scorer : Make a scorer from a performance metric or
        loss function.

    """
    _required_parameters = ["estimator", "param_grid"]

    @_deprecate_positional_args
    def __init__(self, estimator, param_grid, *, scoring=None,
                 n_jobs=None, refit=True, cv=None,
                 verbose=0, pre_dispatch='2*n_jobs',
                 error_score=np.nan, return_train_score=False):
        super().__init__(
            estimator=estimator, scoring=scoring,
            n_jobs=n_jobs, refit=refit, cv=cv, verbose=verbose,
            pre_dispatch=pre_dispatch, error_score=error_score,
            return_train_score=return_train_score)
        self.param_grid = param_grid
        _check_param_grid(param_grid)

    def _run_search(self, evaluate_candidates):
        """Search all candidates in param_grid"""
        evaluate_candidates(ParameterGrid(self.param_grid))


class RandomizedSearchCV(BaseSearchCV):
    """Randomized search on hyper parameters.

    RandomizedSearchCV implements a "fit" and a "score" method.
    It also implements "score_samples", "predict", "predict_proba",
    "decision_function", "transform" and "inverse_transform" if they are
    implemented in the estimator used.

    The parameters of the estimator used to apply these methods are optimized
    by cross-validated search over parameter settings.

    In contrast to GridSearchCV, not all parameter values are tried out, but
    rather a fixed number of parameter settings is sampled from the specified
    distributions. The number of parameter settings that are tried is
    given by n_iter.

    If all parameters are presented as a list,
    sampling without replacement is performed. If at least one parameter
    is given as a distribution, sampling with replacement is used.
    It is highly recommended to use continuous distributions for continuous
    parameters.

    Read more in the :ref:`User Guide <randomized_parameter_search>`.

    .. versionadded:: 0.14

    Parameters
    ----------
    estimator : estimator object.
        A object of that type is instantiated for each grid point.
        This is assumed to implement the scikit-learn estimator interface.
        Either estimator needs to provide a ``score`` function,
        or ``scoring`` must be passed.

    param_distributions : dict or list of dicts
        Dictionary with parameters names (`str`) as keys and distributions
        or lists of parameters to try. Distributions must provide a ``rvs``
        method for sampling (such as those from scipy.stats.distributions).
        If a list is given, it is sampled uniformly.
        If a list of dicts is given, first a dict is sampled uniformly, and
        then a parameter is sampled using that dict as above.

    n_iter : int, default=10
        Number of parameter settings that are sampled. n_iter trades
        off runtime vs quality of the solution.

    scoring : str, callable, list, tuple or dict, default=None
        Strategy to evaluate the performance of the cross-validated model on
        the test set.

        If `scoring` represents a single score, one can use:

        - a single string (see :ref:`scoring_parameter`);
        - a callable (see :ref:`scoring`) that returns a single value.

        If `scoring` represents multiple scores, one can use:

        - a list or tuple of unique strings;
        - a callable returning a dictionary where the keys are the metric
          names and the values are the metric scores;
        - a dictionary with metric names as keys and callables a values.

        See :ref:`multimetric_grid_search` for an example.

        If None, the estimator's score method is used.

    n_jobs : int, default=None
        Number of jobs to run in parallel.
        ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
        ``-1`` means using all processors. See :term:`Glossary <n_jobs>`
        for more details.

        .. versionchanged:: v0.20
           `n_jobs` default changed from 1 to None

    refit : bool, str, or callable, default=True
        Refit an estimator using the best found parameters on the whole
        dataset.

        For multiple metric evaluation, this needs to be a `str` denoting the
        scorer that would be used to find the best parameters for refitting
        the estimator at the end.

        Where there are considerations other than maximum score in
        choosing a best estimator, ``refit`` can be set to a function which
        returns the selected ``best_index_`` given the ``cv_results``. In that
        case, the ``best_estimator_`` and ``best_params_`` will be set
        according to the returned ``best_index_`` while the ``best_score_``
        attribute will not be available.

        The refitted estimator is made available at the ``best_estimator_``
        attribute and permits using ``predict`` directly on this
        ``RandomizedSearchCV`` instance.

        Also for multiple metric evaluation, the attributes ``best_index_``,
        ``best_score_`` and ``best_params_`` will only be available if
        ``refit`` is set and all of them will be determined w.r.t this specific
        scorer.

        See ``scoring`` parameter to know more about multiple metric
        evaluation.

        .. versionchanged:: 0.20
            Support for callable added.

    cv : int, cross-validation generator or an iterable, default=None
        Determines the cross-validation splitting strategy.
        Possible inputs for cv are:

        - None, to use the default 5-fold cross validation,
        - integer, to specify the number of folds in a `(Stratified)KFold`,
        - :term:`CV splitter`,
        - An iterable yielding (train, test) splits as arrays of indices.

        For integer/None inputs, if the estimator is a classifier and ``y`` is
        either binary or multiclass, :class:`StratifiedKFold` is used. In all
        other cases, :class:`KFold` is used.

        Refer :ref:`User Guide <cross_validation>` for the various
        cross-validation strategies that can be used here.

        .. versionchanged:: 0.22
            ``cv`` default value if None changed from 3-fold to 5-fold.

    verbose : int
        Controls the verbosity: the higher, the more messages.

    pre_dispatch : int, or str, default=None
        Controls the number of jobs that get dispatched during parallel
        execution. Reducing this number can be useful to avoid an
        explosion of memory consumption when more jobs get dispatched
        than CPUs can process. This parameter can be:

            - None, in which case all the jobs are immediately
              created and spawned. Use this for lightweight and
              fast-running jobs, to avoid delays due to on-demand
              spawning of the jobs

            - An int, giving the exact number of total jobs that are
              spawned

            - A str, giving an expression as a function of n_jobs,
              as in '2*n_jobs'

    random_state : int, RandomState instance or None, default=None
        Pseudo random number generator state used for random uniform sampling
        from lists of possible values instead of scipy.stats distributions.
        Pass an int for reproducible output across multiple
        function calls.
        See :term:`Glossary <random_state>`.

    error_score : 'raise' or numeric, default=np.nan
        Value to assign to the score if an error occurs in estimator fitting.
        If set to 'raise', the error is raised. If a numeric value is given,
        FitFailedWarning is raised. This parameter does not affect the refit
        step, which will always raise the error.

    return_train_score : bool, default=False
        If ``False``, the ``cv_results_`` attribute will not include training
        scores.
        Computing training scores is used to get insights on how different
        parameter settings impact the overfitting/underfitting trade-off.
        However computing the scores on the training set can be computationally
        expensive and is not strictly required to select the parameters that
        yield the best generalization performance.

        .. versionadded:: 0.19

        .. versionchanged:: 0.21
            Default value was changed from ``True`` to ``False``

    Attributes
    ----------
    cv_results_ : dict of numpy (masked) ndarrays
        A dict with keys as column headers and values as columns, that can be
        imported into a pandas ``DataFrame``.

        For instance the below given table

        +--------------+-------------+-------------------+---+---------------+
        | param_kernel | param_gamma | split0_test_score |...|rank_test_score|
        +==============+=============+===================+===+===============+
        |    'rbf'     |     0.1     |       0.80        |...|       1       |
        +--------------+-------------+-------------------+---+---------------+
        |    'rbf'     |     0.2     |       0.84        |...|       3       |
        +--------------+-------------+-------------------+---+---------------+
        |    'rbf'     |     0.3     |       0.70        |...|       2       |
        +--------------+-------------+-------------------+---+---------------+

        will be represented by a ``cv_results_`` dict of::

            {
            'param_kernel' : masked_array(data = ['rbf', 'rbf', 'rbf'],
                                          mask = False),
            'param_gamma'  : masked_array(data = [0.1 0.2 0.3], mask = False),
            'split0_test_score'  : [0.80, 0.84, 0.70],
            'split1_test_score'  : [0.82, 0.50, 0.70],
            'mean_test_score'    : [0.81, 0.67, 0.70],
            'std_test_score'     : [0.01, 0.24, 0.00],
            'rank_test_score'    : [1, 3, 2],
            'split0_train_score' : [0.80, 0.92, 0.70],
            'split1_train_score' : [0.82, 0.55, 0.70],
            'mean_train_score'   : [0.81, 0.74, 0.70],
            'std_train_score'    : [0.01, 0.19, 0.00],
            'mean_fit_time'      : [0.73, 0.63, 0.43],
            'std_fit_time'       : [0.01, 0.02, 0.01],
            'mean_score_time'    : [0.01, 0.06, 0.04],
            'std_score_time'     : [0.00, 0.00, 0.00],
            'params'             : [{'kernel' : 'rbf', 'gamma' : 0.1}, ...],
            }

        NOTE

        The key ``'params'`` is used to store a list of parameter
        settings dicts for all the parameter candidates.

        The ``mean_fit_time``, ``std_fit_time``, ``mean_score_time`` and
        ``std_score_time`` are all in seconds.

        For multi-metric evaluation, the scores for all the scorers are
        available in the ``cv_results_`` dict at the keys ending with that
        scorer's name (``'_<scorer_name>'``) instead of ``'_score'`` shown
        above. ('split0_test_precision', 'mean_train_precision' etc.)

    best_estimator_ : estimator
        Estimator that was chosen by the search, i.e. estimator
        which gave highest score (or smallest loss if specified)
        on the left out data. Not available if ``refit=False``.

        For multi-metric evaluation, this attribute is present only if
        ``refit`` is specified.

        See ``refit`` parameter for more information on allowed values.

    best_score_ : float
        Mean cross-validated score of the best_estimator.

        For multi-metric evaluation, this is not available if ``refit`` is
        ``False``. See ``refit`` parameter for more information.

        This attribute is not available if ``refit`` is a function.

    best_params_ : dict
        Parameter setting that gave the best results on the hold out data.

        For multi-metric evaluation, this is not available if ``refit`` is
        ``False``. See ``refit`` parameter for more information.

    best_index_ : int
        The index (of the ``cv_results_`` arrays) which corresponds to the best
        candidate parameter setting.

        The dict at ``search.cv_results_['params'][search.best_index_]`` gives
        the parameter setting for the best model, that gives the highest
        mean score (``search.best_score_``).

        For multi-metric evaluation, this is not available if ``refit`` is
        ``False``. See ``refit`` parameter for more information.

    scorer_ : function or a dict
        Scorer function used on the held out data to choose the best
        parameters for the model.

        For multi-metric evaluation, this attribute holds the validated
        ``scoring`` dict which maps the scorer key to the scorer callable.

    n_splits_ : int
        The number of cross-validation splits (folds/iterations).

    refit_time_ : float
        Seconds used for refitting the best model on the whole dataset.

        This is present only if ``refit`` is not False.

        .. versionadded:: 0.20

    multimetric_ : bool
        Whether or not the scorers compute several metrics.

    Notes
    -----
    The parameters selected are those that maximize the score of the held-out
    data, according to the scoring parameter.

    If `n_jobs` was set to a value higher than one, the data is copied for each
    parameter setting(and not `n_jobs` times). This is done for efficiency
    reasons if individual jobs take very little time, but may raise errors if
    the dataset is large and not enough memory is available.  A workaround in
    this case is to set `pre_dispatch`. Then, the memory is copied only
    `pre_dispatch` many times. A reasonable value for `pre_dispatch` is `2 *
    n_jobs`.

    See Also
    --------
    GridSearchCV : Does exhaustive search over a grid of parameters.
    ParameterSampler : A generator over parameter settings, constructed from
        param_distributions.

    Examples
    --------
    >>> from sklearn.datasets import load_iris
    >>> from sklearn.linear_model import LogisticRegression
    >>> from sklearn.model_selection import RandomizedSearchCV
    >>> from scipy.stats import uniform
    >>> iris = load_iris()
    >>> logistic = LogisticRegression(solver='saga', tol=1e-2, max_iter=200,
    ...                               random_state=0)
    >>> distributions = dict(C=uniform(loc=0, scale=4),
    ...                      penalty=['l2', 'l1'])
    >>> clf = RandomizedSearchCV(logistic, distributions, random_state=0)
    >>> search = clf.fit(iris.data, iris.target)
    >>> search.best_params_
    {'C': 2..., 'penalty': 'l1'}
    """
    _required_parameters = ["estimator", "param_distributions"]

    @_deprecate_positional_args
    def __init__(self, estimator, param_distributions, *, n_iter=10,
                 scoring=None, n_jobs=None, refit=True,
                 cv=None, verbose=0, pre_dispatch='2*n_jobs',
                 random_state=None, error_score=np.nan,
                 return_train_score=False):
        self.param_distributions = param_distributions
        self.n_iter = n_iter
        self.random_state = random_state
        super().__init__(
            estimator=estimator, scoring=scoring,
            n_jobs=n_jobs, refit=refit, cv=cv, verbose=verbose,
            pre_dispatch=pre_dispatch, error_score=error_score,
            return_train_score=return_train_score)

    def _run_search(self, evaluate_candidates):
        """Search n_iter candidates from param_distributions"""
        evaluate_candidates(ParameterSampler(
            self.param_distributions, self.n_iter,
            random_state=self.random_state))