content: """
  The :mod:`sklearn.model_selection._validation` module includes classes and
  functions to validate the model.
  """
  
  # Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
  #         Gael Varoquaux <gael.varoquaux@normalesup.org>
  #         Olivier Grisel <olivier.grisel@ensta.org>
  #         Raghav RV <rvraghav93@gmail.com>
  # License: BSD 3 clause
  
  from __future__ import print_function
  from __future__ import division
  
  import warnings
  import numbers
  import time
  
  import numpy as np
  import scipy.sparse as sp
  
  from ..base import is_classifier, clone
  from ..utils import indexable, check_random_state, safe_indexing
  from ..utils.deprecation import DeprecationDict
  from ..utils.validation import _is_arraylike, _num_samples
  from ..utils.metaestimators import _safe_split
  from ..externals.joblib import Parallel, delayed, logger
  from ..externals.six.moves import zip
  from ..metrics.scorer import check_scoring, _check_multimetric_scoring
  from ..exceptions import FitFailedWarning
  from ._split import check_cv
  from ..preprocessing import LabelEncoder
  
  
  __all__ = ['cross_validate', 'cross_val_score', 'cross_val_predict',
             'permutation_test_score', 'learning_curve', 'validation_curve']
  
  
  def cross_validate(estimator, X, y=None, groups=None, scoring=None, cv=None,
                     n_jobs=1, verbose=0, fit_params=None,
                     pre_dispatch='2*n_jobs', return_train_score="warn"):
      """Evaluate metric(s) by cross-validation and also record fit/score times.
  
      Read more in the :ref:`User Guide <multimetric_cross_validation>`.
  
      Parameters
      ----------
      estimator : estimator object implementing 'fit'
          The object to use to fit the data.
  
      X : array-like
          The data to fit. Can be for example a list, or an array.
  
      y : array-like, optional, default: None
          The target variable to try to predict in the case of
          supervised learning.
  
      groups : array-like, with shape (n_samples,), optional
          Group labels for the samples used while splitting the dataset into
          train/test set.
  
      scoring : string, callable, list/tuple, dict or None, default: None
          A single string (see :ref:`scoring_parameter`) or a callable
          (see :ref:`scoring`) to evaluate the predictions on the test set.
  
          For evaluating multiple metrics, either give a list of (unique) strings
          or a dict with names as keys and callables as values.
  
          NOTE that when using custom scorers, each scorer should return a single
          value. Metric functions returning a list/array of values can be wrapped
          into multiple scorers that return one value each.
  
          See :ref:`multimetric_grid_search` for an example.
  
          If None, the estimator's default scorer (if available) is used.
  
      cv : int, cross-validation generator or an iterable, optional
          Determines the cross-validation splitting strategy.
          Possible inputs for cv are:
            - None, to use the default 3-fold cross validation,
            - integer, to specify the number of folds in a `(Stratified)KFold`,
            - An object to be used as a cross-validation generator.
            - An iterable yielding train, test splits.
  
          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.
  
      n_jobs : integer, optional
          The number of CPUs to use to do the computation. -1 means
          'all CPUs'.
  
      verbose : integer, optional
          The verbosity level.
  
      fit_params : dict, optional
          Parameters to pass to the fit method of the estimator.
  
      pre_dispatch : int, or string, optional
          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 string, giving an expression as a function of n_jobs,
                as in '2*n_jobs'
  
      return_train_score : boolean, optional
          Whether to include train scores.
  
          Current default is ``'warn'``, which behaves as ``True`` in addition
          to raising a warning when a training score is looked up.
          That default will be changed to ``False`` in 0.21.
          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.
  
      Returns
      -------
      scores : dict of float arrays of shape=(n_splits,)
          Array of scores of the estimator for each run of the cross validation.
  
          A dict of arrays containing the score/time arrays for each scorer is
          returned. The possible keys for this ``dict`` are:
  
              ``test_score``
                  The score array for test scores on each cv split.
              ``train_score``
                  The score array for train scores on each cv split.
                  This is available only if ``return_train_score`` parameter
                  is ``True``.
              ``fit_time``
                  The time for fitting the estimator on the train
                  set for each cv split.
              ``score_time``
                  The time for scoring the estimator on the test set for each
                  cv split. (Note time for scoring on the train set is not
                  included even if ``return_train_score`` is set to ``True``
  
      Examples
      --------
      >>> from sklearn import datasets, linear_model
      >>> from sklearn.model_selection import cross_validate
      >>> from sklearn.metrics.scorer import make_scorer
      >>> from sklearn.metrics import confusion_matrix
      >>> from sklearn.svm import LinearSVC
      >>> diabetes = datasets.load_diabetes()
      >>> X = diabetes.data[:150]
      >>> y = diabetes.target[:150]
      >>> lasso = linear_model.Lasso()
  
      Single metric evaluation using ``cross_validate``
  
      >>> cv_results = cross_validate(lasso, X, y, return_train_score=False)
      >>> sorted(cv_results.keys())                         # doctest: +ELLIPSIS
      ['fit_time', 'score_time', 'test_score']
      >>> cv_results['test_score']    # doctest: +ELLIPSIS +NORMALIZE_WHITESPACE
      array([ 0.33...,  0.08...,  0.03...])
  
      Multiple metric evaluation using ``cross_validate``
      (please refer the ``scoring`` parameter doc for more information)
  
      >>> scores = cross_validate(lasso, X, y,
      ...                         scoring=('r2', 'neg_mean_squared_error'))
      >>> print(scores['test_neg_mean_squared_error'])      # doctest: +ELLIPSIS
      [-3635.5... -3573.3... -6114.7...]
      >>> print(scores['train_r2'])                         # doctest: +ELLIPSIS
      [ 0.28...  0.39...  0.22...]
  
      See Also
      ---------
      :func:`sklearn.model_selection.cross_val_score`:
          Run cross-validation for single metric evaluation.
  
      :func:`sklearn.metrics.make_scorer`:
          Make a scorer from a performance metric or loss function.
  
      """
      X, y, groups = indexable(X, y, groups)
  
      cv = check_cv(cv, y, classifier=is_classifier(estimator))
      scorers, _ = _check_multimetric_scoring(estimator, scoring=scoring)
  
      # We clone the estimator to make sure that all the folds are
      # independent, and that it is pickle-able.
      parallel = Parallel(n_jobs=n_jobs, verbose=verbose,
                          pre_dispatch=pre_dispatch)
      scores = parallel(
          delayed(_fit_and_score)(
              clone(estimator), X, y, scorers, train, test, verbose, None,
              fit_params, return_train_score=return_train_score,
              return_times=True)
          for train, test in cv.split(X, y, groups))
  
      if return_train_score:
          train_scores, test_scores, fit_times, score_times = zip(*scores)
          train_scores = _aggregate_score_dicts(train_scores)
      else:
          test_scores, fit_times, score_times = zip(*scores)
      test_scores = _aggregate_score_dicts(test_scores)
  
      # TODO: replace by a dict in 0.21
      ret = DeprecationDict() if return_train_score == 'warn' else {}
      ret['fit_time'] = np.array(fit_times)
      ret['score_time'] = np.array(score_times)
  
      for name in scorers:
          ret['test_%s' % name] = np.array(test_scores[name])
          if return_train_score:
              key = 'train_%s' % name
              ret[key] = np.array(train_scores[name])
              if return_train_score == 'warn':
                  message = (
                      'You are accessing a training score ({!r}), '
                      'which will not be available by default '
                      'any more in 0.21. If you need training scores, '
                      'please set return_train_score=True').format(key)
                  # warn on key access
                  ret.add_warning(key, message, FutureWarning)
  
      return ret
  
  
  def cross_val_score(estimator, X, y=None, groups=None, scoring=None, cv=None,
                      n_jobs=1, verbose=0, fit_params=None,
                      pre_dispatch='2*n_jobs'):
      """Evaluate a score by cross-validation
  
      Read more in the :ref:`User Guide <cross_validation>`.
  
      Parameters
      ----------
      estimator : estimator object implementing 'fit'
          The object to use to fit the data.
  
      X : array-like
          The data to fit. Can be for example a list, or an array.
  
      y : array-like, optional, default: None
          The target variable to try to predict in the case of
          supervised learning.
  
      groups : array-like, with shape (n_samples,), optional
          Group labels for the samples used while splitting the dataset into
          train/test set.
  
      scoring : string, callable or None, optional, default: None
          A string (see model evaluation documentation) or
          a scorer callable object / function with signature
          ``scorer(estimator, X, y)``.
  
      cv : int, cross-validation generator or an iterable, optional
          Determines the cross-validation splitting strategy.
          Possible inputs for cv are:
  
          - None, to use the default 3-fold cross validation,
          - integer, to specify the number of folds in a `(Stratified)KFold`,
          - An object to be used as a cross-validation generator.
          - An iterable yielding train, test splits.
  
          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.
  
      n_jobs : integer, optional
          The number of CPUs to use to do the computation. -1 means
          'all CPUs'.
  
      verbose : integer, optional
          The verbosity level.
  
      fit_params : dict, optional
          Parameters to pass to the fit method of the estimator.
  
      pre_dispatch : int, or string, optional
          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 string, giving an expression as a function of n_jobs,
                as in '2*n_jobs'
  
      Returns
      -------
      scores : array of float, shape=(len(list(cv)),)
          Array of scores of the estimator for each run of the cross validation.
  
      Examples
      --------
      >>> from sklearn import datasets, linear_model
      >>> from sklearn.model_selection import cross_val_score
      >>> diabetes = datasets.load_diabetes()
      >>> X = diabetes.data[:150]
      >>> y = diabetes.target[:150]
      >>> lasso = linear_model.Lasso()
      >>> print(cross_val_score(lasso, X, y))  # doctest: +ELLIPSIS
      [ 0.33150734  0.08022311  0.03531764]
  
      See Also
      ---------
      :func:`sklearn.model_selection.cross_validate`:
          To run cross-validation on multiple metrics and also to return
          train scores, fit times and score times.
  
      :func:`sklearn.metrics.make_scorer`:
          Make a scorer from a performance metric or loss function.
  
      """
      # To ensure multimetric format is not supported
      scorer = check_scoring(estimator, scoring=scoring)
  
      cv_results = cross_validate(estimator=estimator, X=X, y=y, groups=groups,
                                  scoring={'score': scorer}, cv=cv,
                                  return_train_score=False,
                                  n_jobs=n_jobs, verbose=verbose,
                                  fit_params=fit_params,
                                  pre_dispatch=pre_dispatch)
      return cv_results['test_score']
  
  
  def _fit_and_score(estimator, X, y, scorer, train, test, verbose,
                     parameters, fit_params, return_train_score=False,
                     return_parameters=False, return_n_test_samples=False,
                     return_times=False, error_score='raise'):
      """Fit estimator and compute scores for a given dataset split.
  
      Parameters
      ----------
      estimator : estimator object implementing 'fit'
          The object to use to fit the data.
  
      X : array-like of shape at least 2D
          The data to fit.
  
      y : array-like, optional, default: None
          The target variable to try to predict in the case of
          supervised learning.
  
      scorer : A single callable or dict mapping scorer name to the callable
          If it is a single callable, the return value for ``train_scores`` and
          ``test_scores`` is a single float.
  
          For a dict, it should be one mapping the scorer name to the scorer
          callable object / function.
  
          The callable object / fn should have signature
          ``scorer(estimator, X, y)``.
  
      train : array-like, shape (n_train_samples,)
          Indices of training samples.
  
      test : array-like, shape (n_test_samples,)
          Indices of test samples.
  
      verbose : integer
          The verbosity level.
  
      error_score : 'raise' (default) or numeric
          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.
  
      parameters : dict or None
          Parameters to be set on the estimator.
  
      fit_params : dict or None
          Parameters that will be passed to ``estimator.fit``.
  
      return_train_score : boolean, optional, default: False
          Compute and return score on training set.
  
      return_parameters : boolean, optional, default: False
          Return parameters that has been used for the estimator.
  
      return_n_test_samples : boolean, optional, default: False
          Whether to return the ``n_test_samples``
  
      return_times : boolean, optional, default: False
          Whether to return the fit/score times.
  
      Returns
      -------
      train_scores : dict of scorer name -> float, optional
          Score on training set (for all the scorers),
          returned only if `return_train_score` is `True`.
  
      test_scores : dict of scorer name -> float, optional
          Score on testing set (for all the scorers).
  
      n_test_samples : int
          Number of test samples.
  
      fit_time : float
          Time spent for fitting in seconds.
  
      score_time : float
          Time spent for scoring in seconds.
  
      parameters : dict or None, optional
          The parameters that have been evaluated.
      """
      if verbose > 1:
          if parameters is None:
              msg = ''
          else:
              msg = '%s' % (', '.join('%s=%s' % (k, v)
                            for k, v in parameters.items()))
          print("[CV] %s %s" % (msg, (64 - len(msg)) * '.'))
  
      # Adjust length of sample weights
      fit_params = fit_params if fit_params is not None else {}
      fit_params = dict([(k, _index_param_value(X, v, train))
                        for k, v in fit_params.items()])
  
      test_scores = {}
      train_scores = {}
      if parameters is not None:
          estimator.set_params(**parameters)
  
      start_time = time.time()
  
      X_train, y_train = _safe_split(estimator, X, y, train)
      X_test, y_test = _safe_split(estimator, X, y, test, train)
  
      is_multimetric = not callable(scorer)
      n_scorers = len(scorer.keys()) if is_multimetric else 1
  
      try:
          if y_train is None:
              estimator.fit(X_train, **fit_params)
          else:
              estimator.fit(X_train, y_train, **fit_params)
  
      except Exception as e:
          # Note fit time as time until error
          fit_time = time.time() - start_time
          score_time = 0.0
          if error_score == 'raise':
              raise
          elif isinstance(error_score, numbers.Number):
              if is_multimetric:
                  test_scores = dict(zip(scorer.keys(),
                                     [error_score, ] * n_scorers))
                  if return_train_score:
                      train_scores = dict(zip(scorer.keys(),
                                          [error_score, ] * n_scorers))
              else:
                  test_scores = error_score
                  if return_train_score:
                      train_scores = error_score
              warnings.warn("Classifier fit failed. The score on this train-test"
                            " partition for these parameters will be set to %f. "
                            "Details: \n%r" % (error_score, e), FitFailedWarning)
          else:
              raise ValueError("error_score must be the string 'raise' or a"
                               " numeric value. (Hint: if using 'raise', please"
                               " make sure that it has been spelled correctly.)")
  
      else:
          fit_time = time.time() - start_time
          # _score will return dict if is_multimetric is True
          test_scores = _score(estimator, X_test, y_test, scorer, is_multimetric)
          score_time = time.time() - start_time - fit_time
          if return_train_score:
              train_scores = _score(estimator, X_train, y_train, scorer,
                                    is_multimetric)
  
      if verbose > 2:
          if is_multimetric:
              for scorer_name, score in test_scores.items():
                  msg += ", %s=%s" % (scorer_name, score)
          else:
              msg += ", score=%s" % test_scores
      if verbose > 1:
          total_time = score_time + fit_time
          end_msg = "%s, total=%s" % (msg, logger.short_format_time(total_time))
          print("[CV] %s %s" % ((64 - len(end_msg)) * '.', end_msg))
  
      ret = [train_scores, test_scores] if return_train_score else [test_scores]
  
      if return_n_test_samples:
          ret.append(_num_samples(X_test))
      if return_times:
          ret.extend([fit_time, score_time])
      if return_parameters:
          ret.append(parameters)
      return ret
  
  
  def _score(estimator, X_test, y_test, scorer, is_multimetric=False):
      """Compute the score(s) of an estimator on a given test set.
  
      Will return a single float if is_multimetric is False and a dict of floats,
      if is_multimetric is True
      """
      if is_multimetric:
          return _multimetric_score(estimator, X_test, y_test, scorer)
      else:
          if y_test is None:
              score = scorer(estimator, X_test)
          else:
              score = scorer(estimator, X_test, y_test)
  
          if hasattr(score, 'item'):
              try:
                  # e.g. unwrap memmapped scalars
                  score = score.item()
              except ValueError:
                  # non-scalar?
                  pass
  
          if not isinstance(score, numbers.Number):
              raise ValueError("scoring must return a number, got %s (%s) "
                               "instead. (scorer=%r)"
                               % (str(score), type(score), scorer))
      return score
  
  
  def _multimetric_score(estimator, X_test, y_test, scorers):
      """Return a dict of score for multimetric scoring"""
      scores = {}
  
      for name, scorer in scorers.items():
          if y_test is None:
              score = scorer(estimator, X_test)
          else:
              score = scorer(estimator, X_test, y_test)
  
          if hasattr(score, 'item'):
              try:
                  # e.g. unwrap memmapped scalars
                  score = score.item()
              except ValueError:
                  # non-scalar?
                  pass
          scores[name] = score
  
          if not isinstance(score, numbers.Number):
              raise ValueError("scoring must return a number, got %s (%s) "
                               "instead. (scorer=%s)"
                               % (str(score), type(score), name))
      return scores
  
  
  def cross_val_predict(estimator, X, y=None, groups=None, cv=None, n_jobs=1,
                        verbose=0, fit_params=None, pre_dispatch='2*n_jobs',
                        method='predict'):
      """Generate cross-validated estimates for each input data point
  
      Read more in the :ref:`User Guide <cross_validation>`.
  
      Parameters
      ----------
      estimator : estimator object implementing 'fit' and 'predict'
          The object to use to fit the data.
  
      X : array-like
          The data to fit. Can be, for example a list, or an array at least 2d.
  
      y : array-like, optional, default: None
          The target variable to try to predict in the case of
          supervised learning.
  
      groups : array-like, with shape (n_samples,), optional
          Group labels for the samples used while splitting the dataset into
          train/test set.
  
      cv : int, cross-validation generator or an iterable, optional
          Determines the cross-validation splitting strategy.
          Possible inputs for cv are:
  
          - None, to use the default 3-fold cross validation,
          - integer, to specify the number of folds in a `(Stratified)KFold`,
          - An object to be used as a cross-validation generator.
          - An iterable yielding train, test splits.
  
          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.
  
      n_jobs : integer, optional
          The number of CPUs to use to do the computation. -1 means
          'all CPUs'.
  
      verbose : integer, optional
          The verbosity level.
  
      fit_params : dict, optional
          Parameters to pass to the fit method of the estimator.
  
      pre_dispatch : int, or string, optional
          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 string, giving an expression as a function of n_jobs,
                as in '2*n_jobs'
  
      method : string, optional, default: 'predict'
          Invokes the passed method name of the passed estimator. For
          method='predict_proba', the columns correspond to the classes
          in sorted order.
  
      Returns
      -------
      predictions : ndarray
          This is the result of calling ``method``
  
      Notes
      -----
      In the case that one or more classes are absent in a training portion, a
      default score needs to be assigned to all instances for that class if
      ``method`` produces columns per class, as in {'decision_function',
      'predict_proba', 'predict_log_proba'}.  For ``predict_proba`` this value is
      0.  In order to ensure finite output, we approximate negative infinity by
      the minimum finite float value for the dtype in other cases.
  
      Examples
      --------
      >>> from sklearn import datasets, linear_model
      >>> from sklearn.model_selection import cross_val_predict
      >>> diabetes = datasets.load_diabetes()
      >>> X = diabetes.data[:150]
      >>> y = diabetes.target[:150]
      >>> lasso = linear_model.Lasso()
      >>> y_pred = cross_val_predict(lasso, X, y)
      """
      X, y, groups = indexable(X, y, groups)
  
      cv = check_cv(cv, y, classifier=is_classifier(estimator))
  
      if method in ['decision_function', 'predict_proba', 'predict_log_proba']:
          le = LabelEncoder()
          y = le.fit_transform(y)
  
      # We clone the estimator to make sure that all the folds are
      # independent, and that it is pickle-able.
      parallel = Parallel(n_jobs=n_jobs, verbose=verbose,
                          pre_dispatch=pre_dispatch)
      prediction_blocks = parallel(delayed(_fit_and_predict)(
          clone(estimator), X, y, train, test, verbose, fit_params, method)
          for train, test in cv.split(X, y, groups))
  
      # Concatenate the predictions
      predictions = [pred_block_i for pred_block_i, _ in prediction_blocks]
      test_indices = np.concatenate([indices_i
                                     for _, indices_i in prediction_blocks])
  
      if not _check_is_permutation(test_indices, _num_samples(X)):
          raise ValueError('cross_val_predict only works for partitions')
  
      inv_test_indices = np.empty(len(test_indices), dtype=int)
      inv_test_indices[test_indices] = np.arange(len(test_indices))
  
      # Check for sparse predictions
      if sp.issparse(predictions[0]):
          predictions = sp.vstack(predictions, format=predictions[0].format)
      else:
          predictions = np.concatenate(predictions)
      return predictions[inv_test_indices]
  
  
  def _fit_and_predict(estimator, X, y, train, test, verbose, fit_params,
                       method):
      """Fit estimator and predict values for a given dataset split.
  
      Read more in the :ref:`User Guide <cross_validation>`.
  
      Parameters
      ----------
      estimator : estimator object implementing 'fit' and 'predict'
          The object to use to fit the data.
  
      X : array-like of shape at least 2D
          The data to fit.
  
      y : array-like, optional, default: None
          The target variable to try to predict in the case of
          supervised learning.
  
      train : array-like, shape (n_train_samples,)
          Indices of training samples.
  
      test : array-like, shape (n_test_samples,)
          Indices of test samples.
  
      verbose : integer
          The verbosity level.
  
      fit_params : dict or None
          Parameters that will be passed to ``estimator.fit``.
  
      method : string
          Invokes the passed method name of the passed estimator.
  
      Returns
      -------
      predictions : sequence
          Result of calling 'estimator.method'
  
      test : array-like
          This is the value of the test parameter
      """
      # Adjust length of sample weights
      fit_params = fit_params if fit_params is not None else {}
      fit_params = dict([(k, _index_param_value(X, v, train))
                        for k, v in fit_params.items()])
  
      X_train, y_train = _safe_split(estimator, X, y, train)
      X_test, _ = _safe_split(estimator, X, y, test, train)
  
      if y_train is None:
          estimator.fit(X_train, **fit_params)
      else:
          estimator.fit(X_train, y_train, **fit_params)
      func = getattr(estimator, method)
      predictions = func(X_test)
      if method in ['decision_function', 'predict_proba', 'predict_log_proba']:
          n_classes = len(set(y))
          if n_classes != len(estimator.classes_):
              recommendation = (
                  'To fix this, use a cross-validation '
                  'technique resulting in properly '
                  'stratified folds')
              warnings.warn('Number of classes in training fold ({}) does '
                            'not match total number of classes ({}). '
                            'Results may not be appropriate for your use case. '
                            '{}'.format(len(estimator.classes_),
                                        n_classes, recommendation),
                            RuntimeWarning)
              if method == 'decision_function':
                  if (predictions.ndim == 2 and
                          predictions.shape[1] != len(estimator.classes_)):
                      # This handles the case when the shape of predictions
                      # does not match the number of classes used to train
                      # it with. This case is found when sklearn.svm.SVC is
                      # set to `decision_function_shape='ovo'`.
                      raise ValueError('Output shape {} of {} does not match '
                                       'number of classes ({}) in fold. '
                                       'Irregular decision_function outputs '
                                       'are not currently supported by '
                                       'cross_val_predict'.format(
                                          predictions.shape, method,
                                          len(estimator.classes_),
                                          recommendation))
                  if len(estimator.classes_) <= 2:
                      # In this special case, `predictions` contains a 1D array.
                      raise ValueError('Only {} class/es in training fold, this '
                                       'is not supported for decision_function '
                                       'with imbalanced folds. {}'.format(
                                          len(estimator.classes_),
                                          recommendation))
  
              float_min = np.finfo(predictions.dtype).min
              default_values = {'decision_function': float_min,
                                'predict_log_proba': float_min,
                                'predict_proba': 0}
              predictions_for_all_classes = np.full((_num_samples(predictions),
                                                     n_classes),
                                                    default_values[method])
              predictions_for_all_classes[:, estimator.classes_] = predictions
              predictions = predictions_for_all_classes
      return predictions, test
  
  
  def _check_is_permutation(indices, n_samples):
      """Check whether indices is a reordering of the array np.arange(n_samples)
  
      Parameters
      ----------
      indices : ndarray
          integer array to test
      n_samples : int
          number of expected elements
  
      Returns
      -------
      is_partition : bool
          True iff sorted(indices) is np.arange(n)
      """
      if len(indices) != n_samples:
          return False
      hit = np.zeros(n_samples, dtype=bool)
      hit[indices] = True
      if not np.all(hit):
          return False
      return True
  
  
  def _index_param_value(X, v, indices):
      """Private helper function for parameter value indexing."""
      if not _is_arraylike(v) or _num_samples(v) != _num_samples(X):
          # pass through: skip indexing
          return v
      if sp.issparse(v):
          v = v.tocsr()
      return safe_indexing(v, indices)
  
  
  def permutation_test_score(estimator, X, y, groups=None, cv=None,
                             n_permutations=100, n_jobs=1, random_state=0,
                             verbose=0, scoring=None):
      """Evaluate the significance of a cross-validated score with permutations
  
      Read more in the :ref:`User Guide <cross_validation>`.
  
      Parameters
      ----------
      estimator : estimator object implementing 'fit'
          The object to use to fit the data.
  
      X : array-like of shape at least 2D
          The data to fit.
  
      y : array-like
          The target variable to try to predict in the case of
          supervised learning.
  
      groups : array-like, with shape (n_samples,), optional
          Labels to constrain permutation within groups, i.e. ``y`` values
          are permuted among samples with the same group identifier.
          When not specified, ``y`` values are permuted among all samples.
  
          When a grouped cross-validator is used, the group labels are
          also passed on to the ``split`` method of the cross-validator. The
          cross-validator uses them for grouping the samples  while splitting
          the dataset into train/test set.
  
      scoring : string, callable or None, optional, default: None
          A single string (see :ref:`scoring_parameter`) or a callable
          (see :ref:`scoring`) to evaluate the predictions on the test set.
  
          If None the estimator's default scorer, if available, is used.
  
      cv : int, cross-validation generator or an iterable, optional
          Determines the cross-validation splitting strategy.
          Possible inputs for cv are:
  
          - None, to use the default 3-fold cross validation,
          - integer, to specify the number of folds in a `(Stratified)KFold`,
          - An object to be used as a cross-validation generator.
          - An iterable yielding train, test splits.
  
          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.
  
      n_permutations : integer, optional
          Number of times to permute ``y``.
  
      n_jobs : integer, optional
          The number of CPUs to use to do the computation. -1 means
          'all CPUs'.
  
      random_state : int, RandomState instance or None, optional (default=0)
          If int, random_state is the seed used by the random number generator;
          If RandomState instance, random_state is the random number generator;
          If None, the random number generator is the RandomState instance used
          by `np.random`.
  
      verbose : integer, optional
          The verbosity level.
  
      Returns
      -------
      score : float
          The true score without permuting targets.
  
      permutation_scores : array, shape (n_permutations,)
          The scores obtained for each permutations.
  
      pvalue : float
          The p-value, which approximates the probability that the score would
          be obtained by chance. This is calculated as:
  
          `(C + 1) / (n_permutations + 1)`
  
          Where C is the number of permutations whose score >= the true score.
  
          The best possible p-value is 1/(n_permutations + 1), the worst is 1.0.
  
      Notes
      -----
      This function implements Test 1 in:
  
          Ojala and Garriga. Permutation Tests for Studying Classifier
          Performance.  The Journal of Machine Learning Research (2010)
          vol. 11
  
      """
      X, y, groups = indexable(X, y, groups)
  
      cv = check_cv(cv, y, classifier=is_classifier(estimator))
      scorer = check_scoring(estimator, scoring=scoring)
      random_state = check_random_state(random_state)
  
      # We clone the estimator to make sure that all the folds are
      # independent, and that it is pickle-able.
      score = _permutation_test_score(clone(estimator), X, y, groups, cv, scorer)
      permutation_scores = Parallel(n_jobs=n_jobs, verbose=verbose)(
          delayed(_permutation_test_score)(
              clone(estimator), X, _shuffle(y, groups, random_state),
              groups, cv, scorer)
          for _ in range(n_permutations))
      permutation_scores = np.array(permutation_scores)
      pvalue = (np.sum(permutation_scores >= score) + 1.0) / (n_permutations + 1)
      return score, permutation_scores, pvalue
  
  
  permutation_test_score.__test__ = False  # to avoid a pb with nosetests
  
  
  def _permutation_test_score(estimator, X, y, groups, cv, scorer):
      """Auxiliary function for permutation_test_score"""
      avg_score = []
      for train, test in cv.split(X, y, groups):
          X_train, y_train = _safe_split(estimator, X, y, train)
          X_test, y_test = _safe_split(estimator, X, y, test, train)
          estimator.fit(X_train, y_train)
          avg_score.append(scorer(estimator, X_test, y_test))
      return np.mean(avg_score)
  
  
  def _shuffle(y, groups, random_state):
      """Return a shuffled copy of y eventually shuffle among same groups."""
      if groups is None:
          indices = random_state.permutation(len(y))
      else:
          indices = np.arange(len(groups))
          for group in np.unique(groups):
              this_mask = (groups == group)
              indices[this_mask] = random_state.permutation(indices[this_mask])
      return safe_indexing(y, indices)
  
  
  def learning_curve(estimator, X, y, groups=None,
                     train_sizes=np.linspace(0.1, 1.0, 5), cv=None, scoring=None,
                     exploit_incremental_learning=False, n_jobs=1,
                     pre_dispatch="all", verbose=0, shuffle=False,
                     random_state=None):
      """Learning curve.
  
      Determines cross-validated training and test scores for different training
      set sizes.
  
      A cross-validation generator splits the whole dataset k times in training
      and test data. Subsets of the training set with varying sizes will be used
      to train the estimator and a score for each training subset size and the
      test set will be computed. Afterwards, the scores will be averaged over
      all k runs for each training subset size.
  
      Read more in the :ref:`User Guide <learning_curve>`.
  
      Parameters
      ----------
      estimator : object type that implements the "fit" and "predict" methods
          An object of that type which is cloned for each validation.
  
      X : array-like, 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, shape (n_samples) or (n_samples, n_features), optional
          Target relative to X for classification or regression;
          None for unsupervised learning.
  
      groups : array-like, with shape (n_samples,), optional
          Group labels for the samples used while splitting the dataset into
          train/test set.
  
      train_sizes : array-like, shape (n_ticks,), dtype float or int
          Relative or absolute numbers of training examples that will be used to
          generate the learning curve. If the dtype is float, it is regarded as a
          fraction of the maximum size of the training set (that is determined
          by the selected validation method), i.e. it has to be within (0, 1].
          Otherwise it is interpreted as absolute sizes of the training sets.
          Note that for classification the number of samples usually have to
          be big enough to contain at least one sample from each class.
          (default: np.linspace(0.1, 1.0, 5))
  
      cv : int, cross-validation generator or an iterable, optional
          Determines the cross-validation splitting strategy.
          Possible inputs for cv are:
  
          - None, to use the default 3-fold cross validation,
          - integer, to specify the number of folds in a `(Stratified)KFold`,
          - An object to be used as a cross-validation generator.
          - An iterable yielding train, test splits.
  
          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.
  
      scoring : string, callable or None, optional, default: None
          A string (see model evaluation documentation) or
          a scorer callable object / function with signature
          ``scorer(estimator, X, y)``.
  
      exploit_incremental_learning : boolean, optional, default: False
          If the estimator supports incremental learning, this will be
          used to speed up fitting for different training set sizes.
  
      n_jobs : integer, optional
          Number of jobs to run in parallel (default 1).
  
      pre_dispatch : integer or string, optional
          Number of predispatched jobs for parallel execution (default is
          all). The option can reduce the allocated memory. The string can
          be an expression like '2*n_jobs'.
  
      verbose : integer, optional
          Controls the verbosity: the higher, the more messages.
  
      shuffle : boolean, optional
          Whether to shuffle training data before taking prefixes of it
          based on``train_sizes``.
  
      random_state : int, RandomState instance or None, optional (default=None)
          If int, random_state is the seed used by the random number generator;
          If RandomState instance, random_state is the random number generator;
          If None, the random number generator is the RandomState instance used
          by `np.random`. Used when ``shuffle`` is True.
  
      Returns
      -------
      train_sizes_abs : array, shape = (n_unique_ticks,), dtype int
          Numbers of training examples that has been used to generate the
          learning curve. Note that the number of ticks might be less
          than n_ticks because duplicate entries will be removed.
  
      train_scores : array, shape (n_ticks, n_cv_folds)
          Scores on training sets.
  
      test_scores : array, shape (n_ticks, n_cv_folds)
          Scores on test set.
  
      Notes
      -----
      See :ref:`examples/model_selection/plot_learning_curve.py
      <sphx_glr_auto_examples_model_selection_plot_learning_curve.py>`
      """
      if exploit_incremental_learning and not hasattr(estimator, "partial_fit"):
          raise ValueError("An estimator must support the partial_fit interface "
                           "to exploit incremental learning")
      X, y, groups = indexable(X, y, groups)
  
      cv = check_cv(cv, y, classifier=is_classifier(estimator))
      # Store it as list as we will be iterating over the list multiple times
      cv_iter = list(cv.split(X, y, groups))
  
      scorer = check_scoring(estimator, scoring=scoring)
  
      n_max_training_samples = len(cv_iter[0][0])
      # Because the lengths of folds can be significantly different, it is
      # not guaranteed that we use all of the available training data when we
      # use the first 'n_max_training_samples' samples.
      train_sizes_abs = _translate_train_sizes(train_sizes,
                                               n_max_training_samples)
      n_unique_ticks = train_sizes_abs.shape[0]
      if verbose > 0:
          print("[learning_curve] Training set sizes: " + str(train_sizes_abs))
  
      parallel = Parallel(n_jobs=n_jobs, pre_dispatch=pre_dispatch,
                          verbose=verbose)
  
      if shuffle:
          rng = check_random_state(random_state)
          cv_iter = ((rng.permutation(train), test) for train, test in cv_iter)
  
      if exploit_incremental_learning:
          classes = np.unique(y) if is_classifier(estimator) else None
          out = parallel(delayed(_incremental_fit_estimator)(
              clone(estimator), X, y, classes, train, test, train_sizes_abs,
              scorer, verbose) for train, test in cv_iter)
      else:
          train_test_proportions = []
          for train, test in cv_iter:
              for n_train_samples in train_sizes_abs:
                  train_test_proportions.append((train[:n_train_samples], test))
  
          out = parallel(delayed(_fit_and_score)(
              clone(estimator), X, y, scorer, train, test,
              verbose, parameters=None, fit_params=None, return_train_score=True)
              for train, test in train_test_proportions)
          out = np.array(out)
          n_cv_folds = out.shape[0] // n_unique_ticks
          out = out.reshape(n_cv_folds, n_unique_ticks, 2)
  
      out = np.asarray(out).transpose((2, 1, 0))
  
      return train_sizes_abs, out[0], out[1]
  
  
  def _translate_train_sizes(train_sizes, n_max_training_samples):
      """Determine absolute sizes of training subsets and validate 'train_sizes'.
  
      Examples:
          _translate_train_sizes([0.5, 1.0], 10) -> [5, 10]
          _translate_train_sizes([5, 10], 10) -> [5, 10]
  
      Parameters
      ----------
      train_sizes : array-like, shape (n_ticks,), dtype float or int
          Numbers of training examples that will be used to generate the
          learning curve. If the dtype is float, it is regarded as a
          fraction of 'n_max_training_samples', i.e. it has to be within (0, 1].
  
      n_max_training_samples : int
          Maximum number of training samples (upper bound of 'train_sizes').
  
      Returns
      -------
      train_sizes_abs : array, shape (n_unique_ticks,), dtype int
          Numbers of training examples that will be used to generate the
          learning curve. Note that the number of ticks might be less
          than n_ticks because duplicate entries will be removed.
      """
      train_sizes_abs = np.asarray(train_sizes)
      n_ticks = train_sizes_abs.shape[0]
      n_min_required_samples = np.min(train_sizes_abs)
      n_max_required_samples = np.max(train_sizes_abs)
      if np.issubdtype(train_sizes_abs.dtype, np.floating):
          if n_min_required_samples <= 0.0 or n_max_required_samples > 1.0:
              raise ValueError("train_sizes has been interpreted as fractions "
                               "of the maximum number of training samples and "
                               "must be within (0, 1], but is within [%f, %f]."
                               % (n_min_required_samples,
                                  n_max_required_samples))
          train_sizes_abs = (train_sizes_abs * n_max_training_samples).astype(
                               dtype=np.int, copy=False)
          train_sizes_abs = np.clip(train_sizes_abs, 1,
                                    n_max_training_samples)
      else:
          if (n_min_required_samples <= 0 or
                  n_max_required_samples > n_max_training_samples):
              raise ValueError("train_sizes has been interpreted as absolute "
                               "numbers of training samples and must be within "
                               "(0, %d], but is within [%d, %d]."
                               % (n_max_training_samples,
                                  n_min_required_samples,
                                  n_max_required_samples))
  
      train_sizes_abs = np.unique(train_sizes_abs)
      if n_ticks > train_sizes_abs.shape[0]:
          warnings.warn("Removed duplicate entries from 'train_sizes'. Number "
                        "of ticks will be less than the size of "
                        "'train_sizes' %d instead of %d)."
                        % (train_sizes_abs.shape[0], n_ticks), RuntimeWarning)
  
      return train_sizes_abs
  
  
  def _incremental_fit_estimator(estimator, X, y, classes, train, test,
                                 train_sizes, scorer, verbose):
      """Train estimator on training subsets incrementally and compute scores."""
      train_scores, test_scores = [], []
      partitions = zip(train_sizes, np.split(train, train_sizes)[:-1])
      for n_train_samples, partial_train in partitions:
          train_subset = train[:n_train_samples]
          X_train, y_train = _safe_split(estimator, X, y, train_subset)
          X_partial_train, y_partial_train = _safe_split(estimator, X, y,
                                                         partial_train)
          X_test, y_test = _safe_split(estimator, X, y, test, train_subset)
          if y_partial_train is None:
              estimator.partial_fit(X_partial_train, classes=classes)
          else:
              estimator.partial_fit(X_partial_train, y_partial_train,
                                    classes=classes)
          train_scores.append(_score(estimator, X_train, y_train, scorer))
          test_scores.append(_score(estimator, X_test, y_test, scorer))
      return np.array((train_scores, test_scores)).T
  
  
  def validation_curve(estimator, X, y, param_name, param_range, groups=None,
                       cv=None, scoring=None, n_jobs=1, pre_dispatch="all",
                       verbose=0):
      """Validation curve.
  
      Determine training and test scores for varying parameter values.
  
      Compute scores for an estimator with different values of a specified
      parameter. This is similar to grid search with one parameter. However, this
      will also compute training scores and is merely a utility for plotting the
      results.
  
      Read more in the :ref:`User Guide <learning_curve>`.
  
      Parameters
      ----------
      estimator : object type that implements the "fit" and "predict" methods
          An object of that type which is cloned for each validation.
  
      X : array-like, 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, shape (n_samples) or (n_samples, n_features), optional
          Target relative to X for classification or regression;
          None for unsupervised learning.
  
      param_name : string
          Name of the parameter that will be varied.
  
      param_range : array-like, shape (n_values,)
          The values of the parameter that will be evaluated.
  
      groups : array-like, with shape (n_samples,), optional
          Group labels for the samples used while splitting the dataset into
          train/test set.
  
      cv : int, cross-validation generator or an iterable, optional
          Determines the cross-validation splitting strategy.
          Possible inputs for cv are:
  
          - None, to use the default 3-fold cross validation,
          - integer, to specify the number of folds in a `(Stratified)KFold`,
          - An object to be used as a cross-validation generator.
          - An iterable yielding train, test splits.
  
          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.
  
      scoring : string, callable or None, optional, default: None
          A string (see model evaluation documentation) or
          a scorer callable object / function with signature
          ``scorer(estimator, X, y)``.
  
      n_jobs : integer, optional
          Number of jobs to run in parallel (default 1).
  
      pre_dispatch : integer or string, optional
          Number of predispatched jobs for parallel execution (default is
          all). The option can reduce the allocated memory. The string can
          be an expression like '2*n_jobs'.
  
      verbose : integer, optional
          Controls the verbosity: the higher, the more messages.
  
      Returns
      -------
      train_scores : array, shape (n_ticks, n_cv_folds)
          Scores on training sets.
  
      test_scores : array, shape (n_ticks, n_cv_folds)
          Scores on test set.
  
      Notes
      -----
      See :ref:`sphx_glr_auto_examples_model_selection_plot_validation_curve.py`
  
      """
      X, y, groups = indexable(X, y, groups)
  
      cv = check_cv(cv, y, classifier=is_classifier(estimator))
      scorer = check_scoring(estimator, scoring=scoring)
  
      parallel = Parallel(n_jobs=n_jobs, pre_dispatch=pre_dispatch,
                          verbose=verbose)
      out = parallel(delayed(_fit_and_score)(
          clone(estimator), X, y, scorer, train, test, verbose,
          parameters={param_name: v}, fit_params=None, return_train_score=True)
          # NOTE do not change order of iteration to allow one time cv splitters
          for train, test in cv.split(X, y, groups) for v in param_range)
      out = np.asarray(out)
      n_params = len(param_range)
      n_cv_folds = out.shape[0] // n_params
      out = out.reshape(n_cv_folds, n_params, 2).transpose((2, 1, 0))
  
      return out[0], out[1]
  
  
  def _aggregate_score_dicts(scores):
      """Aggregate the list of dict to dict of np ndarray
  
      The aggregated output of _fit_and_score will be a list of dict
      of form [{'prec': 0.1, 'acc':1.0}, {'prec': 0.1, 'acc':1.0}, ...]
      Convert it to a dict of array {'prec': np.array([0.1 ...]), ...}
  
      Parameters
      ----------
  
      scores : list of dict
          List of dicts of the scores for all scorers. This is a flat list,
          assumed originally to be of row major order.
  
      Example
      -------
  
      >>> scores = [{'a': 1, 'b':10}, {'a': 2, 'b':2}, {'a': 3, 'b':3},
      ...           {'a': 10, 'b': 10}]                         # doctest: +SKIP
      >>> _aggregate_score_dicts(scores)                        # doctest: +SKIP
      {'a': array([1, 2, 3, 10]),
       'b': array([10, 2, 3, 10])}
      """
      out = {}
      for key in scores[0]:
          out[key] = np.asarray([score[key] for score in scores])
      return out
  