content: """
  Randomized Lasso/Logistic: feature selection based on Lasso and
  sparse Logistic Regression
  """
  
  # Author: Gael Varoquaux, Alexandre Gramfort
  #
  # License: BSD 3 clause
  import itertools
  from abc import ABCMeta, abstractmethod
  import warnings
  
  import numpy as np
  from scipy.sparse import issparse
  from scipy import sparse
  from scipy.interpolate import interp1d
  
  from .base import center_data
  from ..base import BaseEstimator, TransformerMixin
  from ..externals import six
  from ..externals.joblib import Memory, Parallel, delayed
  from ..utils import (as_float_array, check_random_state, check_X_y,
                       check_array, safe_mask, ConvergenceWarning)
  from ..utils.validation import check_is_fitted
  from .least_angle import lars_path, LassoLarsIC
  from .logistic import LogisticRegression
  
  
  ###############################################################################
  # Randomized linear model: feature selection
  
  def _resample_model(estimator_func, X, y, scaling=.5, n_resampling=200,
                      n_jobs=1, verbose=False, pre_dispatch='3*n_jobs',
                      random_state=None, sample_fraction=.75, **params):
      random_state = check_random_state(random_state)
      # We are generating 1 - weights, and not weights
      n_samples, n_features = X.shape
  
      if not (0 < scaling < 1):
          raise ValueError(
              "'scaling' should be between 0 and 1. Got %r instead." % scaling)
  
      scaling = 1. - scaling
      scores_ = 0.0
      for active_set in Parallel(n_jobs=n_jobs, verbose=verbose,
                                 pre_dispatch=pre_dispatch)(
              delayed(estimator_func)(
                  X, y, weights=scaling * random_state.random_integers(
                      0, 1, size=(n_features,)),
                  mask=(random_state.rand(n_samples) < sample_fraction),
                  verbose=max(0, verbose - 1),
                  **params)
              for _ in range(n_resampling)):
          scores_ += active_set
  
      scores_ /= n_resampling
      return scores_
  
  
  class BaseRandomizedLinearModel(six.with_metaclass(ABCMeta, BaseEstimator,
                                                     TransformerMixin)):
      """Base class to implement randomized linear models for feature selection
  
      This implements the strategy by Meinshausen and Buhlman:
      stability selection with randomized sampling, and random re-weighting of
      the penalty.
      """
  
      @abstractmethod
      def __init__(self):
          pass
  
      _center_data = staticmethod(center_data)
  
      def fit(self, X, y):
          """Fit the model using X, y as training data.
  
          Parameters
          ----------
          X : array-like, sparse matrix shape = [n_samples, n_features]
              Training data.
  
          y : array-like, shape = [n_samples]
              Target values.
  
          Returns
          -------
          self : object
              Returns an instance of self.
          """
          X, y = check_X_y(X, y, ['csr', 'csc'], y_numeric=True,
                           ensure_min_samples=2)
          X = as_float_array(X, copy=False)
          n_samples, n_features = X.shape
  
          X, y, X_mean, y_mean, X_std = self._center_data(X, y,
                                                          self.fit_intercept,
                                                          self.normalize)
  
          estimator_func, params = self._make_estimator_and_params(X, y)
          memory = self.memory
          if isinstance(memory, six.string_types):
              memory = Memory(cachedir=memory)
  
          scores_ = memory.cache(
              _resample_model, ignore=['verbose', 'n_jobs', 'pre_dispatch']
          )(
              estimator_func, X, y,
              scaling=self.scaling, n_resampling=self.n_resampling,
              n_jobs=self.n_jobs, verbose=self.verbose,
              pre_dispatch=self.pre_dispatch, random_state=self.random_state,
              sample_fraction=self.sample_fraction, **params)
  
          if scores_.ndim == 1:
              scores_ = scores_[:, np.newaxis]
          self.all_scores_ = scores_
          self.scores_ = np.max(self.all_scores_, axis=1)
          return self
  
      def _make_estimator_and_params(self, X, y):
          """Return the parameters passed to the estimator"""
          raise NotImplementedError
  
      def get_support(self, indices=False):
          """Return a mask, or list, of the features/indices selected."""
          check_is_fitted(self, 'scores_')
  
          mask = self.scores_ > self.selection_threshold
          return mask if not indices else np.where(mask)[0]
  
      # XXX: the two function below are copy/pasted from feature_selection,
      # Should we add an intermediate base class?
      def transform(self, X):
          """Transform a new matrix using the selected features"""
          mask = self.get_support()
          X = check_array(X)
          if len(mask) != X.shape[1]:
              raise ValueError("X has a different shape than during fitting.")
          return check_array(X)[:, safe_mask(X, mask)]
  
      def inverse_transform(self, X):
          """Transform a new matrix using the selected features"""
          support = self.get_support()
          if X.ndim == 1:
              X = X[None, :]
          Xt = np.zeros((X.shape[0], support.size))
          Xt[:, support] = X
          return Xt
  
  
  ###############################################################################
  # Randomized lasso: regression settings
  
  def _randomized_lasso(X, y, weights, mask, alpha=1., verbose=False,
                        precompute=False, eps=np.finfo(np.float).eps,
                        max_iter=500):
      X = X[safe_mask(X, mask)]
      y = y[mask]
  
      # Center X and y to avoid fit the intercept
      X -= X.mean(axis=0)
      y -= y.mean()
  
      alpha = np.atleast_1d(np.asarray(alpha, dtype=np.float))
  
      X = (1 - weights) * X
      with warnings.catch_warnings():
          warnings.simplefilter('ignore', ConvergenceWarning)
          alphas_, _, coef_ = lars_path(X, y,
                                        Gram=precompute, copy_X=False,
                                        copy_Gram=False, alpha_min=np.min(alpha),
                                        method='lasso', verbose=verbose,
                                        max_iter=max_iter, eps=eps)
  
      if len(alpha) > 1:
          if len(alphas_) > 1:  # np.min(alpha) < alpha_min
              interpolator = interp1d(alphas_[::-1], coef_[:, ::-1],
                                      bounds_error=False, fill_value=0.)
              scores = (interpolator(alpha) != 0.0)
          else:
              scores = np.zeros((X.shape[1], len(alpha)), dtype=np.bool)
      else:
          scores = coef_[:, -1] != 0.0
      return scores
  
  
  class RandomizedLasso(BaseRandomizedLinearModel):
      """Randomized Lasso.
  
      Randomized Lasso works by resampling the train data and computing
      a Lasso on each resampling. In short, the features selected more
      often are good features. It is also known as stability selection.
  
      Read more in the :ref:`User Guide <randomized_l1>`.
  
      Parameters
      ----------
      alpha : float, 'aic', or 'bic', optional
          The regularization parameter alpha parameter in the Lasso.
          Warning: this is not the alpha parameter in the stability selection
          article which is scaling.
  
      scaling : float, optional
          The alpha parameter in the stability selection article used to
          randomly scale the features. Should be between 0 and 1.
  
      sample_fraction : float, optional
          The fraction of samples to be used in each randomized design.
          Should be between 0 and 1. If 1, all samples are used.
  
      n_resampling : int, optional
          Number of randomized models.
  
      selection_threshold: float, optional
          The score above which features should be selected.
  
      fit_intercept : boolean, optional
          whether to calculate the intercept for this model. If set
          to false, no intercept will be used in calculations
          (e.g. data is expected to be already centered).
  
      verbose : boolean or integer, optional
          Sets the verbosity amount
  
      normalize : boolean, optional, default True
          If True, the regressors X will be normalized before regression.
  
      precompute : True | False | 'auto'
          Whether to use a precomputed Gram matrix to speed up
          calculations. If set to 'auto' let us decide. The Gram
          matrix can also be passed as argument.
  
      max_iter : integer, optional
          Maximum number of iterations to perform in the Lars algorithm.
  
      eps : float, optional
          The machine-precision regularization in the computation of the
          Cholesky diagonal factors. Increase this for very ill-conditioned
          systems. Unlike the 'tol' parameter in some iterative
          optimization-based algorithms, this parameter does not control
          the tolerance of the optimization.
  
      n_jobs : integer, optional
          Number of CPUs to use during the resampling. If '-1', use
          all the CPUs
  
      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`.
  
      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'
  
      memory : Instance of joblib.Memory or string
          Used for internal caching. By default, no caching is done.
          If a string is given, it is the path to the caching directory.
  
      Attributes
      ----------
      scores_ : array, shape = [n_features]
          Feature scores between 0 and 1.
  
      all_scores_ : array, shape = [n_features, n_reg_parameter]
          Feature scores between 0 and 1 for all values of the regularization \
          parameter. The reference article suggests ``scores_`` is the max of \
          ``all_scores_``.
  
      Examples
      --------
      >>> from sklearn.linear_model import RandomizedLasso
      >>> randomized_lasso = RandomizedLasso()
  
      Notes
      -----
      See examples/linear_model/plot_sparse_recovery.py for an example.
  
      References
      ----------
      Stability selection
      Nicolai Meinshausen, Peter Buhlmann
      Journal of the Royal Statistical Society: Series B
      Volume 72, Issue 4, pages 417-473, September 2010
      DOI: 10.1111/j.1467-9868.2010.00740.x
  
      See also
      --------
      RandomizedLogisticRegression, LogisticRegression
      """
      def __init__(self, alpha='aic', scaling=.5, sample_fraction=.75,
                   n_resampling=200, selection_threshold=.25,
                   fit_intercept=True, verbose=False,
                   normalize=True, precompute='auto',
                   max_iter=500,
                   eps=np.finfo(np.float).eps, random_state=None,
                   n_jobs=1, pre_dispatch='3*n_jobs',
                   memory=Memory(cachedir=None, verbose=0)):
          self.alpha = alpha
          self.scaling = scaling
          self.sample_fraction = sample_fraction
          self.n_resampling = n_resampling
          self.fit_intercept = fit_intercept
          self.max_iter = max_iter
          self.verbose = verbose
          self.normalize = normalize
          self.precompute = precompute
          self.eps = eps
          self.random_state = random_state
          self.n_jobs = n_jobs
          self.selection_threshold = selection_threshold
          self.pre_dispatch = pre_dispatch
          self.memory = memory
  
      def _make_estimator_and_params(self, X, y):
          assert self.precompute in (True, False, None, 'auto')
          alpha = self.alpha
          if alpha in ('aic', 'bic'):
              model = LassoLarsIC(precompute=self.precompute,
                                  criterion=self.alpha,
                                  max_iter=self.max_iter,
                                  eps=self.eps)
              model.fit(X, y)
              self.alpha_ = alpha = model.alpha_
          return _randomized_lasso, dict(alpha=alpha, max_iter=self.max_iter,
                                         eps=self.eps,
                                         precompute=self.precompute)
  
  
  ###############################################################################
  # Randomized logistic: classification settings
  
  def _randomized_logistic(X, y, weights, mask, C=1., verbose=False,
                           fit_intercept=True, tol=1e-3):
      X = X[safe_mask(X, mask)]
      y = y[mask]
      if issparse(X):
          size = len(weights)
          weight_dia = sparse.dia_matrix((1 - weights, 0), (size, size))
          X = X * weight_dia
      else:
          X *= (1 - weights)
  
      C = np.atleast_1d(np.asarray(C, dtype=np.float))
      scores = np.zeros((X.shape[1], len(C)), dtype=np.bool)
  
      for this_C, this_scores in zip(C, scores.T):
          # XXX : would be great to do it with a warm_start ...
          clf = LogisticRegression(C=this_C, tol=tol, penalty='l1', dual=False,
                                   fit_intercept=fit_intercept)
          clf.fit(X, y)
          this_scores[:] = np.any(
              np.abs(clf.coef_) > 10 * np.finfo(np.float).eps, axis=0)
      return scores
  
  
  class RandomizedLogisticRegression(BaseRandomizedLinearModel):
      """Randomized Logistic Regression
  
      Randomized Regression works by resampling the train data and computing
      a LogisticRegression on each resampling. In short, the features selected
      more often are good features. It is also known as stability selection.
  
      Read more in the :ref:`User Guide <randomized_l1>`.
  
      Parameters
      ----------
      C : float, optional, default=1
          The regularization parameter C in the LogisticRegression.
  
      scaling : float, optional, default=0.5
          The alpha parameter in the stability selection article used to
          randomly scale the features. Should be between 0 and 1.
  
      sample_fraction : float, optional, default=0.75
          The fraction of samples to be used in each randomized design.
          Should be between 0 and 1. If 1, all samples are used.
  
      n_resampling : int, optional, default=200
          Number of randomized models.
  
      selection_threshold : float, optional, default=0.25
          The score above which features should be selected.
  
      fit_intercept : boolean, optional, default=True
          whether to calculate the intercept for this model. If set
          to false, no intercept will be used in calculations
          (e.g. data is expected to be already centered).
  
      verbose : boolean or integer, optional
          Sets the verbosity amount
  
      normalize : boolean, optional, default=True
          If True, the regressors X will be normalized before regression.
  
      tol : float, optional, default=1e-3
           tolerance for stopping criteria of LogisticRegression
  
      n_jobs : integer, optional
          Number of CPUs to use during the resampling. If '-1', use
          all the CPUs
  
      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`.
  
      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'
  
      memory : Instance of joblib.Memory or string
          Used for internal caching. By default, no caching is done.
          If a string is given, it is the path to the caching directory.
  
      Attributes
      ----------
      scores_ : array, shape = [n_features]
          Feature scores between 0 and 1.
  
      all_scores_ : array, shape = [n_features, n_reg_parameter]
          Feature scores between 0 and 1 for all values of the regularization \
          parameter. The reference article suggests ``scores_`` is the max \
          of ``all_scores_``.
  
      Examples
      --------
      >>> from sklearn.linear_model import RandomizedLogisticRegression
      >>> randomized_logistic = RandomizedLogisticRegression()
  
      Notes
      -----
      See examples/linear_model/plot_sparse_recovery.py for an example.
  
      References
      ----------
      Stability selection
      Nicolai Meinshausen, Peter Buhlmann
      Journal of the Royal Statistical Society: Series B
      Volume 72, Issue 4, pages 417-473, September 2010
      DOI: 10.1111/j.1467-9868.2010.00740.x
  
      See also
      --------
      RandomizedLasso, Lasso, ElasticNet
      """
      def __init__(self, C=1, scaling=.5, sample_fraction=.75,
                   n_resampling=200,
                   selection_threshold=.25, tol=1e-3,
                   fit_intercept=True, verbose=False,
                   normalize=True,
                   random_state=None,
                   n_jobs=1, pre_dispatch='3*n_jobs',
                   memory=Memory(cachedir=None, verbose=0)):
          self.C = C
          self.scaling = scaling
          self.sample_fraction = sample_fraction
          self.n_resampling = n_resampling
          self.fit_intercept = fit_intercept
          self.verbose = verbose
          self.normalize = normalize
          self.tol = tol
          self.random_state = random_state
          self.n_jobs = n_jobs
          self.selection_threshold = selection_threshold
          self.pre_dispatch = pre_dispatch
          self.memory = memory
  
      def _make_estimator_and_params(self, X, y):
          params = dict(C=self.C, tol=self.tol,
                        fit_intercept=self.fit_intercept)
          return _randomized_logistic, params
  
      def _center_data(self, X, y, fit_intercept, normalize=False):
          """Center the data in X but not in y"""
          X, _, Xmean, _, X_std = center_data(X, y, fit_intercept,
                                              normalize=normalize)
          return X, y, Xmean, y, X_std
  
  
  ###############################################################################
  # Stability paths
  def _lasso_stability_path(X, y, mask, weights, eps):
      "Inner loop of lasso_stability_path"
      X = X * weights[np.newaxis, :]
      X = X[safe_mask(X, mask), :]
      y = y[mask]
  
      alpha_max = np.max(np.abs(np.dot(X.T, y))) / X.shape[0]
      alpha_min = eps * alpha_max  # set for early stopping in path
      with warnings.catch_warnings():
          warnings.simplefilter('ignore', ConvergenceWarning)
          alphas, _, coefs = lars_path(X, y, method='lasso', verbose=False,
                                       alpha_min=alpha_min)
      # Scale alpha by alpha_max
      alphas /= alphas[0]
      # Sort alphas in assending order
      alphas = alphas[::-1]
      coefs = coefs[:, ::-1]
      # Get rid of the alphas that are too small
      mask = alphas >= eps
      # We also want to keep the first one: it should be close to the OLS
      # solution
      mask[0] = True
      alphas = alphas[mask]
      coefs = coefs[:, mask]
      return alphas, coefs
  
  
  def lasso_stability_path(X, y, scaling=0.5, random_state=None,
                           n_resampling=200, n_grid=100,
                           sample_fraction=0.75,
                           eps=4 * np.finfo(np.float).eps, n_jobs=1,
                           verbose=False):
      """Stabiliy path based on randomized Lasso estimates
  
      Read more in the :ref:`User Guide <randomized_l1>`.
  
      Parameters
      ----------
      X : array-like, shape = [n_samples, n_features]
          training data.
  
      y : array-like, shape = [n_samples]
          target values.
  
      scaling : float, optional, default=0.5
          The alpha parameter in the stability selection article used to
          randomly scale the features. Should be between 0 and 1.
  
      random_state : integer or numpy.random.RandomState, optional
          The generator used to randomize the design.
  
      n_resampling : int, optional, default=200
          Number of randomized models.
  
      n_grid : int, optional, default=100
          Number of grid points. The path is linearly reinterpolated
          on a grid between 0 and 1 before computing the scores.
  
      sample_fraction : float, optional, default=0.75
          The fraction of samples to be used in each randomized design.
          Should be between 0 and 1. If 1, all samples are used.
  
      eps : float, optional
          Smallest value of alpha / alpha_max considered
  
      n_jobs : integer, optional
          Number of CPUs to use during the resampling. If '-1', use
          all the CPUs
  
      verbose : boolean or integer, optional
          Sets the verbosity amount
  
      Returns
      -------
      alphas_grid : array, shape ~ [n_grid]
          The grid points between 0 and 1: alpha/alpha_max
  
      scores_path : array, shape = [n_features, n_grid]
          The scores for each feature along the path.
  
      Notes
      -----
      See examples/linear_model/plot_sparse_recovery.py for an example.
      """
      rng = check_random_state(random_state)
  
      if not (0 < scaling < 1):
          raise ValueError("Parameter 'scaling' should be between 0 and 1."
                           " Got %r instead." % scaling)
  
      n_samples, n_features = X.shape
  
      paths = Parallel(n_jobs=n_jobs, verbose=verbose)(
          delayed(_lasso_stability_path)(
              X, y, mask=rng.rand(n_samples) < sample_fraction,
              weights=1. - scaling * rng.random_integers(0, 1,
                                                         size=(n_features,)),
              eps=eps)
          for k in range(n_resampling))
  
      all_alphas = sorted(list(set(itertools.chain(*[p[0] for p in paths]))))
      # Take approximately n_grid values
      stride = int(max(1, int(len(all_alphas) / float(n_grid))))
      all_alphas = all_alphas[::stride]
      if not all_alphas[-1] == 1:
          all_alphas.append(1.)
      all_alphas = np.array(all_alphas)
      scores_path = np.zeros((n_features, len(all_alphas)))
  
      for alphas, coefs in paths:
          if alphas[0] != 0:
              alphas = np.r_[0, alphas]
              coefs = np.c_[np.ones((n_features, 1)), coefs]
          if alphas[-1] != all_alphas[-1]:
              alphas = np.r_[alphas, all_alphas[-1]]
              coefs = np.c_[coefs, np.zeros((n_features, 1))]
          scores_path += (interp1d(alphas, coefs,
                          kind='nearest', bounds_error=False,
                          fill_value=0, axis=-1)(all_alphas) != 0)
  
      scores_path /= n_resampling
      return all_alphas, scores_path
  