text: # Authors: Peter Prettenhofer <peter.prettenhofer@gmail.com> (main author)
  #          Mathieu Blondel (partial_fit support)
  #
  # License: BSD 3 clause
  """Classification, regression and One-Class SVM using Stochastic Gradient
  Descent (SGD).
  """
  
  import numpy as np
  import warnings
  
  from abc import ABCMeta, abstractmethod
  
  from joblib import Parallel
  
  from ..base import clone, is_classifier
  from ._base import LinearClassifierMixin, SparseCoefMixin
  from ._base import make_dataset
  from ..base import BaseEstimator, RegressorMixin, OutlierMixin
  from ..utils import check_random_state
  from ..utils.metaestimators import available_if
  from ..utils.extmath import safe_sparse_dot
  from ..utils.multiclass import _check_partial_fit_first_call
  from ..utils.validation import check_is_fitted, _check_sample_weight
  from ..utils.fixes import delayed
  from ..exceptions import ConvergenceWarning
  from ..model_selection import StratifiedShuffleSplit, ShuffleSplit
  
  from ._sgd_fast import _plain_sgd
  from ..utils import compute_class_weight
  from ._sgd_fast import Hinge
  from ._sgd_fast import SquaredHinge
  from ._sgd_fast import Log
  from ._sgd_fast import ModifiedHuber
  from ._sgd_fast import SquaredLoss
  from ._sgd_fast import Huber
  from ._sgd_fast import EpsilonInsensitive
  from ._sgd_fast import SquaredEpsilonInsensitive
  from ..utils.fixes import _joblib_parallel_args
  
  LEARNING_RATE_TYPES = {
      "constant": 1,
      "optimal": 2,
      "invscaling": 3,
      "adaptive": 4,
      "pa1": 5,
      "pa2": 6,
  }
  
  PENALTY_TYPES = {"none": 0, "l2": 2, "l1": 1, "elasticnet": 3}
  
  DEFAULT_EPSILON = 0.1
  # Default value of ``epsilon`` parameter.
  
  MAX_INT = np.iinfo(np.int32).max
  
  
  class _ValidationScoreCallback:
      """Callback for early stopping based on validation score"""
  
      def __init__(self, estimator, X_val, y_val, sample_weight_val, classes=None):
          self.estimator = clone(estimator)
          self.estimator.t_ = 1  # to pass check_is_fitted
          if classes is not None:
              self.estimator.classes_ = classes
          self.X_val = X_val
          self.y_val = y_val
          self.sample_weight_val = sample_weight_val
  
      def __call__(self, coef, intercept):
          est = self.estimator
          est.coef_ = coef.reshape(1, -1)
          est.intercept_ = np.atleast_1d(intercept)
          return est.score(self.X_val, self.y_val, self.sample_weight_val)
  
  
  class BaseSGD(SparseCoefMixin, BaseEstimator, metaclass=ABCMeta):
      """Base class for SGD classification and regression."""
  
      def __init__(
          self,
          loss,
          *,
          penalty="l2",
          alpha=0.0001,
          C=1.0,
          l1_ratio=0.15,
          fit_intercept=True,
          max_iter=1000,
          tol=1e-3,
          shuffle=True,
          verbose=0,
          epsilon=0.1,
          random_state=None,
          learning_rate="optimal",
          eta0=0.0,
          power_t=0.5,
          early_stopping=False,
          validation_fraction=0.1,
          n_iter_no_change=5,
          warm_start=False,
          average=False,
      ):
          self.loss = loss
          self.penalty = penalty
          self.learning_rate = learning_rate
          self.epsilon = epsilon
          self.alpha = alpha
          self.C = C
          self.l1_ratio = l1_ratio
          self.fit_intercept = fit_intercept
          self.shuffle = shuffle
          self.random_state = random_state
          self.verbose = verbose
          self.eta0 = eta0
          self.power_t = power_t
          self.early_stopping = early_stopping
          self.validation_fraction = validation_fraction
          self.n_iter_no_change = n_iter_no_change
          self.warm_start = warm_start
          self.average = average
          self.max_iter = max_iter
          self.tol = tol
  
      @abstractmethod
      def fit(self, X, y):
          """Fit model."""
  
      def _validate_params(self, for_partial_fit=False):
          """Validate input params."""
          if not isinstance(self.shuffle, bool):
              raise ValueError("shuffle must be either True or False")
          if not isinstance(self.early_stopping, bool):
              raise ValueError("early_stopping must be either True or False")
          if self.early_stopping and for_partial_fit:
              raise ValueError("early_stopping should be False with partial_fit")
          if self.max_iter is not None and self.max_iter <= 0:
              raise ValueError("max_iter must be > zero. Got %f" % self.max_iter)
          if not (0.0 <= self.l1_ratio <= 1.0):
              raise ValueError("l1_ratio must be in [0, 1]")
          if not isinstance(self, SGDOneClassSVM) and self.alpha < 0.0:
              raise ValueError("alpha must be >= 0")
          if self.n_iter_no_change < 1:
              raise ValueError("n_iter_no_change must be >= 1")
          if not (0.0 < self.validation_fraction < 1.0):
              raise ValueError("validation_fraction must be in range (0, 1)")
          if self.learning_rate in ("constant", "invscaling", "adaptive"):
              if self.eta0 <= 0.0:
                  raise ValueError("eta0 must be > 0")
          if self.learning_rate == "optimal" and self.alpha == 0:
              raise ValueError(
                  "alpha must be > 0 since "
                  "learning_rate is 'optimal'. alpha is used "
                  "to compute the optimal learning rate."
              )
  
          # raises ValueError if not registered
          self._get_penalty_type(self.penalty)
          self._get_learning_rate_type(self.learning_rate)
  
          if self.loss not in self.loss_functions:
              raise ValueError("The loss %s is not supported. " % self.loss)
  
          if self.loss == "squared_loss":
              warnings.warn(
                  "The loss 'squared_loss' was deprecated in v1.0 and will be "
                  "removed in version 1.2. Use `loss='squared_error'` which is "
                  "equivalent.",
                  FutureWarning,
              )
  
      def _get_loss_function(self, loss):
          """Get concrete ``LossFunction`` object for str ``loss``."""
          try:
              loss_ = self.loss_functions[loss]
              loss_class, args = loss_[0], loss_[1:]
              if loss in ("huber", "epsilon_insensitive", "squared_epsilon_insensitive"):
                  args = (self.epsilon,)
              return loss_class(*args)
          except KeyError as e:
              raise ValueError("The loss %s is not supported. " % loss) from e
  
      def _get_learning_rate_type(self, learning_rate):
          try:
              return LEARNING_RATE_TYPES[learning_rate]
          except KeyError as e:
              raise ValueError(
                  "learning rate %s is not supported. " % learning_rate
              ) from e
  
      def _get_penalty_type(self, penalty):
          penalty = str(penalty).lower()
          try:
              return PENALTY_TYPES[penalty]
          except KeyError as e:
              raise ValueError("Penalty %s is not supported. " % penalty) from e
  
      def _allocate_parameter_mem(
          self, n_classes, n_features, coef_init=None, intercept_init=None, one_class=0
      ):
          """Allocate mem for parameters; initialize if provided."""
          if n_classes > 2:
              # allocate coef_ for multi-class
              if coef_init is not None:
                  coef_init = np.asarray(coef_init, order="C")
                  if coef_init.shape != (n_classes, n_features):
                      raise ValueError("Provided ``coef_`` does not match dataset. ")
                  self.coef_ = coef_init
              else:
                  self.coef_ = np.zeros(
                      (n_classes, n_features), dtype=np.float64, order="C"
                  )
  
              # allocate intercept_ for multi-class
              if intercept_init is not None:
                  intercept_init = np.asarray(intercept_init, order="C")
                  if intercept_init.shape != (n_classes,):
                      raise ValueError("Provided intercept_init does not match dataset.")
                  self.intercept_ = intercept_init
              else:
                  self.intercept_ = np.zeros(n_classes, dtype=np.float64, order="C")
          else:
              # allocate coef_
              if coef_init is not None:
                  coef_init = np.asarray(coef_init, dtype=np.float64, order="C")
                  coef_init = coef_init.ravel()
                  if coef_init.shape != (n_features,):
                      raise ValueError("Provided coef_init does not match dataset.")
                  self.coef_ = coef_init
              else:
                  self.coef_ = np.zeros(n_features, dtype=np.float64, order="C")
  
              # allocate intercept_
              if intercept_init is not None:
                  intercept_init = np.asarray(intercept_init, dtype=np.float64)
                  if intercept_init.shape != (1,) and intercept_init.shape != ():
                      raise ValueError("Provided intercept_init does not match dataset.")
                  if one_class:
                      self.offset_ = intercept_init.reshape(
                          1,
                      )
                  else:
                      self.intercept_ = intercept_init.reshape(
                          1,
                      )
              else:
                  if one_class:
                      self.offset_ = np.zeros(1, dtype=np.float64, order="C")
                  else:
                      self.intercept_ = np.zeros(1, dtype=np.float64, order="C")
  
          # initialize average parameters
          if self.average > 0:
              self._standard_coef = self.coef_
              self._average_coef = np.zeros(self.coef_.shape, dtype=np.float64, order="C")
              if one_class:
                  self._standard_intercept = 1 - self.offset_
              else:
                  self._standard_intercept = self.intercept_
  
              self._average_intercept = np.zeros(
                  self._standard_intercept.shape, dtype=np.float64, order="C"
              )
  
      def _make_validation_split(self, y):
          """Split the dataset between training set and validation set.
  
          Parameters
          ----------
          y : ndarray of shape (n_samples, )
              Target values.
  
          Returns
          -------
          validation_mask : ndarray of shape (n_samples, )
              Equal to 1 on the validation set, 0 on the training set.
          """
          n_samples = y.shape[0]
          validation_mask = np.zeros(n_samples, dtype=np.uint8)
          if not self.early_stopping:
              # use the full set for training, with an empty validation set
              return validation_mask
  
          if is_classifier(self):
              splitter_type = StratifiedShuffleSplit
          else:
              splitter_type = ShuffleSplit
          cv = splitter_type(
              test_size=self.validation_fraction, random_state=self.random_state
          )
          idx_train, idx_val = next(cv.split(np.zeros(shape=(y.shape[0], 1)), y))
          if idx_train.shape[0] == 0 or idx_val.shape[0] == 0:
              raise ValueError(
                  "Splitting %d samples into a train set and a validation set "
                  "with validation_fraction=%r led to an empty set (%d and %d "
                  "samples). Please either change validation_fraction, increase "
                  "number of samples, or disable early_stopping."
                  % (
                      n_samples,
                      self.validation_fraction,
                      idx_train.shape[0],
                      idx_val.shape[0],
                  )
              )
  
          validation_mask[idx_val] = 1
          return validation_mask
  
      def _make_validation_score_cb(
          self, validation_mask, X, y, sample_weight, classes=None
      ):
          if not self.early_stopping:
              return None
  
          return _ValidationScoreCallback(
              self,
              X[validation_mask],
              y[validation_mask],
              sample_weight[validation_mask],
              classes=classes,
          )
  
  
  def _prepare_fit_binary(est, y, i):
      """Initialization for fit_binary.
  
      Returns y, coef, intercept, average_coef, average_intercept.
      """
      y_i = np.ones(y.shape, dtype=np.float64, order="C")
      y_i[y != est.classes_[i]] = -1.0
      average_intercept = 0
      average_coef = None
  
      if len(est.classes_) == 2:
          if not est.average:
              coef = est.coef_.ravel()
              intercept = est.intercept_[0]
          else:
              coef = est._standard_coef.ravel()
              intercept = est._standard_intercept[0]
              average_coef = est._average_coef.ravel()
              average_intercept = est._average_intercept[0]
      else:
          if not est.average:
              coef = est.coef_[i]
              intercept = est.intercept_[i]
          else:
              coef = est._standard_coef[i]
              intercept = est._standard_intercept[i]
              average_coef = est._average_coef[i]
              average_intercept = est._average_intercept[i]
  
      return y_i, coef, intercept, average_coef, average_intercept
  
  
  def fit_binary(
      est,
      i,
      X,
      y,
      alpha,
      C,
      learning_rate,
      max_iter,
      pos_weight,
      neg_weight,
      sample_weight,
      validation_mask=None,
      random_state=None,
  ):
      """Fit a single binary classifier.
  
      The i'th class is considered the "positive" class.
  
      Parameters
      ----------
      est : Estimator object
          The estimator to fit
  
      i : int
          Index of the positive class
  
      X : numpy array or sparse matrix of shape [n_samples,n_features]
          Training data
  
      y : numpy array of shape [n_samples, ]
          Target values
  
      alpha : float
          The regularization parameter
  
      C : float
          Maximum step size for passive aggressive
  
      learning_rate : str
          The learning rate. Accepted values are 'constant', 'optimal',
          'invscaling', 'pa1' and 'pa2'.
  
      max_iter : int
          The maximum number of iterations (epochs)
  
      pos_weight : float
          The weight of the positive class
  
      neg_weight : float
          The weight of the negative class
  
      sample_weight : numpy array of shape [n_samples, ]
          The weight of each sample
  
      validation_mask : numpy array of shape [n_samples, ], default=None
          Precomputed validation mask in case _fit_binary is called in the
          context of a one-vs-rest reduction.
  
      random_state : int, RandomState instance, 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`.
      """
      # if average is not true, average_coef, and average_intercept will be
      # unused
      y_i, coef, intercept, average_coef, average_intercept = _prepare_fit_binary(
          est, y, i
      )
      assert y_i.shape[0] == y.shape[0] == sample_weight.shape[0]
  
      random_state = check_random_state(random_state)
      dataset, intercept_decay = make_dataset(
          X, y_i, sample_weight, random_state=random_state
      )
  
      penalty_type = est._get_penalty_type(est.penalty)
      learning_rate_type = est._get_learning_rate_type(learning_rate)
  
      if validation_mask is None:
          validation_mask = est._make_validation_split(y_i)
      classes = np.array([-1, 1], dtype=y_i.dtype)
      validation_score_cb = est._make_validation_score_cb(
          validation_mask, X, y_i, sample_weight, classes=classes
      )
  
      # numpy mtrand expects a C long which is a signed 32 bit integer under
      # Windows
      seed = random_state.randint(MAX_INT)
  
      tol = est.tol if est.tol is not None else -np.inf
  
      coef, intercept, average_coef, average_intercept, n_iter_ = _plain_sgd(
          coef,
          intercept,
          average_coef,
          average_intercept,
          est.loss_function_,
          penalty_type,
          alpha,
          C,
          est.l1_ratio,
          dataset,
          validation_mask,
          est.early_stopping,
          validation_score_cb,
          int(est.n_iter_no_change),
          max_iter,
          tol,
          int(est.fit_intercept),
          int(est.verbose),
          int(est.shuffle),
          seed,
          pos_weight,
          neg_weight,
          learning_rate_type,
          est.eta0,
          est.power_t,
          0,
          est.t_,
          intercept_decay,
          est.average,
      )
  
      if est.average:
          if len(est.classes_) == 2:
              est._average_intercept[0] = average_intercept
          else:
              est._average_intercept[i] = average_intercept
  
      return coef, intercept, n_iter_
  
  
  class BaseSGDClassifier(LinearClassifierMixin, BaseSGD, metaclass=ABCMeta):
  
      # TODO: Remove squared_loss in v1.2
      loss_functions = {
          "hinge": (Hinge, 1.0),
          "squared_hinge": (SquaredHinge, 1.0),
          "perceptron": (Hinge, 0.0),
          "log": (Log,),
          "modified_huber": (ModifiedHuber,),
          "squared_error": (SquaredLoss,),
          "squared_loss": (SquaredLoss,),
          "huber": (Huber, DEFAULT_EPSILON),
          "epsilon_insensitive": (EpsilonInsensitive, DEFAULT_EPSILON),
          "squared_epsilon_insensitive": (SquaredEpsilonInsensitive, DEFAULT_EPSILON),
      }
  
      @abstractmethod
      def __init__(
          self,
          loss="hinge",
          *,
          penalty="l2",
          alpha=0.0001,
          l1_ratio=0.15,
          fit_intercept=True,
          max_iter=1000,
          tol=1e-3,
          shuffle=True,
          verbose=0,
          epsilon=DEFAULT_EPSILON,
          n_jobs=None,
          random_state=None,
          learning_rate="optimal",
          eta0=0.0,
          power_t=0.5,
          early_stopping=False,
          validation_fraction=0.1,
          n_iter_no_change=5,
          class_weight=None,
          warm_start=False,
          average=False,
      ):
  
          super().__init__(
              loss=loss,
              penalty=penalty,
              alpha=alpha,
              l1_ratio=l1_ratio,
              fit_intercept=fit_intercept,
              max_iter=max_iter,
              tol=tol,
              shuffle=shuffle,
              verbose=verbose,
              epsilon=epsilon,
              random_state=random_state,
              learning_rate=learning_rate,
              eta0=eta0,
              power_t=power_t,
              early_stopping=early_stopping,
              validation_fraction=validation_fraction,
              n_iter_no_change=n_iter_no_change,
              warm_start=warm_start,
              average=average,
          )
          self.class_weight = class_weight
          self.n_jobs = n_jobs
  
      def _partial_fit(
          self,
          X,
          y,
          alpha,
          C,
          loss,
          learning_rate,
          max_iter,
          classes,
          sample_weight,
          coef_init,
          intercept_init,
      ):
          first_call = not hasattr(self, "classes_")
          X, y = self._validate_data(
              X,
              y,
              accept_sparse="csr",
              dtype=np.float64,
              order="C",
              accept_large_sparse=False,
              reset=first_call,
          )
  
          n_samples, n_features = X.shape
  
          _check_partial_fit_first_call(self, classes)
  
          n_classes = self.classes_.shape[0]
  
          # Allocate datastructures from input arguments
          self._expanded_class_weight = compute_class_weight(
              self.class_weight, classes=self.classes_, y=y
          )
          sample_weight = _check_sample_weight(sample_weight, X)
  
          if getattr(self, "coef_", None) is None or coef_init is not None:
              self._allocate_parameter_mem(
                  n_classes, n_features, coef_init, intercept_init
              )
          elif n_features != self.coef_.shape[-1]:
              raise ValueError(
                  "Number of features %d does not match previous data %d."
                  % (n_features, self.coef_.shape[-1])
              )
  
          self.loss_function_ = self._get_loss_function(loss)
          if not hasattr(self, "t_"):
              self.t_ = 1.0
  
          # delegate to concrete training procedure
          if n_classes > 2:
              self._fit_multiclass(
                  X,
                  y,
                  alpha=alpha,
                  C=C,
                  learning_rate=learning_rate,
                  sample_weight=sample_weight,
                  max_iter=max_iter,
              )
          elif n_classes == 2:
              self._fit_binary(
                  X,
                  y,
                  alpha=alpha,
                  C=C,
                  learning_rate=learning_rate,
                  sample_weight=sample_weight,
                  max_iter=max_iter,
              )
          else:
              raise ValueError(
                  "The number of classes has to be greater than one; got %d class"
                  % n_classes
              )
  
          return self
  
      def _fit(
          self,
          X,
          y,
          alpha,
          C,
          loss,
          learning_rate,
          coef_init=None,
          intercept_init=None,
          sample_weight=None,
      ):
          self._validate_params()
          if hasattr(self, "classes_"):
              # delete the attribute otherwise _partial_fit thinks it's not the first call
              delattr(self, "classes_")
  
          # labels can be encoded as float, int, or string literals
          # np.unique sorts in asc order; largest class id is positive class
          y = self._validate_data(y=y)
          classes = np.unique(y)
  
          if self.warm_start and hasattr(self, "coef_"):
              if coef_init is None:
                  coef_init = self.coef_
              if intercept_init is None:
                  intercept_init = self.intercept_
          else:
              self.coef_ = None
              self.intercept_ = None
  
          if self.average > 0:
              self._standard_coef = self.coef_
              self._standard_intercept = self.intercept_
              self._average_coef = None
              self._average_intercept = None
  
          # Clear iteration count for multiple call to fit.
          self.t_ = 1.0
  
          self._partial_fit(
              X,
              y,
              alpha,
              C,
              loss,
              learning_rate,
              self.max_iter,
              classes,
              sample_weight,
              coef_init,
              intercept_init,
          )
  
          if (
              self.tol is not None
              and self.tol > -np.inf
              and self.n_iter_ == self.max_iter
          ):
              warnings.warn(
                  "Maximum number of iteration reached before "
                  "convergence. Consider increasing max_iter to "
                  "improve the fit.",
                  ConvergenceWarning,
              )
          return self
  
      def _fit_binary(self, X, y, alpha, C, sample_weight, learning_rate, max_iter):
          """Fit a binary classifier on X and y."""
          coef, intercept, n_iter_ = fit_binary(
              self,
              1,
              X,
              y,
              alpha,
              C,
              learning_rate,
              max_iter,
              self._expanded_class_weight[1],
              self._expanded_class_weight[0],
              sample_weight,
              random_state=self.random_state,
          )
  
          self.t_ += n_iter_ * X.shape[0]
          self.n_iter_ = n_iter_
  
          # need to be 2d
          if self.average > 0:
              if self.average <= self.t_ - 1:
                  self.coef_ = self._average_coef.reshape(1, -1)
                  self.intercept_ = self._average_intercept
              else:
                  self.coef_ = self._standard_coef.reshape(1, -1)
                  self._standard_intercept = np.atleast_1d(intercept)
                  self.intercept_ = self._standard_intercept
          else:
              self.coef_ = coef.reshape(1, -1)
              # intercept is a float, need to convert it to an array of length 1
              self.intercept_ = np.atleast_1d(intercept)
  
      def _fit_multiclass(self, X, y, alpha, C, learning_rate, sample_weight, max_iter):
          """Fit a multi-class classifier by combining binary classifiers
  
          Each binary classifier predicts one class versus all others. This
          strategy is called OvA (One versus All) or OvR (One versus Rest).
          """
          # Precompute the validation split using the multiclass labels
          # to ensure proper balancing of the classes.
          validation_mask = self._make_validation_split(y)
  
          # Use joblib to fit OvA in parallel.
          # Pick the random seed for each job outside of fit_binary to avoid
          # sharing the estimator random state between threads which could lead
          # to non-deterministic behavior
          random_state = check_random_state(self.random_state)
          seeds = random_state.randint(MAX_INT, size=len(self.classes_))
          result = Parallel(
              n_jobs=self.n_jobs,
              verbose=self.verbose,
              **_joblib_parallel_args(require="sharedmem"),
          )(
              delayed(fit_binary)(
                  self,
                  i,
                  X,
                  y,
                  alpha,
                  C,
                  learning_rate,
                  max_iter,
                  self._expanded_class_weight[i],
                  1.0,
                  sample_weight,
                  validation_mask=validation_mask,
                  random_state=seed,
              )
              for i, seed in enumerate(seeds)
          )
  
          # take the maximum of n_iter_ over every binary fit
          n_iter_ = 0.0
          for i, (_, intercept, n_iter_i) in enumerate(result):
              self.intercept_[i] = intercept
              n_iter_ = max(n_iter_, n_iter_i)
  
          self.t_ += n_iter_ * X.shape[0]
          self.n_iter_ = n_iter_
  
          if self.average > 0:
              if self.average <= self.t_ - 1.0:
                  self.coef_ = self._average_coef
                  self.intercept_ = self._average_intercept
              else:
                  self.coef_ = self._standard_coef
                  self._standard_intercept = np.atleast_1d(self.intercept_)
                  self.intercept_ = self._standard_intercept
  
      def partial_fit(self, X, y, classes=None, sample_weight=None):
          """Perform one epoch of stochastic gradient descent on given samples.
  
          Internally, this method uses ``max_iter = 1``. Therefore, it is not
          guaranteed that a minimum of the cost function is reached after calling
          it once. Matters such as objective convergence, early stopping, and
          learning rate adjustments should be handled by the user.
  
          Parameters
          ----------
          X : {array-like, sparse matrix}, shape (n_samples, n_features)
              Subset of the training data.
  
          y : ndarray of shape (n_samples,)
              Subset of the target values.
  
          classes : ndarray of shape (n_classes,), default=None
              Classes across all calls to partial_fit.
              Can be obtained by via `np.unique(y_all)`, where y_all is the
              target vector of the entire dataset.
              This argument is required for the first call to partial_fit
              and can be omitted in the subsequent calls.
              Note that y doesn't need to contain all labels in `classes`.
  
          sample_weight : array-like, shape (n_samples,), default=None
              Weights applied to individual samples.
              If not provided, uniform weights are assumed.
  
          Returns
          -------
          self : object
              Returns an instance of self.
          """
          self._validate_params(for_partial_fit=True)
          if self.class_weight in ["balanced"]:
              raise ValueError(
                  "class_weight '{0}' is not supported for "
                  "partial_fit. In order to use 'balanced' weights,"
                  " use compute_class_weight('{0}', "
                  "classes=classes, y=y). "
                  "In place of y you can us a large enough sample "
                  "of the full training set target to properly "
                  "estimate the class frequency distributions. "
                  "Pass the resulting weights as the class_weight "
                  "parameter.".format(self.class_weight)
              )
          return self._partial_fit(
              X,
              y,
              alpha=self.alpha,
              C=1.0,
              loss=self.loss,
              learning_rate=self.learning_rate,
              max_iter=1,
              classes=classes,
              sample_weight=sample_weight,
              coef_init=None,
              intercept_init=None,
          )
  
      def fit(self, X, y, coef_init=None, intercept_init=None, sample_weight=None):
          """Fit linear model with Stochastic Gradient Descent.
  
          Parameters
          ----------
          X : {array-like, sparse matrix}, shape (n_samples, n_features)
              Training data.
  
          y : ndarray of shape (n_samples,)
              Target values.
  
          coef_init : ndarray of shape (n_classes, n_features), default=None
              The initial coefficients to warm-start the optimization.
  
          intercept_init : ndarray of shape (n_classes,), default=None
              The initial intercept to warm-start the optimization.
  
          sample_weight : array-like, shape (n_samples,), default=None
              Weights applied to individual samples.
              If not provided, uniform weights are assumed. These weights will
              be multiplied with class_weight (passed through the
              constructor) if class_weight is specified.
  
          Returns
          -------
          self : object
              Returns an instance of self.
          """
          return self._fit(
              X,
              y,
              alpha=self.alpha,
              C=1.0,
              loss=self.loss,
              learning_rate=self.learning_rate,
              coef_init=coef_init,
              intercept_init=intercept_init,
              sample_weight=sample_weight,
          )
  
  
  class SGDClassifier(BaseSGDClassifier):
      """Linear classifiers (SVM, logistic regression, etc.) with SGD training.
  
      This estimator implements regularized linear models with stochastic
      gradient descent (SGD) learning: the gradient of the loss is estimated
      each sample at a time and the model is updated along the way with a
      decreasing strength schedule (aka learning rate). SGD allows minibatch
      (online/out-of-core) learning via the `partial_fit` method.
      For best results using the default learning rate schedule, the data should
      have zero mean and unit variance.
  
      This implementation works with data represented as dense or sparse arrays
      of floating point values for the features. The model it fits can be
      controlled with the loss parameter; by default, it fits a linear support
      vector machine (SVM).
  
      The regularizer is a penalty added to the loss function that shrinks model
      parameters towards the zero vector using either the squared euclidean norm
      L2 or the absolute norm L1 or a combination of both (Elastic Net). If the
      parameter update crosses the 0.0 value because of the regularizer, the
      update is truncated to 0.0 to allow for learning sparse models and achieve
      online feature selection.
  
      Read more in the :ref:`User Guide <sgd>`.
  
      Parameters
      ----------
      loss : str, default='hinge'
          The loss function to be used. Defaults to 'hinge', which gives a
          linear SVM.
  
          The possible options are 'hinge', 'log', 'modified_huber',
          'squared_hinge', 'perceptron', or a regression loss: 'squared_error',
          'huber', 'epsilon_insensitive', or 'squared_epsilon_insensitive'.
  
          The 'log' loss gives logistic regression, a probabilistic classifier.
          'modified_huber' is another smooth loss that brings tolerance to
          outliers as well as probability estimates.
          'squared_hinge' is like hinge but is quadratically penalized.
          'perceptron' is the linear loss used by the perceptron algorithm.
          The other losses are designed for regression but can be useful in
          classification as well; see
          :class:`~sklearn.linear_model.SGDRegressor` for a description.
  
          More details about the losses formulas can be found in the
          :ref:`User Guide <sgd_mathematical_formulation>`.
  
          .. deprecated:: 1.0
              The loss 'squared_loss' was deprecated in v1.0 and will be removed
              in version 1.2. Use `loss='squared_error'` which is equivalent.
  
      penalty : {'l2', 'l1', 'elasticnet'}, default='l2'
          The penalty (aka regularization term) to be used. Defaults to 'l2'
          which is the standard regularizer for linear SVM models. 'l1' and
          'elasticnet' might bring sparsity to the model (feature selection)
          not achievable with 'l2'.
  
      alpha : float, default=0.0001
          Constant that multiplies the regularization term. The higher the
          value, the stronger the regularization.
          Also used to compute the learning rate when set to `learning_rate` is
          set to 'optimal'.
  
      l1_ratio : float, default=0.15
          The Elastic Net mixing parameter, with 0 <= l1_ratio <= 1.
          l1_ratio=0 corresponds to L2 penalty, l1_ratio=1 to L1.
          Only used if `penalty` is 'elasticnet'.
  
      fit_intercept : bool, default=True
          Whether the intercept should be estimated or not. If False, the
          data is assumed to be already centered.
  
      max_iter : int, default=1000
          The maximum number of passes over the training data (aka epochs).
          It only impacts the behavior in the ``fit`` method, and not the
          :meth:`partial_fit` method.
  
          .. versionadded:: 0.19
  
      tol : float, default=1e-3
          The stopping criterion. If it is not None, training will stop
          when (loss > best_loss - tol) for ``n_iter_no_change`` consecutive
          epochs.
          Convergence is checked against the training loss or the
          validation loss depending on the `early_stopping` parameter.
  
          .. versionadded:: 0.19
  
      shuffle : bool, default=True
          Whether or not the training data should be shuffled after each epoch.
  
      verbose : int, default=0
          The verbosity level.
  
      epsilon : float, default=0.1
          Epsilon in the epsilon-insensitive loss functions; only if `loss` is
          'huber', 'epsilon_insensitive', or 'squared_epsilon_insensitive'.
          For 'huber', determines the threshold at which it becomes less
          important to get the prediction exactly right.
          For epsilon-insensitive, any differences between the current prediction
          and the correct label are ignored if they are less than this threshold.
  
      n_jobs : int, default=None
          The number of CPUs to use to do the OVA (One Versus All, for
          multi-class problems) computation.
          ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
          ``-1`` means using all processors. See :term:`Glossary <n_jobs>`
          for more details.
  
      random_state : int, RandomState instance, default=None
          Used for shuffling the data, when ``shuffle`` is set to ``True``.
          Pass an int for reproducible output across multiple function calls.
          See :term:`Glossary <random_state>`.
  
      learning_rate : str, default='optimal'
          The learning rate schedule:
  
          - 'constant': `eta = eta0`
          - 'optimal': `eta = 1.0 / (alpha * (t + t0))`
            where t0 is chosen by a heuristic proposed by Leon Bottou.
          - 'invscaling': `eta = eta0 / pow(t, power_t)`
          - 'adaptive': eta = eta0, as long as the training keeps decreasing.
            Each time n_iter_no_change consecutive epochs fail to decrease the
            training loss by tol or fail to increase validation score by tol if
            early_stopping is True, the current learning rate is divided by 5.
  
              .. versionadded:: 0.20
                  Added 'adaptive' option
  
      eta0 : double, default=0.0
          The initial learning rate for the 'constant', 'invscaling' or
          'adaptive' schedules. The default value is 0.0 as eta0 is not used by
          the default schedule 'optimal'.
  
      power_t : double, default=0.5
          The exponent for inverse scaling learning rate [default 0.5].
  
      early_stopping : bool, default=False
          Whether to use early stopping to terminate training when validation
          score is not improving. If set to True, it will automatically set aside
          a stratified fraction of training data as validation and terminate
          training when validation score returned by the `score` method is not
          improving by at least tol for n_iter_no_change consecutive epochs.
  
          .. versionadded:: 0.20
              Added 'early_stopping' option
  
      validation_fraction : float, default=0.1
          The proportion of training data to set aside as validation set for
          early stopping. Must be between 0 and 1.
          Only used if `early_stopping` is True.
  
          .. versionadded:: 0.20
              Added 'validation_fraction' option
  
      n_iter_no_change : int, default=5
          Number of iterations with no improvement to wait before stopping
          fitting.
          Convergence is checked against the training loss or the
          validation loss depending on the `early_stopping` parameter.
  
          .. versionadded:: 0.20
              Added 'n_iter_no_change' option
  
      class_weight : dict, {class_label: weight} or "balanced", default=None
          Preset for the class_weight fit parameter.
  
          Weights associated with classes. If not given, all classes
          are supposed to have weight one.
  
          The "balanced" mode uses the values of y to automatically adjust
          weights inversely proportional to class frequencies in the input data
          as ``n_samples / (n_classes * np.bincount(y))``.
  
      warm_start : bool, default=False
          When set to True, reuse the solution of the previous call to fit as
          initialization, otherwise, just erase the previous solution.
          See :term:`the Glossary <warm_start>`.
  
          Repeatedly calling fit or partial_fit when warm_start is True can
          result in a different solution than when calling fit a single time
          because of the way the data is shuffled.
          If a dynamic learning rate is used, the learning rate is adapted
          depending on the number of samples already seen. Calling ``fit`` resets
          this counter, while ``partial_fit`` will result in increasing the
          existing counter.
  
      average : bool or int, default=False
          When set to True, computes the averaged SGD weights across all
          updates and stores the result in the ``coef_`` attribute. If set to
          an int greater than 1, averaging will begin once the total number of
          samples seen reaches `average`. So ``average=10`` will begin
          averaging after seeing 10 samples.
  
      Attributes
      ----------
      coef_ : ndarray of shape (1, n_features) if n_classes == 2 else \
              (n_classes, n_features)
          Weights assigned to the features.
  
      intercept_ : ndarray of shape (1,) if n_classes == 2 else (n_classes,)
          Constants in decision function.
  
      n_iter_ : int
          The actual number of iterations before reaching the stopping criterion.
          For multiclass fits, it is the maximum over every binary fit.
  
      loss_function_ : concrete ``LossFunction``
  
      classes_ : array of shape (n_classes,)
  
      t_ : int
          Number of weight updates performed during training.
          Same as ``(n_iter_ * n_samples)``.
  
      n_features_in_ : int
          Number of features seen during :term:`fit`.
  
          .. versionadded:: 0.24
  
      feature_names_in_ : ndarray of shape (`n_features_in_`,)
          Names of features seen during :term:`fit`. Defined only when `X`
          has feature names that are all strings.
  
          .. versionadded:: 1.0
  
      See Also
      --------
      sklearn.svm.LinearSVC : Linear support vector classification.
      LogisticRegression : Logistic regression.
      Perceptron : Inherits from SGDClassifier. ``Perceptron()`` is equivalent to
          ``SGDClassifier(loss="perceptron", eta0=1, learning_rate="constant",
          penalty=None)``.
  
      Examples
      --------
      >>> import numpy as np
      >>> from sklearn.linear_model import SGDClassifier
      >>> from sklearn.preprocessing import StandardScaler
      >>> from sklearn.pipeline import make_pipeline
      >>> X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]])
      >>> Y = np.array([1, 1, 2, 2])
      >>> # Always scale the input. The most convenient way is to use a pipeline.
      >>> clf = make_pipeline(StandardScaler(),
      ...                     SGDClassifier(max_iter=1000, tol=1e-3))
      >>> clf.fit(X, Y)
      Pipeline(steps=[('standardscaler', StandardScaler()),
                      ('sgdclassifier', SGDClassifier())])
      >>> print(clf.predict([[-0.8, -1]]))
      [1]
      """
  
      def __init__(
          self,
          loss="hinge",
          *,
          penalty="l2",
          alpha=0.0001,
          l1_ratio=0.15,
          fit_intercept=True,
          max_iter=1000,
          tol=1e-3,
          shuffle=True,
          verbose=0,
          epsilon=DEFAULT_EPSILON,
          n_jobs=None,
          random_state=None,
          learning_rate="optimal",
          eta0=0.0,
          power_t=0.5,
          early_stopping=False,
          validation_fraction=0.1,
          n_iter_no_change=5,
          class_weight=None,
          warm_start=False,
          average=False,
      ):
          super().__init__(
              loss=loss,
              penalty=penalty,
              alpha=alpha,
              l1_ratio=l1_ratio,
              fit_intercept=fit_intercept,
              max_iter=max_iter,
              tol=tol,
              shuffle=shuffle,
              verbose=verbose,
              epsilon=epsilon,
              n_jobs=n_jobs,
              random_state=random_state,
              learning_rate=learning_rate,
              eta0=eta0,
              power_t=power_t,
              early_stopping=early_stopping,
              validation_fraction=validation_fraction,
              n_iter_no_change=n_iter_no_change,
              class_weight=class_weight,
              warm_start=warm_start,
              average=average,
          )
  
      def _check_proba(self):
          if self.loss not in ("log", "modified_huber"):
              raise AttributeError(
                  "probability estimates are not available for loss=%r" % self.loss
              )
          return True
  
      @available_if(_check_proba)
      def predict_proba(self, X):
          """Probability estimates.
  
          This method is only available for log loss and modified Huber loss.
  
          Multiclass probability estimates are derived from binary (one-vs.-rest)
          estimates by simple normalization, as recommended by Zadrozny and
          Elkan.
  
          Binary probability estimates for loss="modified_huber" are given by
          (clip(decision_function(X), -1, 1) + 1) / 2. For other loss functions
          it is necessary to perform proper probability calibration by wrapping
          the classifier with
          :class:`~sklearn.calibration.CalibratedClassifierCV` instead.
  
          Parameters
          ----------
          X : {array-like, sparse matrix}, shape (n_samples, n_features)
              Input data for prediction.
  
          Returns
          -------
          ndarray of shape (n_samples, n_classes)
              Returns the probability of the sample for each class in the model,
              where classes are ordered as they are in `self.classes_`.
  
          References
          ----------
          Zadrozny and Elkan, "Transforming classifier scores into multiclass
          probability estimates", SIGKDD'02,
          https://dl.acm.org/doi/pdf/10.1145/775047.775151
  
          The justification for the formula in the loss="modified_huber"
          case is in the appendix B in:
          http://jmlr.csail.mit.edu/papers/volume2/zhang02c/zhang02c.pdf
          """
          check_is_fitted(self)
  
          if self.loss == "log":
              return self._predict_proba_lr(X)
  
          elif self.loss == "modified_huber":
              binary = len(self.classes_) == 2
              scores = self.decision_function(X)
  
              if binary:
                  prob2 = np.ones((scores.shape[0], 2))
                  prob = prob2[:, 1]
              else:
                  prob = scores
  
              np.clip(scores, -1, 1, prob)
              prob += 1.0
              prob /= 2.0
  
              if binary:
                  prob2[:, 0] -= prob
                  prob = prob2
              else:
                  # the above might assign zero to all classes, which doesn't
                  # normalize neatly; work around this to produce uniform
                  # probabilities
                  prob_sum = prob.sum(axis=1)
                  all_zero = prob_sum == 0
                  if np.any(all_zero):
                      prob[all_zero, :] = 1
                      prob_sum[all_zero] = len(self.classes_)
  
                  # normalize
                  prob /= prob_sum.reshape((prob.shape[0], -1))
  
              return prob
  
          else:
              raise NotImplementedError(
                  "predict_(log_)proba only supported when"
                  " loss='log' or loss='modified_huber' "
                  "(%r given)"
                  % self.loss
              )
  
      @available_if(_check_proba)
      def predict_log_proba(self, X):
          """Log of probability estimates.
  
          This method is only available for log loss and modified Huber loss.
  
          When loss="modified_huber", probability estimates may be hard zeros
          and ones, so taking the logarithm is not possible.
  
          See ``predict_proba`` for details.
  
          Parameters
          ----------
          X : {array-like, sparse matrix} of shape (n_samples, n_features)
              Input data for prediction.
  
          Returns
          -------
          T : array-like, shape (n_samples, n_classes)
              Returns the log-probability of the sample for each class in the
              model, where classes are ordered as they are in
              `self.classes_`.
          """
          return np.log(self.predict_proba(X))
  
      def _more_tags(self):
          return {
              "_xfail_checks": {
                  "check_sample_weights_invariance": (
                      "zero sample_weight is not equivalent to removing samples"
                  ),
              }
          }
  
  
  class BaseSGDRegressor(RegressorMixin, BaseSGD):
  
      # TODO: Remove squared_loss in v1.2
      loss_functions = {
          "squared_error": (SquaredLoss,),
          "squared_loss": (SquaredLoss,),
          "huber": (Huber, DEFAULT_EPSILON),
          "epsilon_insensitive": (EpsilonInsensitive, DEFAULT_EPSILON),
          "squared_epsilon_insensitive": (SquaredEpsilonInsensitive, DEFAULT_EPSILON),
      }
  
      @abstractmethod
      def __init__(
          self,
          loss="squared_error",
          *,
          penalty="l2",
          alpha=0.0001,
          l1_ratio=0.15,
          fit_intercept=True,
          max_iter=1000,
          tol=1e-3,
          shuffle=True,
          verbose=0,
          epsilon=DEFAULT_EPSILON,
          random_state=None,
          learning_rate="invscaling",
          eta0=0.01,
          power_t=0.25,
          early_stopping=False,
          validation_fraction=0.1,
          n_iter_no_change=5,
          warm_start=False,
          average=False,
      ):
          super().__init__(
              loss=loss,
              penalty=penalty,
              alpha=alpha,
              l1_ratio=l1_ratio,
              fit_intercept=fit_intercept,
              max_iter=max_iter,
              tol=tol,
              shuffle=shuffle,
              verbose=verbose,
              epsilon=epsilon,
              random_state=random_state,
              learning_rate=learning_rate,
              eta0=eta0,
              power_t=power_t,
              early_stopping=early_stopping,
              validation_fraction=validation_fraction,
              n_iter_no_change=n_iter_no_change,
              warm_start=warm_start,
              average=average,
          )
  
      def _partial_fit(
          self,
          X,
          y,
          alpha,
          C,
          loss,
          learning_rate,
          max_iter,
          sample_weight,
          coef_init,
          intercept_init,
      ):
          first_call = getattr(self, "coef_", None) is None
          X, y = self._validate_data(
              X,
              y,
              accept_sparse="csr",
              copy=False,
              order="C",
              dtype=np.float64,
              accept_large_sparse=False,
              reset=first_call,
          )
          y = y.astype(np.float64, copy=False)
  
          n_samples, n_features = X.shape
  
          sample_weight = _check_sample_weight(sample_weight, X)
  
          # Allocate datastructures from input arguments
          if first_call:
              self._allocate_parameter_mem(1, n_features, coef_init, intercept_init)
          if self.average > 0 and getattr(self, "_average_coef", None) is None:
              self._average_coef = np.zeros(n_features, dtype=np.float64, order="C")
              self._average_intercept = np.zeros(1, dtype=np.float64, order="C")
  
          self._fit_regressor(
              X, y, alpha, C, loss, learning_rate, sample_weight, max_iter
          )
  
          return self
  
      def partial_fit(self, X, y, sample_weight=None):
          """Perform one epoch of stochastic gradient descent on given samples.
  
          Internally, this method uses ``max_iter = 1``. Therefore, it is not
          guaranteed that a minimum of the cost function is reached after calling
          it once. Matters such as objective convergence and early stopping
          should be handled by the user.
  
          Parameters
          ----------
          X : {array-like, sparse matrix}, shape (n_samples, n_features)
              Subset of training data.
  
          y : numpy array of shape (n_samples,)
              Subset of target values.
  
          sample_weight : array-like, shape (n_samples,), default=None
              Weights applied to individual samples.
              If not provided, uniform weights are assumed.
  
          Returns
          -------
          self : object
              Returns an instance of self.
          """
          self._validate_params(for_partial_fit=True)
          return self._partial_fit(
              X,
              y,
              self.alpha,
              C=1.0,
              loss=self.loss,
              learning_rate=self.learning_rate,
              max_iter=1,
              sample_weight=sample_weight,
              coef_init=None,
              intercept_init=None,
          )
  
      def _fit(
          self,
          X,
          y,
          alpha,
          C,
          loss,
          learning_rate,
          coef_init=None,
          intercept_init=None,
          sample_weight=None,
      ):
          self._validate_params()
          if self.warm_start and getattr(self, "coef_", None) is not None:
              if coef_init is None:
                  coef_init = self.coef_
              if intercept_init is None:
                  intercept_init = self.intercept_
          else:
              self.coef_ = None
              self.intercept_ = None
  
          # Clear iteration count for multiple call to fit.
          self.t_ = 1.0
  
          self._partial_fit(
              X,
              y,
              alpha,
              C,
              loss,
              learning_rate,
              self.max_iter,
              sample_weight,
              coef_init,
              intercept_init,
          )
  
          if (
              self.tol is not None
              and self.tol > -np.inf
              and self.n_iter_ == self.max_iter
          ):
              warnings.warn(
                  "Maximum number of iteration reached before "
                  "convergence. Consider increasing max_iter to "
                  "improve the fit.",
                  ConvergenceWarning,
              )
  
          return self
  
      def fit(self, X, y, coef_init=None, intercept_init=None, sample_weight=None):
          """Fit linear model with Stochastic Gradient Descent.
  
          Parameters
          ----------
          X : {array-like, sparse matrix}, shape (n_samples, n_features)
              Training data.
  
          y : ndarray of shape (n_samples,)
              Target values.
  
          coef_init : ndarray of shape (n_features,), default=None
              The initial coefficients to warm-start the optimization.
  
          intercept_init : ndarray of shape (1,), default=None
              The initial intercept to warm-start the optimization.
  
          sample_weight : array-like, shape (n_samples,), default=None
              Weights applied to individual samples (1. for unweighted).
  
          Returns
          -------
          self : object
              Fitted `SGDRegressor` estimator.
          """
          return self._fit(
              X,
              y,
              alpha=self.alpha,
              C=1.0,
              loss=self.loss,
              learning_rate=self.learning_rate,
              coef_init=coef_init,
              intercept_init=intercept_init,
              sample_weight=sample_weight,
          )
  
      def _decision_function(self, X):
          """Predict using the linear model
  
          Parameters
          ----------
          X : {array-like, sparse matrix}, shape (n_samples, n_features)
  
          Returns
          -------
          ndarray of shape (n_samples,)
             Predicted target values per element in X.
          """
          check_is_fitted(self)
  
          X = self._validate_data(X, accept_sparse="csr", reset=False)
  
          scores = safe_sparse_dot(X, self.coef_.T, dense_output=True) + self.intercept_
          return scores.ravel()
  
      def predict(self, X):
          """Predict using the linear model.
  
          Parameters
          ----------
          X : {array-like, sparse matrix}, shape (n_samples, n_features)
              Input data.
  
          Returns
          -------
          ndarray of shape (n_samples,)
             Predicted target values per element in X.
          """
          return self._decision_function(X)
  
      def _fit_regressor(
          self, X, y, alpha, C, loss, learning_rate, sample_weight, max_iter
      ):
          dataset, intercept_decay = make_dataset(X, y, sample_weight)
  
          loss_function = self._get_loss_function(loss)
          penalty_type = self._get_penalty_type(self.penalty)
          learning_rate_type = self._get_learning_rate_type(learning_rate)
  
          if not hasattr(self, "t_"):
              self.t_ = 1.0
  
          validation_mask = self._make_validation_split(y)
          validation_score_cb = self._make_validation_score_cb(
              validation_mask, X, y, sample_weight
          )
  
          random_state = check_random_state(self.random_state)
          # numpy mtrand expects a C long which is a signed 32 bit integer under
          # Windows
          seed = random_state.randint(0, np.iinfo(np.int32).max)
  
          tol = self.tol if self.tol is not None else -np.inf
  
          if self.average:
              coef = self._standard_coef
              intercept = self._standard_intercept
              average_coef = self._average_coef
              average_intercept = self._average_intercept
          else:
              coef = self.coef_
              intercept = self.intercept_
              average_coef = None  # Not used
              average_intercept = [0]  # Not used
  
          coef, intercept, average_coef, average_intercept, self.n_iter_ = _plain_sgd(
              coef,
              intercept[0],
              average_coef,
              average_intercept[0],
              loss_function,
              penalty_type,
              alpha,
              C,
              self.l1_ratio,
              dataset,
              validation_mask,
              self.early_stopping,
              validation_score_cb,
              int(self.n_iter_no_change),
              max_iter,
              tol,
              int(self.fit_intercept),
              int(self.verbose),
              int(self.shuffle),
              seed,
              1.0,
              1.0,
              learning_rate_type,
              self.eta0,
              self.power_t,
              0,
              self.t_,
              intercept_decay,
              self.average,
          )
  
          self.t_ += self.n_iter_ * X.shape[0]
  
          if self.average > 0:
              self._average_intercept = np.atleast_1d(average_intercept)
              self._standard_intercept = np.atleast_1d(intercept)
  
              if self.average <= self.t_ - 1.0:
                  # made enough updates for averaging to be taken into account
                  self.coef_ = average_coef
                  self.intercept_ = np.atleast_1d(average_intercept)
              else:
                  self.coef_ = coef
                  self.intercept_ = np.atleast_1d(intercept)
  
          else:
              self.intercept_ = np.atleast_1d(intercept)
  
  
  class SGDRegressor(BaseSGDRegressor):
      """Linear model fitted by minimizing a regularized empirical loss with SGD.
  
      SGD stands for Stochastic Gradient Descent: the gradient of the loss is
      estimated each sample at a time and the model is updated along the way with
      a decreasing strength schedule (aka learning rate).
  
      The regularizer is a penalty added to the loss function that shrinks model
      parameters towards the zero vector using either the squared euclidean norm
      L2 or the absolute norm L1 or a combination of both (Elastic Net). If the
      parameter update crosses the 0.0 value because of the regularizer, the
      update is truncated to 0.0 to allow for learning sparse models and achieve
      online feature selection.
  
      This implementation works with data represented as dense numpy arrays of
      floating point values for the features.
  
      Read more in the :ref:`User Guide <sgd>`.
  
      Parameters
      ----------
      loss : str, default='squared_error'
          The loss function to be used. The possible values are 'squared_error',
          'huber', 'epsilon_insensitive', or 'squared_epsilon_insensitive'
  
          The 'squared_error' refers to the ordinary least squares fit.
          'huber' modifies 'squared_error' to focus less on getting outliers
          correct by switching from squared to linear loss past a distance of
          epsilon. 'epsilon_insensitive' ignores errors less than epsilon and is
          linear past that; this is the loss function used in SVR.
          'squared_epsilon_insensitive' is the same but becomes squared loss past
          a tolerance of epsilon.
  
          More details about the losses formulas can be found in the
          :ref:`User Guide <sgd_mathematical_formulation>`.
  
          .. deprecated:: 1.0
              The loss 'squared_loss' was deprecated in v1.0 and will be removed
              in version 1.2. Use `loss='squared_error'` which is equivalent.
  
      penalty : {'l2', 'l1', 'elasticnet'}, default='l2'
          The penalty (aka regularization term) to be used. Defaults to 'l2'
          which is the standard regularizer for linear SVM models. 'l1' and
          'elasticnet' might bring sparsity to the model (feature selection)
          not achievable with 'l2'.
  
      alpha : float, default=0.0001
          Constant that multiplies the regularization term. The higher the
          value, the stronger the regularization.
          Also used to compute the learning rate when set to `learning_rate` is
          set to 'optimal'.
  
      l1_ratio : float, default=0.15
          The Elastic Net mixing parameter, with 0 <= l1_ratio <= 1.
          l1_ratio=0 corresponds to L2 penalty, l1_ratio=1 to L1.
          Only used if `penalty` is 'elasticnet'.
  
      fit_intercept : bool, default=True
          Whether the intercept should be estimated or not. If False, the
          data is assumed to be already centered.
  
      max_iter : int, default=1000
          The maximum number of passes over the training data (aka epochs).
          It only impacts the behavior in the ``fit`` method, and not the
          :meth:`partial_fit` method.
  
          .. versionadded:: 0.19
  
      tol : float, default=1e-3
          The stopping criterion. If it is not None, training will stop
          when (loss > best_loss - tol) for ``n_iter_no_change`` consecutive
          epochs.
          Convergence is checked against the training loss or the
          validation loss depending on the `early_stopping` parameter.
  
          .. versionadded:: 0.19
  
      shuffle : bool, default=True
          Whether or not the training data should be shuffled after each epoch.
  
      verbose : int, default=0
          The verbosity level.
  
      epsilon : float, default=0.1
          Epsilon in the epsilon-insensitive loss functions; only if `loss` is
          'huber', 'epsilon_insensitive', or 'squared_epsilon_insensitive'.
          For 'huber', determines the threshold at which it becomes less
          important to get the prediction exactly right.
          For epsilon-insensitive, any differences between the current prediction
          and the correct label are ignored if they are less than this threshold.
  
      random_state : int, RandomState instance, default=None
          Used for shuffling the data, when ``shuffle`` is set to ``True``.
          Pass an int for reproducible output across multiple function calls.
          See :term:`Glossary <random_state>`.
  
      learning_rate : str, default='invscaling'
          The learning rate schedule:
  
          - 'constant': `eta = eta0`
          - 'optimal': `eta = 1.0 / (alpha * (t + t0))`
            where t0 is chosen by a heuristic proposed by Leon Bottou.
          - 'invscaling': `eta = eta0 / pow(t, power_t)`
          - 'adaptive': eta = eta0, as long as the training keeps decreasing.
            Each time n_iter_no_change consecutive epochs fail to decrease the
            training loss by tol or fail to increase validation score by tol if
            early_stopping is True, the current learning rate is divided by 5.
  
              .. versionadded:: 0.20
                  Added 'adaptive' option
  
      eta0 : double, default=0.01
          The initial learning rate for the 'constant', 'invscaling' or
          'adaptive' schedules. The default value is 0.01.
  
      power_t : double, default=0.25
          The exponent for inverse scaling learning rate.
  
      early_stopping : bool, default=False
          Whether to use early stopping to terminate training when validation
          score is not improving. If set to True, it will automatically set aside
          a fraction of training data as validation and terminate
          training when validation score returned by the `score` method is not
          improving by at least `tol` for `n_iter_no_change` consecutive
          epochs.
  
          .. versionadded:: 0.20
              Added 'early_stopping' option
  
      validation_fraction : float, default=0.1
          The proportion of training data to set aside as validation set for
          early stopping. Must be between 0 and 1.
          Only used if `early_stopping` is True.
  
          .. versionadded:: 0.20
              Added 'validation_fraction' option
  
      n_iter_no_change : int, default=5
          Number of iterations with no improvement to wait before stopping
          fitting.
          Convergence is checked against the training loss or the
          validation loss depending on the `early_stopping` parameter.
  
          .. versionadded:: 0.20
              Added 'n_iter_no_change' option
  
      warm_start : bool, default=False
          When set to True, reuse the solution of the previous call to fit as
          initialization, otherwise, just erase the previous solution.
          See :term:`the Glossary <warm_start>`.
  
          Repeatedly calling fit or partial_fit when warm_start is True can
          result in a different solution than when calling fit a single time
          because of the way the data is shuffled.
          If a dynamic learning rate is used, the learning rate is adapted
          depending on the number of samples already seen. Calling ``fit`` resets
          this counter, while ``partial_fit``  will result in increasing the
          existing counter.
  
      average : bool or int, default=False
          When set to True, computes the averaged SGD weights across all
          updates and stores the result in the ``coef_`` attribute. If set to
          an int greater than 1, averaging will begin once the total number of
          samples seen reaches `average`. So ``average=10`` will begin
          averaging after seeing 10 samples.
  
      Attributes
      ----------
      coef_ : ndarray of shape (n_features,)
          Weights assigned to the features.
  
      intercept_ : ndarray of shape (1,)
          The intercept term.
  
      n_iter_ : int
          The actual number of iterations before reaching the stopping criterion.
  
      t_ : int
          Number of weight updates performed during training.
          Same as ``(n_iter_ * n_samples)``.
  
      n_features_in_ : int
          Number of features seen during :term:`fit`.
  
          .. versionadded:: 0.24
  
      feature_names_in_ : ndarray of shape (`n_features_in_`,)
          Names of features seen during :term:`fit`. Defined only when `X`
          has feature names that are all strings.
  
          .. versionadded:: 1.0
  
      See Also
      --------
      HuberRegressor : Linear regression model that is robust to outliers.
      Lars : Least Angle Regression model.
      Lasso : Linear Model trained with L1 prior as regularizer.
      RANSACRegressor : RANSAC (RANdom SAmple Consensus) algorithm.
      Ridge : Linear least squares with l2 regularization.
      sklearn.svm.SVR : Epsilon-Support Vector Regression.
      TheilSenRegressor : Theil-Sen Estimator robust multivariate regression model.
  
      Examples
      --------
      >>> import numpy as np
      >>> from sklearn.linear_model import SGDRegressor
      >>> from sklearn.pipeline import make_pipeline
      >>> from sklearn.preprocessing import StandardScaler
      >>> n_samples, n_features = 10, 5
      >>> rng = np.random.RandomState(0)
      >>> y = rng.randn(n_samples)
      >>> X = rng.randn(n_samples, n_features)
      >>> # Always scale the input. The most convenient way is to use a pipeline.
      >>> reg = make_pipeline(StandardScaler(),
      ...                     SGDRegressor(max_iter=1000, tol=1e-3))
      >>> reg.fit(X, y)
      Pipeline(steps=[('standardscaler', StandardScaler()),
                      ('sgdregressor', SGDRegressor())])
      """
  
      def __init__(
          self,
          loss="squared_error",
          *,
          penalty="l2",
          alpha=0.0001,
          l1_ratio=0.15,
          fit_intercept=True,
          max_iter=1000,
          tol=1e-3,
          shuffle=True,
          verbose=0,
          epsilon=DEFAULT_EPSILON,
          random_state=None,
          learning_rate="invscaling",
          eta0=0.01,
          power_t=0.25,
          early_stopping=False,
          validation_fraction=0.1,
          n_iter_no_change=5,
          warm_start=False,
          average=False,
      ):
          super().__init__(
              loss=loss,
              penalty=penalty,
              alpha=alpha,
              l1_ratio=l1_ratio,
              fit_intercept=fit_intercept,
              max_iter=max_iter,
              tol=tol,
              shuffle=shuffle,
              verbose=verbose,
              epsilon=epsilon,
              random_state=random_state,
              learning_rate=learning_rate,
              eta0=eta0,
              power_t=power_t,
              early_stopping=early_stopping,
              validation_fraction=validation_fraction,
              n_iter_no_change=n_iter_no_change,
              warm_start=warm_start,
              average=average,
          )
  
      def _more_tags(self):
          return {
              "_xfail_checks": {
                  "check_sample_weights_invariance": (
                      "zero sample_weight is not equivalent to removing samples"
                  ),
              }
          }
  
  
  class SGDOneClassSVM(BaseSGD, OutlierMixin):
      """Solves linear One-Class SVM using Stochastic Gradient Descent.
  
      This implementation is meant to be used with a kernel approximation
      technique (e.g. `sklearn.kernel_approximation.Nystroem`) to obtain results
      similar to `sklearn.svm.OneClassSVM` which uses a Gaussian kernel by
      default.
  
      Read more in the :ref:`User Guide <sgd_online_one_class_svm>`.
  
      .. versionadded:: 1.0
  
      Parameters
      ----------
      nu : float, optional
          The nu parameter of the One Class SVM: an upper bound on the
          fraction of training errors and a lower bound of the fraction of
          support vectors. Should be in the interval (0, 1]. By default 0.5
          will be taken.
  
      fit_intercept : bool
          Whether the intercept should be estimated or not. Defaults to True.
  
      max_iter : int, optional
          The maximum number of passes over the training data (aka epochs).
          It only impacts the behavior in the ``fit`` method, and not the
          `partial_fit`. Defaults to 1000.
  
      tol : float or None, optional
          The stopping criterion. If it is not None, the iterations will stop
          when (loss > previous_loss - tol). Defaults to 1e-3.
  
      shuffle : bool, optional
          Whether or not the training data should be shuffled after each epoch.
          Defaults to True.
  
      verbose : int, optional
          The verbosity level.
  
      random_state : int, RandomState instance or None, optional (default=None)
          The seed of the pseudo random number generator to use when shuffling
          the data.  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`.
  
      learning_rate : str, optional
          The learning rate schedule to use with `fit`. (If using `partial_fit`,
          learning rate must be controlled directly).
  
          'constant':
              eta = eta0
          'optimal': [default]
              eta = 1.0 / (alpha * (t + t0))
              where t0 is chosen by a heuristic proposed by Leon Bottou.
          'invscaling':
              eta = eta0 / pow(t, power_t)
          'adaptive':
              eta = eta0, as long as the training keeps decreasing.
              Each time n_iter_no_change consecutive epochs fail to decrease the
              training loss by tol or fail to increase validation score by tol if
              early_stopping is True, the current learning rate is divided by 5.
  
      eta0 : double
          The initial learning rate for the 'constant', 'invscaling' or
          'adaptive' schedules. The default value is 0.0 as eta0 is not used by
          the default schedule 'optimal'.
  
      power_t : double
          The exponent for inverse scaling learning rate [default 0.5].
  
      warm_start : bool, optional
          When set to True, reuse the solution of the previous call to fit as
          initialization, otherwise, just erase the previous solution.
          See :term:`the Glossary <warm_start>`.
  
          Repeatedly calling fit or partial_fit when warm_start is True can
          result in a different solution than when calling fit a single time
          because of the way the data is shuffled.
          If a dynamic learning rate is used, the learning rate is adapted
          depending on the number of samples already seen. Calling ``fit`` resets
          this counter, while ``partial_fit``  will result in increasing the
          existing counter.
  
      average : bool or int, optional
          When set to True, computes the averaged SGD weights and stores the
          result in the ``coef_`` attribute. If set to an int greater than 1,
          averaging will begin once the total number of samples seen reaches
          average. So ``average=10`` will begin averaging after seeing 10
          samples.
  
      Attributes
      ----------
      coef_ : array, shape (1, n_features)
          Weights assigned to the features.
  
      offset_ : array, shape (1,)
          Offset used to define the decision function from the raw scores.
          We have the relation: decision_function = score_samples - offset.
  
      n_iter_ : int
          The actual number of iterations to reach the stopping criterion.
  
      t_ : int
          Number of weight updates performed during training.
          Same as ``(n_iter_ * n_samples)``.
  
      loss_function_ : concrete ``LossFunction``
  
      n_features_in_ : int
          Number of features seen during :term:`fit`.
  
          .. versionadded:: 0.24
  
      feature_names_in_ : ndarray of shape (`n_features_in_`,)
          Names of features seen during :term:`fit`. Defined only when `X`
          has feature names that are all strings.
  
          .. versionadded:: 1.0
  
      See Also
      --------
      sklearn.svm.OneClassSVM : Unsupervised Outlier Detection.
  
      Notes
      -----
      This estimator has a linear complexity in the number of training samples
      and is thus better suited than the `sklearn.svm.OneClassSVM`
      implementation for datasets with a large number of training samples (say
      > 10,000).
  
      Examples
      --------
      >>> import numpy as np
      >>> from sklearn import linear_model
      >>> X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]])
      >>> clf = linear_model.SGDOneClassSVM(random_state=42)
      >>> clf.fit(X)
      SGDOneClassSVM(random_state=42)
  
      >>> print(clf.predict([[4, 4]]))
      [1]
      """
  
      loss_functions = {"hinge": (Hinge, 1.0)}
  
      def __init__(
          self,
          nu=0.5,
          fit_intercept=True,
          max_iter=1000,
          tol=1e-3,
          shuffle=True,
          verbose=0,
          random_state=None,
          learning_rate="optimal",
          eta0=0.0,
          power_t=0.5,
          warm_start=False,
          average=False,
      ):
  
          alpha = nu / 2
          self.nu = nu
          super(SGDOneClassSVM, self).__init__(
              loss="hinge",
              penalty="l2",
              alpha=alpha,
              C=1.0,
              l1_ratio=0,
              fit_intercept=fit_intercept,
              max_iter=max_iter,
              tol=tol,
              shuffle=shuffle,
              verbose=verbose,
              epsilon=DEFAULT_EPSILON,
              random_state=random_state,
              learning_rate=learning_rate,
              eta0=eta0,
              power_t=power_t,
              early_stopping=False,
              validation_fraction=0.1,
              n_iter_no_change=5,
              warm_start=warm_start,
              average=average,
          )
  
      def _validate_params(self, for_partial_fit=False):
          """Validate input params."""
          if not (0 < self.nu <= 1):
              raise ValueError("nu must be in (0, 1], got nu=%f" % self.nu)
  
          super(SGDOneClassSVM, self)._validate_params(for_partial_fit=for_partial_fit)
  
      def _fit_one_class(self, X, alpha, C, sample_weight, learning_rate, max_iter):
          """Uses SGD implementation with X and y=np.ones(n_samples)."""
  
          # The One-Class SVM uses the SGD implementation with
          # y=np.ones(n_samples).
          n_samples = X.shape[0]
          y = np.ones(n_samples, dtype=np.float64, order="C")
  
          dataset, offset_decay = make_dataset(X, y, sample_weight)
  
          penalty_type = self._get_penalty_type(self.penalty)
          learning_rate_type = self._get_learning_rate_type(learning_rate)
  
          # early stopping is set to False for the One-Class SVM. thus
          # validation_mask and validation_score_cb will be set to values
          # associated to early_stopping=False in _make_validation_split and
          # _make_validation_score_cb respectively.
          validation_mask = self._make_validation_split(y)
          validation_score_cb = self._make_validation_score_cb(
              validation_mask, X, y, sample_weight
          )
  
          random_state = check_random_state(self.random_state)
          # numpy mtrand expects a C long which is a signed 32 bit integer under
          # Windows
          seed = random_state.randint(0, np.iinfo(np.int32).max)
  
          tol = self.tol if self.tol is not None else -np.inf
  
          one_class = 1
          # There are no class weights for the One-Class SVM and they are
          # therefore set to 1.
          pos_weight = 1
          neg_weight = 1
  
          if self.average:
              coef = self._standard_coef
              intercept = self._standard_intercept
              average_coef = self._average_coef
              average_intercept = self._average_intercept
          else:
              coef = self.coef_
              intercept = 1 - self.offset_
              average_coef = None  # Not used
              average_intercept = [0]  # Not used
  
          coef, intercept, average_coef, average_intercept, self.n_iter_ = _plain_sgd(
              coef,
              intercept[0],
              average_coef,
              average_intercept[0],
              self.loss_function_,
              penalty_type,
              alpha,
              C,
              self.l1_ratio,
              dataset,
              validation_mask,
              self.early_stopping,
              validation_score_cb,
              int(self.n_iter_no_change),
              max_iter,
              tol,
              int(self.fit_intercept),
              int(self.verbose),
              int(self.shuffle),
              seed,
              neg_weight,
              pos_weight,
              learning_rate_type,
              self.eta0,
              self.power_t,
              one_class,
              self.t_,
              offset_decay,
              self.average,
          )
  
          self.t_ += self.n_iter_ * n_samples
  
          if self.average > 0:
  
              self._average_intercept = np.atleast_1d(average_intercept)
              self._standard_intercept = np.atleast_1d(intercept)
  
              if self.average <= self.t_ - 1.0:
                  # made enough updates for averaging to be taken into account
                  self.coef_ = average_coef
                  self.offset_ = 1 - np.atleast_1d(average_intercept)
              else:
                  self.coef_ = coef
                  self.offset_ = 1 - np.atleast_1d(intercept)
  
          else:
              self.offset_ = 1 - np.atleast_1d(intercept)
  
      def _partial_fit(
          self,
          X,
          alpha,
          C,
          loss,
          learning_rate,
          max_iter,
          sample_weight,
          coef_init,
          offset_init,
      ):
          first_call = getattr(self, "coef_", None) is None
          X = self._validate_data(
              X,
              None,
              accept_sparse="csr",
              dtype=np.float64,
              order="C",
              accept_large_sparse=False,
              reset=first_call,
          )
  
          n_features = X.shape[1]
  
          # Allocate datastructures from input arguments
          sample_weight = _check_sample_weight(sample_weight, X)
  
          # We use intercept = 1 - offset where intercept is the intercept of
          # the SGD implementation and offset is the offset of the One-Class SVM
          # optimization problem.
          if getattr(self, "coef_", None) is None or coef_init is not None:
              self._allocate_parameter_mem(1, n_features, coef_init, offset_init, 1)
          elif n_features != self.coef_.shape[-1]:
              raise ValueError(
                  "Number of features %d does not match previous data %d."
                  % (n_features, self.coef_.shape[-1])
              )
  
          if self.average and getattr(self, "_average_coef", None) is None:
              self._average_coef = np.zeros(n_features, dtype=np.float64, order="C")
              self._average_intercept = np.zeros(1, dtype=np.float64, order="C")
  
          self.loss_function_ = self._get_loss_function(loss)
          if not hasattr(self, "t_"):
              self.t_ = 1.0
  
          # delegate to concrete training procedure
          self._fit_one_class(
              X,
              alpha=alpha,
              C=C,
              learning_rate=learning_rate,
              sample_weight=sample_weight,
              max_iter=max_iter,
          )
  
          return self
  
      def partial_fit(self, X, y=None, sample_weight=None):
          """Fit linear One-Class SVM with Stochastic Gradient Descent.
  
          Parameters
          ----------
          X : {array-like, sparse matrix}, shape (n_samples, n_features)
              Subset of the training data.
          y : Ignored
              Not used, present for API consistency by convention.
  
          sample_weight : array-like, shape (n_samples,), optional
              Weights applied to individual samples.
              If not provided, uniform weights are assumed.
  
          Returns
          -------
          self : object
              Returns a fitted instance of self.
          """
  
          alpha = self.nu / 2
          self._validate_params(for_partial_fit=True)
  
          return self._partial_fit(
              X,
              alpha,
              C=1.0,
              loss=self.loss,
              learning_rate=self.learning_rate,
              max_iter=1,
              sample_weight=sample_weight,
              coef_init=None,
              offset_init=None,
          )
  
      def _fit(
          self,
          X,
          alpha,
          C,
          loss,
          learning_rate,
          coef_init=None,
          offset_init=None,
          sample_weight=None,
      ):
          self._validate_params()
  
          if self.warm_start and hasattr(self, "coef_"):
              if coef_init is None:
                  coef_init = self.coef_
              if offset_init is None:
                  offset_init = self.offset_
          else:
              self.coef_ = None
              self.offset_ = None
  
          # Clear iteration count for multiple call to fit.
          self.t_ = 1.0
  
          self._partial_fit(
              X,
              alpha,
              C,
              loss,
              learning_rate,
              self.max_iter,
              sample_weight,
              coef_init,
              offset_init,
          )
  
          if (
              self.tol is not None
              and self.tol > -np.inf
              and self.n_iter_ == self.max_iter
          ):
              warnings.warn(
                  "Maximum number of iteration reached before "
                  "convergence. Consider increasing max_iter to "
                  "improve the fit.",
                  ConvergenceWarning,
              )
  
          return self
  
      def fit(self, X, y=None, coef_init=None, offset_init=None, sample_weight=None):
          """Fit linear One-Class SVM with Stochastic Gradient Descent.
  
          This solves an equivalent optimization problem of the
          One-Class SVM primal optimization problem and returns a weight vector
          w and an offset rho such that the decision function is given by
          <w, x> - rho.
  
          Parameters
          ----------
          X : {array-like, sparse matrix}, shape (n_samples, n_features)
              Training data.
          y : Ignored
              Not used, present for API consistency by convention.
  
          coef_init : array, shape (n_classes, n_features)
              The initial coefficients to warm-start the optimization.
  
          offset_init : array, shape (n_classes,)
              The initial offset to warm-start the optimization.
  
          sample_weight : array-like, shape (n_samples,), optional
              Weights applied to individual samples.
              If not provided, uniform weights are assumed. These weights will
              be multiplied with class_weight (passed through the
              constructor) if class_weight is specified.
  
          Returns
          -------
          self : object
              Returns a fitted instance of self.
          """
  
          alpha = self.nu / 2
          self._fit(
              X,
              alpha=alpha,
              C=1.0,
              loss=self.loss,
              learning_rate=self.learning_rate,
              coef_init=coef_init,
              offset_init=offset_init,
              sample_weight=sample_weight,
          )
  
          return self
  
      def decision_function(self, X):
          """Signed distance to the separating hyperplane.
  
          Signed distance is positive for an inlier and negative for an
          outlier.
  
          Parameters
          ----------
          X : {array-like, sparse matrix}, shape (n_samples, n_features)
              Testing data.
  
          Returns
          -------
          dec : array-like, shape (n_samples,)
              Decision function values of the samples.
          """
  
          check_is_fitted(self, "coef_")
  
          X = self._validate_data(X, accept_sparse="csr", reset=False)
          decisions = safe_sparse_dot(X, self.coef_.T, dense_output=True) - self.offset_
  
          return decisions.ravel()
  
      def score_samples(self, X):
          """Raw scoring function of the samples.
  
          Parameters
          ----------
          X : {array-like, sparse matrix}, shape (n_samples, n_features)
              Testing data.
  
          Returns
          -------
          score_samples : array-like, shape (n_samples,)
              Unshiffted scoring function values of the samples.
          """
          score_samples = self.decision_function(X) + self.offset_
          return score_samples
  
      def predict(self, X):
          """Return labels (1 inlier, -1 outlier) of the samples.
  
          Parameters
          ----------
          X : {array-like, sparse matrix}, shape (n_samples, n_features)
              Testing data.
  
          Returns
          -------
          y : array, shape (n_samples,)
              Labels of the samples.
          """
          y = (self.decision_function(X) >= 0).astype(np.int32)
          y[y == 0] = -1  # for consistency with outlier detectors
          return y
  
      def _more_tags(self):
          return {
              "_xfail_checks": {
                  "check_sample_weights_invariance": (
                      "zero sample_weight is not equivalent to removing samples"
                  )
              }
          }
  