content: # -*- coding: utf-8 -*-
  
  """
  The :mod:`sklearn.naive_bayes` module implements Naive Bayes algorithms. These
  are supervised learning methods based on applying Bayes' theorem with strong
  (naive) feature independence assumptions.
  """
  
  # Author: Vincent Michel <vincent.michel@inria.fr>
  #         Minor fixes by Fabian Pedregosa
  #         Amit Aides <amitibo@tx.technion.ac.il>
  #         Yehuda Finkelstein <yehudaf@tx.technion.ac.il>
  #         Lars Buitinck <L.J.Buitinck@uva.nl>
  #         Jan Hendrik Metzen <jhm@informatik.uni-bremen.de>
  #         (parts based on earlier work by Mathieu Blondel)
  #
  # License: BSD 3 clause
  
  from abc import ABCMeta, abstractmethod
  
  import numpy as np
  from scipy.sparse import issparse
  
  from .base import BaseEstimator, ClassifierMixin
  from .preprocessing import binarize
  from .preprocessing import LabelBinarizer
  from .preprocessing import label_binarize
  from .utils import check_X_y, check_array
  from .utils.extmath import safe_sparse_dot, logsumexp
  from .utils.multiclass import _check_partial_fit_first_call
  from .utils.fixes import in1d
  from .utils.validation import check_is_fitted
  from .externals import six
  
  __all__ = ['BernoulliNB', 'GaussianNB', 'MultinomialNB']
  
  
  class BaseNB(six.with_metaclass(ABCMeta, BaseEstimator, ClassifierMixin)):
      """Abstract base class for naive Bayes estimators"""
  
      @abstractmethod
      def _joint_log_likelihood(self, X):
          """Compute the unnormalized posterior log probability of X
  
          I.e. ``log P(c) + log P(x|c)`` for all rows x of X, as an array-like of
          shape [n_classes, n_samples].
  
          Input is passed to _joint_log_likelihood as-is by predict,
          predict_proba and predict_log_proba.
          """
  
      def predict(self, X):
          """
          Perform classification on an array of test vectors X.
  
          Parameters
          ----------
          X : array-like, shape = [n_samples, n_features]
  
          Returns
          -------
          C : array, shape = [n_samples]
              Predicted target values for X
          """
          jll = self._joint_log_likelihood(X)
          return self.classes_[np.argmax(jll, axis=1)]
  
      def predict_log_proba(self, X):
          """
          Return log-probability estimates for the test vector X.
  
          Parameters
          ----------
          X : array-like, shape = [n_samples, n_features]
  
          Returns
          -------
          C : array-like, shape = [n_samples, n_classes]
              Returns the log-probability of the samples for each class in
              the model. The columns correspond to the classes in sorted
              order, as they appear in the attribute `classes_`.
          """
          jll = self._joint_log_likelihood(X)
          # normalize by P(x) = P(f_1, ..., f_n)
          log_prob_x = logsumexp(jll, axis=1)
          return jll - np.atleast_2d(log_prob_x).T
  
      def predict_proba(self, X):
          """
          Return probability estimates for the test vector X.
  
          Parameters
          ----------
          X : array-like, shape = [n_samples, n_features]
  
          Returns
          -------
          C : array-like, shape = [n_samples, n_classes]
              Returns the probability of the samples for each class in
              the model. The columns correspond to the classes in sorted
              order, as they appear in the attribute `classes_`.
          """
          return np.exp(self.predict_log_proba(X))
  
  
  class GaussianNB(BaseNB):
      """
      Gaussian Naive Bayes (GaussianNB)
  
      Can perform online updates to model parameters via `partial_fit` method.
      For details on algorithm used to update feature means and variance online,
      see Stanford CS tech report STAN-CS-79-773 by Chan, Golub, and LeVeque:
  
          http://i.stanford.edu/pub/cstr/reports/cs/tr/79/773/CS-TR-79-773.pdf
  
      Read more in the :ref:`User Guide <gaussian_naive_bayes>`.
  
      Attributes
      ----------
      class_prior_ : array, shape (n_classes,)
          probability of each class.
  
      class_count_ : array, shape (n_classes,)
          number of training samples observed in each class.
  
      theta_ : array, shape (n_classes, n_features)
          mean of each feature per class
  
      sigma_ : array, shape (n_classes, n_features)
          variance of each feature per class
  
      Examples
      --------
      >>> import numpy as np
      >>> X = np.array([[-1, -1], [-2, -1], [-3, -2], [1, 1], [2, 1], [3, 2]])
      >>> Y = np.array([1, 1, 1, 2, 2, 2])
      >>> from sklearn.naive_bayes import GaussianNB
      >>> clf = GaussianNB()
      >>> clf.fit(X, Y)
      GaussianNB()
      >>> print(clf.predict([[-0.8, -1]]))
      [1]
      >>> clf_pf = GaussianNB()
      >>> clf_pf.partial_fit(X, Y, np.unique(Y))
      GaussianNB()
      >>> print(clf_pf.predict([[-0.8, -1]]))
      [1]
      """
  
      def fit(self, X, y, sample_weight=None):
          """Fit Gaussian Naive Bayes according to X, y
  
          Parameters
          ----------
          X : array-like, shape (n_samples, n_features)
              Training vectors, where n_samples is the number of samples
              and n_features is the number of features.
  
          y : array-like, shape (n_samples,)
              Target values.
  
          sample_weight : array-like, shape (n_samples,), optional
              Weights applied to individual samples (1. for unweighted).
  
          Returns
          -------
          self : object
              Returns self.
          """
          X, y = check_X_y(X, y)
          return self._partial_fit(X, y, np.unique(y), _refit=True,
                                   sample_weight=sample_weight)
  
      @staticmethod
      def _update_mean_variance(n_past, mu, var, X, sample_weight=None):
          """Compute online update of Gaussian mean and variance.
  
          Given starting sample count, mean, and variance, a new set of
          points X, and optionally sample weights, return the updated mean and
          variance. (NB - each dimension (column) in X is treated as independent
          -- you get variance, not covariance).
  
          Can take scalar mean and variance, or vector mean and variance to
          simultaneously update a number of independent Gaussians.
  
          See Stanford CS tech report STAN-CS-79-773 by Chan, Golub, and LeVeque:
  
          http://i.stanford.edu/pub/cstr/reports/cs/tr/79/773/CS-TR-79-773.pdf
  
          Parameters
          ----------
          n_past : int
              Number of samples represented in old mean and variance. If sample
              weights were given, this should contain the sum of sample
              weights represented in old mean and variance.
  
          mu : array-like, shape (number of Gaussians,)
              Means for Gaussians in original set.
  
          var : array-like, shape (number of Gaussians,)
              Variances for Gaussians in original set.
  
          sample_weight : array-like, shape (n_samples,), optional
              Weights applied to individual samples (1. for unweighted).
  
          Returns
          -------
          total_mu : array-like, shape (number of Gaussians,)
              Updated mean for each Gaussian over the combined set.
  
          total_var : array-like, shape (number of Gaussians,)
              Updated variance for each Gaussian over the combined set.
          """
          if X.shape[0] == 0:
              return mu, var
  
          # Compute (potentially weighted) mean and variance of new datapoints
          if sample_weight is not None:
              n_new = float(sample_weight.sum())
              new_mu = np.average(X, axis=0, weights=sample_weight / n_new)
              new_var = np.average((X - new_mu) ** 2, axis=0,
                                   weights=sample_weight / n_new)
          else:
              n_new = X.shape[0]
              new_var = np.var(X, axis=0)
              new_mu = np.mean(X, axis=0)
  
          if n_past == 0:
              return new_mu, new_var
  
          n_total = float(n_past + n_new)
  
          # Combine mean of old and new data, taking into consideration
          # (weighted) number of observations
          total_mu = (n_new * new_mu + n_past * mu) / n_total
  
          # Combine variance of old and new data, taking into consideration
          # (weighted) number of observations. This is achieved by combining
          # the sum-of-squared-differences (ssd)
          old_ssd = n_past * var
          new_ssd = n_new * new_var
          total_ssd = (old_ssd + new_ssd +
                       (n_past / float(n_new * n_total)) *
                       (n_new * mu - n_new * new_mu) ** 2)
          total_var = total_ssd / n_total
  
          return total_mu, total_var
  
      def partial_fit(self, X, y, classes=None, sample_weight=None):
          """Incremental fit on a batch of samples.
  
          This method is expected to be called several times consecutively
          on different chunks of a dataset so as to implement out-of-core
          or online learning.
  
          This is especially useful when the whole dataset is too big to fit in
          memory at once.
  
          This method has some performance and numerical stability overhead,
          hence it is better to call partial_fit on chunks of data that are
          as large as possible (as long as fitting in the memory budget) to
          hide the overhead.
  
          Parameters
          ----------
          X : array-like, shape (n_samples, n_features)
              Training vectors, where n_samples is the number of samples and
              n_features is the number of features.
  
          y : array-like, shape (n_samples,)
              Target values.
  
          classes : array-like, shape (n_classes,)
              List of all the classes that can possibly appear in the y vector.
  
              Must be provided at the first call to partial_fit, can be omitted
              in subsequent calls.
  
          sample_weight : array-like, shape (n_samples,), optional
              Weights applied to individual samples (1. for unweighted).
  
          Returns
          -------
          self : object
              Returns self.
          """
          return self._partial_fit(X, y, classes, _refit=False,
                                   sample_weight=sample_weight)
  
      def _partial_fit(self, X, y, classes=None, _refit=False,
                       sample_weight=None):
          """Actual implementation of Gaussian NB fitting.
  
          Parameters
          ----------
          X : array-like, shape (n_samples, n_features)
              Training vectors, where n_samples is the number of samples and
              n_features is the number of features.
  
          y : array-like, shape (n_samples,)
              Target values.
  
          classes : array-like, shape (n_classes,)
              List of all the classes that can possibly appear in the y vector.
  
              Must be provided at the first call to partial_fit, can be omitted
              in subsequent calls.
  
          _refit: bool
              If true, act as though this were the first time we called
              _partial_fit (ie, throw away any past fitting and start over).
  
          sample_weight : array-like, shape (n_samples,), optional
              Weights applied to individual samples (1. for unweighted).
  
          Returns
          -------
          self : object
              Returns self.
          """
  
          X, y = check_X_y(X, y)
          epsilon = 1e-9
  
          if _refit:
              self.classes_ = None
  
          if _check_partial_fit_first_call(self, classes):
              # This is the first call to partial_fit:
              # initialize various cumulative counters
              n_features = X.shape[1]
              n_classes = len(self.classes_)
              self.theta_ = np.zeros((n_classes, n_features))
              self.sigma_ = np.zeros((n_classes, n_features))
              self.class_prior_ = np.zeros(n_classes)
              self.class_count_ = np.zeros(n_classes)
          else:
              if X.shape[1] != self.theta_.shape[1]:
                  msg = "Number of features %d does not match previous data %d."
                  raise ValueError(msg % (X.shape[1], self.theta_.shape[1]))
              # Put epsilon back in each time
              self.sigma_[:, :] -= epsilon
  
          classes = self.classes_
  
          unique_y = np.unique(y)
          unique_y_in_classes = in1d(unique_y, classes)
  
          if not np.all(unique_y_in_classes):
              raise ValueError("The target label(s) %s in y do not exist in the "
                               "initial classes %s" %
                               (y[~unique_y_in_classes], classes))
  
          for y_i in unique_y:
              i = classes.searchsorted(y_i)
              X_i = X[y == y_i, :]
  
              if sample_weight is not None:
                  sw_i = sample_weight[y == y_i]
                  N_i = sw_i.sum()
              else:
                  sw_i = None
                  N_i = X_i.shape[0]
  
              new_theta, new_sigma = self._update_mean_variance(
                  self.class_count_[i], self.theta_[i, :], self.sigma_[i, :],
                  X_i, sw_i)
  
              self.theta_[i, :] = new_theta
              self.sigma_[i, :] = new_sigma
              self.class_count_[i] += N_i
  
          self.sigma_[:, :] += epsilon
          self.class_prior_[:] = self.class_count_ / np.sum(self.class_count_)
          return self
  
      def _joint_log_likelihood(self, X):
          check_is_fitted(self, "classes_")
  
          X = check_array(X)
          joint_log_likelihood = []
          for i in range(np.size(self.classes_)):
              jointi = np.log(self.class_prior_[i])
              n_ij = - 0.5 * np.sum(np.log(2. * np.pi * self.sigma_[i, :]))
              n_ij -= 0.5 * np.sum(((X - self.theta_[i, :]) ** 2) /
                                   (self.sigma_[i, :]), 1)
              joint_log_likelihood.append(jointi + n_ij)
  
          joint_log_likelihood = np.array(joint_log_likelihood).T
          return joint_log_likelihood
  
  
  class BaseDiscreteNB(BaseNB):
      """Abstract base class for naive Bayes on discrete/categorical data
  
      Any estimator based on this class should provide:
  
      __init__
      _joint_log_likelihood(X) as per BaseNB
      """
  
      def _update_class_log_prior(self, class_prior=None):
          n_classes = len(self.classes_)
          if class_prior is not None:
              if len(class_prior) != n_classes:
                  raise ValueError("Number of priors must match number of"
                                   " classes.")
              self.class_log_prior_ = np.log(class_prior)
          elif self.fit_prior:
              # empirical prior, with sample_weight taken into account
              self.class_log_prior_ = (np.log(self.class_count_)
                                       - np.log(self.class_count_.sum()))
          else:
              self.class_log_prior_ = np.zeros(n_classes) - np.log(n_classes)
  
      def partial_fit(self, X, y, classes=None, sample_weight=None):
          """Incremental fit on a batch of samples.
  
          This method is expected to be called several times consecutively
          on different chunks of a dataset so as to implement out-of-core
          or online learning.
  
          This is especially useful when the whole dataset is too big to fit in
          memory at once.
  
          This method has some performance overhead hence it is better to call
          partial_fit on chunks of data that are as large as possible
          (as long as fitting in the memory budget) to hide the overhead.
  
          Parameters
          ----------
          X : {array-like, sparse matrix}, shape = [n_samples, n_features]
              Training vectors, where n_samples is the number of samples and
              n_features is the number of features.
  
          y : array-like, shape = [n_samples]
              Target values.
  
          classes : array-like, shape = [n_classes]
              List of all the classes that can possibly appear in the y vector.
  
              Must be provided at the first call to partial_fit, can be omitted
              in subsequent calls.
  
          sample_weight : array-like, shape = [n_samples], optional
              Weights applied to individual samples (1. for unweighted).
  
          Returns
          -------
          self : object
              Returns self.
          """
          X = check_array(X, accept_sparse='csr', dtype=np.float64)
          _, n_features = X.shape
  
          if _check_partial_fit_first_call(self, classes):
              # This is the first call to partial_fit:
              # initialize various cumulative counters
              n_effective_classes = len(classes) if len(classes) > 1 else 2
              self.class_count_ = np.zeros(n_effective_classes, dtype=np.float64)
              self.feature_count_ = np.zeros((n_effective_classes, n_features),
                                             dtype=np.float64)
          elif n_features != self.coef_.shape[1]:
              msg = "Number of features %d does not match previous data %d."
              raise ValueError(msg % (n_features, self.coef_.shape[-1]))
  
          Y = label_binarize(y, classes=self.classes_)
          if Y.shape[1] == 1:
              Y = np.concatenate((1 - Y, Y), axis=1)
  
          n_samples, n_classes = Y.shape
  
          if X.shape[0] != Y.shape[0]:
              msg = "X.shape[0]=%d and y.shape[0]=%d are incompatible."
              raise ValueError(msg % (X.shape[0], y.shape[0]))
  
          # label_binarize() returns arrays with dtype=np.int64.
          # We convert it to np.float64 to support sample_weight consistently
          Y = Y.astype(np.float64)
          if sample_weight is not None:
              Y *= check_array(sample_weight).T
  
          class_prior = self.class_prior
  
          # Count raw events from data before updating the class log prior
          # and feature log probas
          self._count(X, Y)
  
          # XXX: OPTIM: we could introduce a public finalization method to
          # be called by the user explicitly just once after several consecutive
          # calls to partial_fit and prior any call to predict[_[log_]proba]
          # to avoid computing the smooth log probas at each call to partial fit
          self._update_feature_log_prob()
          self._update_class_log_prior(class_prior=class_prior)
          return self
  
      def fit(self, X, y, sample_weight=None):
          """Fit Naive Bayes classifier according to X, y
  
          Parameters
          ----------
          X : {array-like, sparse matrix}, shape = [n_samples, n_features]
              Training vectors, where n_samples is the number of samples and
              n_features is the number of features.
  
          y : array-like, shape = [n_samples]
              Target values.
  
          sample_weight : array-like, shape = [n_samples], optional
              Weights applied to individual samples (1. for unweighted).
  
          Returns
          -------
          self : object
              Returns self.
          """
          X, y = check_X_y(X, y, 'csr')
          _, n_features = X.shape
  
          labelbin = LabelBinarizer()
          Y = labelbin.fit_transform(y)
          self.classes_ = labelbin.classes_
          if Y.shape[1] == 1:
              Y = np.concatenate((1 - Y, Y), axis=1)
  
          # LabelBinarizer().fit_transform() returns arrays with dtype=np.int64.
          # We convert it to np.float64 to support sample_weight consistently;
          # this means we also don't have to cast X to floating point
          Y = Y.astype(np.float64)
          if sample_weight is not None:
              Y *= check_array(sample_weight).T
  
          class_prior = self.class_prior
  
          # Count raw events from data before updating the class log prior
          # and feature log probas
          n_effective_classes = Y.shape[1]
          self.class_count_ = np.zeros(n_effective_classes, dtype=np.float64)
          self.feature_count_ = np.zeros((n_effective_classes, n_features),
                                         dtype=np.float64)
          self._count(X, Y)
          self._update_feature_log_prob()
          self._update_class_log_prior(class_prior=class_prior)
          return self
  
      # XXX The following is a stopgap measure; we need to set the dimensions
      # of class_log_prior_ and feature_log_prob_ correctly.
      def _get_coef(self):
          return (self.feature_log_prob_[1:]
                  if len(self.classes_) == 2 else self.feature_log_prob_)
  
      def _get_intercept(self):
          return (self.class_log_prior_[1:]
                  if len(self.classes_) == 2 else self.class_log_prior_)
  
      coef_ = property(_get_coef)
      intercept_ = property(_get_intercept)
  
  
  class MultinomialNB(BaseDiscreteNB):
      """
      Naive Bayes classifier for multinomial models
  
      The multinomial Naive Bayes classifier is suitable for classification with
      discrete features (e.g., word counts for text classification). The
      multinomial distribution normally requires integer feature counts. However,
      in practice, fractional counts such as tf-idf may also work.
  
      Read more in the :ref:`User Guide <multinomial_naive_bayes>`.
  
      Parameters
      ----------
      alpha : float, optional (default=1.0)
          Additive (Laplace/Lidstone) smoothing parameter
          (0 for no smoothing).
  
      fit_prior : boolean
          Whether to learn class prior probabilities or not.
          If false, a uniform prior will be used.
  
      class_prior : array-like, size (n_classes,)
          Prior probabilities of the classes. If specified the priors are not
          adjusted according to the data.
  
      Attributes
      ----------
      class_log_prior_ : array, shape (n_classes, )
          Smoothed empirical log probability for each class.
  
      intercept_ : property
          Mirrors ``class_log_prior_`` for interpreting MultinomialNB
          as a linear model.
  
      feature_log_prob_ : array, shape (n_classes, n_features)
          Empirical log probability of features
          given a class, ``P(x_i|y)``.
  
      coef_ : property
          Mirrors ``feature_log_prob_`` for interpreting MultinomialNB
          as a linear model.
  
      class_count_ : array, shape (n_classes,)
          Number of samples encountered for each class during fitting. This
          value is weighted by the sample weight when provided.
  
      feature_count_ : array, shape (n_classes, n_features)
          Number of samples encountered for each (class, feature)
          during fitting. This value is weighted by the sample weight when
          provided.
  
      Examples
      --------
      >>> import numpy as np
      >>> X = np.random.randint(5, size=(6, 100))
      >>> y = np.array([1, 2, 3, 4, 5, 6])
      >>> from sklearn.naive_bayes import MultinomialNB
      >>> clf = MultinomialNB()
      >>> clf.fit(X, y)
      MultinomialNB(alpha=1.0, class_prior=None, fit_prior=True)
      >>> print(clf.predict(X[2]))
      [3]
  
      Notes
      -----
      For the rationale behind the names `coef_` and `intercept_`, i.e.
      naive Bayes as a linear classifier, see J. Rennie et al. (2003),
      Tackling the poor assumptions of naive Bayes text classifiers, ICML.
  
      References
      ----------
      C.D. Manning, P. Raghavan and H. Schuetze (2008). Introduction to
      Information Retrieval. Cambridge University Press, pp. 234-265.
      http://nlp.stanford.edu/IR-book/html/htmledition/naive-bayes-text-classification-1.html
      """
  
      def __init__(self, alpha=1.0, fit_prior=True, class_prior=None):
          self.alpha = alpha
          self.fit_prior = fit_prior
          self.class_prior = class_prior
  
      def _count(self, X, Y):
          """Count and smooth feature occurrences."""
          if np.any((X.data if issparse(X) else X) < 0):
              raise ValueError("Input X must be non-negative")
          self.feature_count_ += safe_sparse_dot(Y.T, X)
          self.class_count_ += Y.sum(axis=0)
  
      def _update_feature_log_prob(self):
          """Apply smoothing to raw counts and recompute log probabilities"""
          smoothed_fc = self.feature_count_ + self.alpha
          smoothed_cc = smoothed_fc.sum(axis=1)
  
          self.feature_log_prob_ = (np.log(smoothed_fc)
                                    - np.log(smoothed_cc.reshape(-1, 1)))
  
      def _joint_log_likelihood(self, X):
          """Calculate the posterior log probability of the samples X"""
          check_is_fitted(self, "classes_")
  
          X = check_array(X, accept_sparse='csr')
          return (safe_sparse_dot(X, self.feature_log_prob_.T)
                  + self.class_log_prior_)
  
  
  class BernoulliNB(BaseDiscreteNB):
      """Naive Bayes classifier for multivariate Bernoulli models.
  
      Like MultinomialNB, this classifier is suitable for discrete data. The
      difference is that while MultinomialNB works with occurrence counts,
      BernoulliNB is designed for binary/boolean features.
  
      Read more in the :ref:`User Guide <bernoulli_naive_bayes>`.
  
      Parameters
      ----------
      alpha : float, optional (default=1.0)
          Additive (Laplace/Lidstone) smoothing parameter
          (0 for no smoothing).
  
      binarize : float or None, optional
          Threshold for binarizing (mapping to booleans) of sample features.
          If None, input is presumed to already consist of binary vectors.
  
      fit_prior : boolean
          Whether to learn class prior probabilities or not.
          If false, a uniform prior will be used.
  
      class_prior : array-like, size=[n_classes,]
          Prior probabilities of the classes. If specified the priors are not
          adjusted according to the data.
  
      Attributes
      ----------
      class_log_prior_ : array, shape = [n_classes]
          Log probability of each class (smoothed).
  
      feature_log_prob_ : array, shape = [n_classes, n_features]
          Empirical log probability of features given a class, P(x_i|y).
  
      class_count_ : array, shape = [n_classes]
          Number of samples encountered for each class during fitting. This
          value is weighted by the sample weight when provided.
  
      feature_count_ : array, shape = [n_classes, n_features]
          Number of samples encountered for each (class, feature)
          during fitting. This value is weighted by the sample weight when
          provided.
  
      Examples
      --------
      >>> import numpy as np
      >>> X = np.random.randint(2, size=(6, 100))
      >>> Y = np.array([1, 2, 3, 4, 4, 5])
      >>> from sklearn.naive_bayes import BernoulliNB
      >>> clf = BernoulliNB()
      >>> clf.fit(X, Y)
      BernoulliNB(alpha=1.0, binarize=0.0, class_prior=None, fit_prior=True)
      >>> print(clf.predict(X[2]))
      [3]
  
      References
      ----------
  
      C.D. Manning, P. Raghavan and H. Schuetze (2008). Introduction to
      Information Retrieval. Cambridge University Press, pp. 234-265.
      http://nlp.stanford.edu/IR-book/html/htmledition/the-bernoulli-model-1.html
  
      A. McCallum and K. Nigam (1998). A comparison of event models for naive
      Bayes text classification. Proc. AAAI/ICML-98 Workshop on Learning for
      Text Categorization, pp. 41-48.
  
      V. Metsis, I. Androutsopoulos and G. Paliouras (2006). Spam filtering with
      naive Bayes -- Which naive Bayes? 3rd Conf. on Email and Anti-Spam (CEAS).
      """
  
      def __init__(self, alpha=1.0, binarize=.0, fit_prior=True,
                   class_prior=None):
          self.alpha = alpha
          self.binarize = binarize
          self.fit_prior = fit_prior
          self.class_prior = class_prior
  
      def _count(self, X, Y):
          """Count and smooth feature occurrences."""
          if self.binarize is not None:
              X = binarize(X, threshold=self.binarize)
          self.feature_count_ += safe_sparse_dot(Y.T, X)
          self.class_count_ += Y.sum(axis=0)
  
      def _update_feature_log_prob(self):
          """Apply smoothing to raw counts and recompute log probabilities"""
          smoothed_fc = self.feature_count_ + self.alpha
          smoothed_cc = self.class_count_ + self.alpha * 2
  
          self.feature_log_prob_ = (np.log(smoothed_fc)
                                    - np.log(smoothed_cc.reshape(-1, 1)))
  
      def _joint_log_likelihood(self, X):
          """Calculate the posterior log probability of the samples X"""
          check_is_fitted(self, "classes_")
  
          X = check_array(X, accept_sparse='csr')
  
          if self.binarize is not None:
              X = binarize(X, threshold=self.binarize)
  
          n_classes, n_features = self.feature_log_prob_.shape
          n_samples, n_features_X = X.shape
  
          if n_features_X != n_features:
              raise ValueError("Expected input with %d features, got %d instead"
                               % (n_features, n_features_X))
  
          neg_prob = np.log(1 - np.exp(self.feature_log_prob_))
          # Compute  neg_prob · (1 - X).T  as  ∑neg_prob - X · neg_prob
          jll = safe_sparse_dot(X, (self.feature_log_prob_ - neg_prob).T)
          jll += self.class_log_prior_ + neg_prob.sum(axis=1)
  
          return jll
  