"BernoulliNB",

"GaussianNB",

"MultinomialNB",

"ComplementNB",

"CategoricalNB",

"""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_samples, n_classes).

Public methods predict, predict_proba, predict_log_proba, and

predict_joint_log_proba pass the input through _check_X before handing it

over to _joint_log_likelihood. The term "joint log likelihood" is used

interchangibly with "joint log probability".

"""

@abstractmethod

def _check_X(self, X):

"""To be overridden in subclasses with the actual checks.

Only used in predict* methods.

"""

def predict_joint_log_proba(self, X):

"""Return joint log probability estimates for the test vector X.

For each row x of X and class y, the joint log probability is given by

``log P(x, y) = log P(y) + log P(x|y),``

where ``log P(y)`` is the class prior probability and ``log P(x|y)`` is

the class-conditional probability.

Parameters

----------

X : array-like of shape (n_samples, n_features)

The input samples.

Returns

-------

C : ndarray of shape (n_samples, n_classes)

Returns the joint 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 :term:`classes_`.

"""

check_is_fitted(self)

X = self._check_X(X)

return self._joint_log_likelihood(X)

def predict(self, X):

"""

Perform classification on an array of test vectors X.

Parameters

----------

X : array-like of shape (n_samples, n_features)

The input samples.

Returns

-------

C : ndarray of shape (n_samples,)

Predicted target values for X.

"""

check_is_fitted(self)

X = self._check_X(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 of shape (n_samples, n_features)

The input samples.

Returns

-------

C : array-like of 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 :term:`classes_`.

"""

check_is_fitted(self)

X = self._check_X(X)

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 of shape (n_samples, n_features)

The input samples.

Returns

-------

C : array-like of 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 :term:`classes_`.

"""

"""

Gaussian Naive Bayes (GaussianNB).

Can perform online updates to model parameters via :meth:`partial_fit`.

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>`.

Parameters

----------

priors : array-like of shape (n_classes,), default=None

Prior probabilities of the classes. If specified, the priors are not

adjusted according to the data.

var_smoothing : float, default=1e-9

Portion of the largest variance of all features that is added to

variances for calculation stability.

.. versionadded:: 0.20

Attributes

----------

class_count_ : ndarray of shape (n_classes,)

number of training samples observed in each class.

class_prior_ : ndarray of shape (n_classes,)

probability of each class.

classes_ : ndarray of shape (n_classes,)

class labels known to the classifier.

epsilon_ : float

absolute additive value to variances.

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

var_ : ndarray of shape (n_classes, n_features)

Variance of each feature per class.

.. versionadded:: 1.0

theta_ : ndarray of shape (n_classes, n_features)

mean of each feature per class.

See Also

--------

BernoulliNB : Naive Bayes classifier for multivariate Bernoulli models.

CategoricalNB : Naive Bayes classifier for categorical features.

ComplementNB : Complement Naive Bayes classifier.

MultinomialNB : Naive Bayes classifier for multinomial models.

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]

"""

_parameter_constraints: dict = {

"priors": ["array-like", None],

"var_smoothing": [Interval(Real, 0, None, closed="left")],

}

def __init__(self, *, priors=None, var_smoothing=1e-9):

self.priors = priors

self.var_smoothing = var_smoothing

@_fit_context(prefer_skip_nested_validation=True)

def fit(self, X, y, sample_weight=None):

"""Fit Gaussian Naive Bayes according to X, y.

Parameters

----------

X : array-like of 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 of shape (n_samples,)

Target values.

sample_weight : array-like of shape (n_samples,), default=None

Weights applied to individual samples (1. for unweighted).

.. versionadded:: 0.17

Gaussian Naive Bayes supports fitting with *sample_weight*.

Returns

-------

self : object

Returns the instance itself.

"""

y = self._validate_data(y=y)

return self._partial_fit(

X, y, np.unique(y), _refit=True, sample_weight=sample_weight

)

def _check_X(self, X):

"""Validate X, used only in predict* methods."""

return self._validate_data(X, reset=False)

@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 of shape (number of Gaussians,)

Means for Gaussians in original set.

var : array-like of shape (number of Gaussians,)

Variances for Gaussians in original set.

sample_weight : array-like of shape (n_samples,), default=None

Weights applied to individual samples (1. for unweighted).

Returns

-------

total_mu : array-like of shape (number of Gaussians,)

Updated mean for each Gaussian over the combined set.

total_var : array-like of 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())

if np.isclose(n_new, 0.0):

return mu, var

new_mu = np.average(X, axis=0, weights=sample_weight)

new_var = np.average((X - new_mu) ** 2, axis=0, weights=sample_weight)

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_new * n_past / n_total) * (mu - new_mu) ** 2

total_var = total_ssd / n_total

return total_mu, total_var

@_fit_context(prefer_skip_nested_validation=True)

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 of 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 of shape (n_samples,)

Target values.

classes : array-like of shape (n_classes,), default=None

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 of shape (n_samples,), default=None

Weights applied to individual samples (1. for unweighted).

.. versionadded:: 0.17

Returns

-------

self : object

Returns the instance itself.

"""

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 of 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 of shape (n_samples,)

Target values.

classes : array-like of shape (n_classes,), default=None

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, default=False

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 of shape (n_samples,), default=None

Weights applied to individual samples (1. for unweighted).

Returns

-------

self : object

"""

if _refit:

self.classes_ = None

first_call = _check_partial_fit_first_call(self, classes)

X, y = self._validate_data(X, y, reset=first_call)

if sample_weight is not None:

sample_weight = _check_sample_weight(sample_weight, X)

# If the ratio of data variance between dimensions is too small, it

# will cause numerical errors. To address this, we artificially

# boost the variance by epsilon, a small fraction of the standard

# deviation of the largest dimension.

self.epsilon_ = self.var_smoothing * np.var(X, axis=0).max()

if first_call:

# 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.var_ = np.zeros((n_classes, n_features))

self.class_count_ = np.zeros(n_classes, dtype=np.float64)

# Initialise the class prior

# Take into account the priors

if self.priors is not None:

priors = np.asarray(self.priors)

# Check that the provided prior matches the number of classes

if len(priors) != n_classes:

raise ValueError("Number of priors must match number of classes.")

# Check that the sum is 1

if not np.isclose(priors.sum(), 1.0):

raise ValueError("The sum of the priors should be 1.")

# Check that the priors are non-negative

if (priors < 0).any():

raise ValueError("Priors must be non-negative.")

self.class_prior_ = priors

else:

# Initialize the priors to zeros for each class

self.class_prior_ = np.zeros(len(self.classes_), dtype=np.float64)

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.var_[:, :] -= self.epsilon_

classes = self.classes_

unique_y = np.unique(y)

unique_y_in_classes = np.isin(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"

% (unique_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.var_[i, :], X_i, sw_i

)

self.theta_[i, :] = new_theta

self.var_[i, :] = new_sigma

self.class_count_[i] += N_i

self.var_[:, :] += self.epsilon_

# Update if only no priors is provided

if self.priors is None:

# Empirical prior, with sample_weight taken into account

self.class_prior_ = self.class_count_ / self.class_count_.sum()

return self

def _joint_log_likelihood(self, 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(2.0 * np.pi * self.var_[i, :]))

n_ij -= 0.5 * np.sum(((X - self.theta_[i, :]) ** 2) / (self.var_[i, :]), 1)

joint_log_likelihood.append(jointi + n_ij)

joint_log_likelihood = np.array(joint_log_likelihood).T

"""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

_update_feature_log_prob(alpha)

_count(X, Y)

"""

_parameter_constraints: dict = {

"alpha": [Interval(Real, 0, None, closed="left"), "array-like"],

"fit_prior": ["boolean"],

"class_prior": ["array-like", None],

"force_alpha": ["boolean"],

}

def __init__(self, alpha=1.0, fit_prior=True, class_prior=None, force_alpha=True):

self.alpha = alpha

self.fit_prior = fit_prior

self.class_prior = class_prior

self.force_alpha = force_alpha

@abstractmethod

def _count(self, X, Y):

"""Update counts that are used to calculate probabilities.

The counts make up a sufficient statistic extracted from the data.

Accordingly, this method is called each time `fit` or `partial_fit`

update the model. `class_count_` and `feature_count_` must be updated

here along with any model specific counts.

Parameters

----------

X : {ndarray, sparse matrix} of shape (n_samples, n_features)

The input samples.

Y : ndarray of shape (n_samples, n_classes)

Binarized class labels.

"""

@abstractmethod

def _update_feature_log_prob(self, alpha):

"""Update feature log probabilities based on counts.

This method is called each time `fit` or `partial_fit` update the

model.

Parameters

----------

alpha : float

smoothing parameter. See :meth:`_check_alpha`.

"""

def _check_X(self, X):

"""Validate X, used only in predict* methods."""

return self._validate_data(X, accept_sparse="csr", reset=False)

def _check_X_y(self, X, y, reset=True):

"""Validate X and y in fit methods."""

return self._validate_data(X, y, accept_sparse="csr", reset=reset)

def _update_class_log_prior(self, class_prior=None):

"""Update class log priors.

The class log priors are based on `class_prior`, class count or the

number of classes. This method is called each time `fit` or

`partial_fit` update the model.

"""

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:

with warnings.catch_warnings():

# silence the warning when count is 0 because class was not yet

# observed

warnings.simplefilter("ignore", RuntimeWarning)

log_class_count = np.log(self.class_count_)

# empirical prior, with sample_weight taken into account

self.class_log_prior_ = log_class_count - np.log(self.class_count_.sum())

else:

self.class_log_prior_ = np.full(n_classes, -np.log(n_classes))

def _check_alpha(self):

alpha = (

np.asarray(self.alpha) if not isinstance(self.alpha, Real) else self.alpha

)

alpha_min = np.min(alpha)

if isinstance(alpha, np.ndarray):

if not alpha.shape[0] == self.n_features_in_:

raise ValueError(

"When alpha is an array, it should contains `n_features`. "

f"Got {alpha.shape[0]} elements instead of {self.n_features_in_}."

)

# check that all alpha are positive

if alpha_min < 0:

raise ValueError("All values in alpha must be greater than 0.")

alpha_lower_bound = 1e-10

if alpha_min < alpha_lower_bound and not self.force_alpha:

warnings.warn(

"alpha too small will result in numeric errors, setting alpha ="

f" {alpha_lower_bound:.1e}. Use `force_alpha=True` to keep alpha"

" unchanged."

)

return np.maximum(alpha, alpha_lower_bound)

return alpha

@_fit_context(prefer_skip_nested_validation=True)

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} of 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 of shape (n_samples,)

Target values.

classes : array-like of shape (n_classes,), default=None

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 of shape (n_samples,), default=None

Weights applied to individual samples (1. for unweighted).

Returns

-------

self : object

Returns the instance itself.

"""

first_call = not hasattr(self, "classes_")

X, y = self._check_X_y(X, y, reset=first_call)

_, 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_classes = len(classes)

self._init_counters(n_classes, n_features)

Y = label_binarize(y, classes=self.classes_)

if Y.shape[1] == 1:

if len(self.classes_) == 2:

Y = np.concatenate((1 - Y, Y), axis=1)

else: # degenerate case: just one class

Y = np.ones_like(Y)

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, copy=False)

if sample_weight is not None:

sample_weight = _check_sample_weight(sample_weight, X)

sample_weight = np.atleast_2d(sample_weight)

Y *= 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

alpha = self._check_alpha()

self._update_feature_log_prob(alpha)

self._update_class_log_prior(class_prior=class_prior)

return self

@_fit_context(prefer_skip_nested_validation=True)

def fit(self, X, y, sample_weight=None):

"""Fit Naive Bayes classifier according to X, y.

Parameters

----------

X : {array-like, sparse matrix} of 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 of shape (n_samples,)

Target values.

sample_weight : array-like of shape (n_samples,), default=None

Weights applied to individual samples (1. for unweighted).

Returns

-------

self : object

Returns the instance itself.

"""

X, y = self._check_X_y(X, y)

_, n_features = X.shape

labelbin = LabelBinarizer()

Y = labelbin.fit_transform(y)

self.classes_ = labelbin.classes_

if Y.shape[1] == 1:

if len(self.classes_) == 2:

Y = np.concatenate((1 - Y, Y), axis=1)

else: # degenerate case: just one class

Y = np.ones_like(Y)

# 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

if sample_weight is not None:

Y = Y.astype(np.float64, copy=False)

sample_weight = _check_sample_weight(sample_weight, X)

sample_weight = np.atleast_2d(sample_weight)

Y *= sample_weight.T

class_prior = self.class_prior

# Count raw events from data before updating the class log prior

# and feature log probas

n_classes = Y.shape[1]

self._init_counters(n_classes, n_features)

self._count(X, Y)

alpha = self._check_alpha()

self._update_feature_log_prob(alpha)

self._update_class_log_prior(class_prior=class_prior)

return self

def _init_counters(self, n_classes, n_features):

self.class_count_ = np.zeros(n_classes, dtype=np.float64)

self.feature_count_ = np.zeros((n_classes, n_features), dtype=np.float64)

def _more_tags(self):

"""

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 or array-like of shape (n_features,), default=1.0

Additive (Laplace/Lidstone) smoothing parameter

(set alpha=0 and force_alpha=True, for no smoothing).

force_alpha : bool, default=True

If False and alpha is less than 1e-10, it will set alpha to

1e-10. If True, alpha will remain unchanged. This may cause

numerical errors if alpha is too close to 0.

.. versionadded:: 1.2

.. versionchanged:: 1.4

The default value of `force_alpha` changed to `True`.

fit_prior : bool, default=True

Whether to learn class prior probabilities or not.

If false, a uniform prior will be used.

class_prior : array-like of shape (n_classes,), default=None

Prior probabilities of the classes. If specified, the priors are not

adjusted according to the data.

Attributes

----------

class_count_ : ndarray of shape (n_classes,)

Number of samples encountered for each class during fitting. This

value is weighted by the sample weight when provided.

class_log_prior_ : ndarray of shape (n_classes,)

Smoothed empirical log probability for each class.

classes_ : ndarray of shape (n_classes,)

Class labels known to the classifier

feature_count_ : ndarray of 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.

feature_log_prob_ : ndarray of shape (n_classes, n_features)

Empirical log probability of features

given a class, ``P(x_i|y)``.

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

--------

BernoulliNB : Naive Bayes classifier for multivariate Bernoulli models.

CategoricalNB : Naive Bayes classifier for categorical features.

ComplementNB : Complement Naive Bayes classifier.

GaussianNB : Gaussian Naive Bayes.

References

----------

C.D. Manning, P. Raghavan and H. Schuetze (2008). Introduction to

Information Retrieval. Cambridge University Press, pp. 234-265.

https://nlp.stanford.edu/IR-book/html/htmledition/naive-bayes-text-classification-1.html

Examples

--------

>>> import numpy as np

>>> rng = np.random.RandomState(1)

>>> X = rng.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()

>>> print(clf.predict(X[2:3]))

[3]

"""

def __init__(

self, *, alpha=1.0, force_alpha=True, fit_prior=True, class_prior=None

):

super().__init__(

alpha=alpha,

fit_prior=fit_prior,

class_prior=class_prior,

force_alpha=force_alpha,

)

def _more_tags(self):

return {"requires_positive_X": True}

def _count(self, X, Y):

"""Count and smooth feature occurrences."""

check_non_negative(X, "MultinomialNB (input X)")

self.feature_count_ += safe_sparse_dot(Y.T, X)

self.class_count_ += Y.sum(axis=0)

def _update_feature_log_prob(self, alpha):

"""Apply smoothing to raw counts and recompute log probabilities"""

smoothed_fc = self.feature_count_ + 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"""

"""The Complement Naive Bayes classifier described in Rennie et al. (2003).

The Complement Naive Bayes classifier was designed to correct the "severe

assumptions" made by the standard Multinomial Naive Bayes classifier. It is

particularly suited for imbalanced data sets.

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

.. versionadded:: 0.20

Parameters

----------

alpha : float or array-like of shape (n_features,), default=1.0

Additive (Laplace/Lidstone) smoothing parameter

(set alpha=0 and force_alpha=True, for no smoothing).

force_alpha : bool, default=True

If False and alpha is less than 1e-10, it will set alpha to

1e-10. If True, alpha will remain unchanged. This may cause

numerical errors if alpha is too close to 0.

.. versionadded:: 1.2

.. versionchanged:: 1.4

The default value of `force_alpha` changed to `True`.

fit_prior : bool, default=True

Only used in edge case with a single class in the training set.

class_prior : array-like of shape (n_classes,), default=None

Prior probabilities of the classes. Not used.

norm : bool, default=False

Whether or not a second normalization of the weights is performed. The

default behavior mirrors the implementations found in Mahout and Weka,

which do not follow the full algorithm described in Table 9 of the

paper.

Attributes

----------

class_count_ : ndarray of shape (n_classes,)

Number of samples encountered for each class during fitting. This

value is weighted by the sample weight when provided.

class_log_prior_ : ndarray of shape (n_classes,)

Smoothed empirical log probability for each class. Only used in edge

case with a single class in the training set.

classes_ : ndarray of shape (n_classes,)

Class labels known to the classifier

feature_all_ : ndarray of shape (n_features,)

Number of samples encountered for each feature during fitting. This

value is weighted by the sample weight when provided.

feature_count_ : ndarray of 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.

feature_log_prob_ : ndarray of shape (n_classes, n_features)

Empirical weights for class complements.

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

--------

BernoulliNB : Naive Bayes classifier for multivariate Bernoulli models.

CategoricalNB : Naive Bayes classifier for categorical features.

GaussianNB : Gaussian Naive Bayes.

MultinomialNB : Naive Bayes classifier for multinomial models.

References

----------

Rennie, J. D., Shih, L., Teevan, J., & Karger, D. R. (2003).

Tackling the poor assumptions of naive bayes text classifiers. In ICML

(Vol. 3, pp. 616-623).

https://people.csail.mit.edu/jrennie/papers/icml03-nb.pdf

Examples

--------

>>> import numpy as np

>>> rng = np.random.RandomState(1)

>>> X = rng.randint(5, size=(6, 100))

>>> y = np.array([1, 2, 3, 4, 5, 6])

>>> from sklearn.naive_bayes import ComplementNB

>>> clf = ComplementNB()

>>> clf.fit(X, y)

ComplementNB()

>>> print(clf.predict(X[2:3]))

[3]

"""

_parameter_constraints: dict = {