# -*- 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
# Jan Hendrik Metzen <jhm@informatik.uni-bremen.de>
# (parts based on earlier work by Mathieu Blondel)
#
# License: BSD 3 clause
import warnings
from abc import ABCMeta, abstractmethod
import numpy as np
from scipy.special import logsumexp
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, deprecated
from .utils.extmath import safe_sparse_dot
from .utils.multiclass import _check_partial_fit_first_call
from .utils.validation import check_is_fitted, check_non_negative, column_or_1d
from .utils.validation import _check_sample_weight
from .utils.validation import _deprecate_positional_args
__all__ = ['BernoulliNB', 'GaussianNB', 'MultinomialNB', 'ComplementNB',
'CategoricalNB']
class _BaseNB(ClassifierMixin, BaseEstimator, metaclass=ABCMeta):
"""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.
"""
@abstractmethod
def _check_X(self, X):
"""To be overridden in subclasses with the actual checks."""
def predict(self, X):
"""
Perform classification on an array of test vectors X.
Parameters
----------
X : array-like of shape (n_samples, n_features)
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)
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)
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_`.
"""
return np.exp(self.predict_log_proba(X))
class GaussianNB(_BaseNB):
"""
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,)
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
sigma_ : ndarray of shape (n_classes, n_features)
variance of each feature per class
theta_ : ndarray of shape (n_classes, n_features)
mean 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]
"""
@_deprecate_positional_args
def __init__(self, *, priors=None, var_smoothing=1e-9):
self.priors = priors
self.var_smoothing = var_smoothing
[docs] 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
"""
X, y = self._validate_data(X, y)
y = column_or_1d(y, warn=True)
return self._partial_fit(X, y, np.unique(y), _refit=True,
sample_weight=sample_weight)
def _check_X(self, X):
return check_array(X)
@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())
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
[docs] 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
"""
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
"""
X, y = check_X_y(X, y)
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 _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_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 provide prior match 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 prior 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.sigma_[:, :] -= self.epsilon_
classes = self.classes_
unique_y = np.unique(y)
unique_y_in_classes = np.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" %
(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.sigma_[i, :],
X_i, sw_i)
self.theta_[i, :] = new_theta
self.sigma_[i, :] = new_sigma
self.class_count_[i] += N_i
self.sigma_[:, :] += 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. * 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
_ALPHA_MIN = 1e-10
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 _check_X(self, X):
return check_array(X, accept_sparse='csr')
def _check_X_y(self, X, y):
return self._validate_data(X, y, accept_sparse='csr')
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:
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):
if np.min(self.alpha) < 0:
raise ValueError('Smoothing parameter alpha = %.1e. '
'alpha should be > 0.' % np.min(self.alpha))
if isinstance(self.alpha, np.ndarray):
if not self.alpha.shape[0] == self.n_features_:
raise ValueError("alpha should be a scalar or a numpy array "
"with shape [n_features]")
if np.min(self.alpha) < _ALPHA_MIN:
warnings.warn('alpha too small will result in numeric errors, '
'setting alpha = %.1e' % _ALPHA_MIN)
return np.maximum(self.alpha, _ALPHA_MIN)
return self.alpha
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
"""
X, y = self._check_X_y(X, y)
_, 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._init_counters(n_effective_classes, n_features)
self.n_features_ = n_features
elif n_features != self.n_features_:
msg = "Number of features %d does not match previous data %d."
raise ValueError(msg % (n_features, self.n_features_))
Y = label_binarize(y, classes=self.classes_)
if Y.shape[1] == 1:
Y = np.concatenate((1 - Y, Y), axis=1)
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
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
"""
X, y = self._check_X_y(X, y)
_, n_features = X.shape
self.n_features_ = n_features
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
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_effective_classes = Y.shape[1]
self._init_counters(n_effective_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_effective_classes, n_features):
self.class_count_ = np.zeros(n_effective_classes, dtype=np.float64)
self.feature_count_ = np.zeros((n_effective_classes, n_features),
dtype=np.float64)
# mypy error: Decorated property not supported
@deprecated("Attribute coef_ was deprecated in " # type: ignore
"version 0.24 and will be removed in 1.1 (renaming of 0.26).")
@property
def coef_(self):
return (self.feature_log_prob_[1:]
if len(self.classes_) == 2 else self.feature_log_prob_)
# mypy error: Decorated property not supported
@deprecated("Attribute intercept_ was deprecated in " # type: ignore
"version 0.24 and will be removed in 1.1 (renaming of 0.26).")
@property
def intercept_(self):
return (self.class_log_prior_[1:]
if len(self.classes_) == 2 else self.class_log_prior_)
def _more_tags(self):
return {'poor_score': True}
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, default=1.0
Additive (Laplace/Lidstone) smoothing parameter
(0 for no smoothing).
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
coef_ : ndarray of shape (n_classes, n_features)
Mirrors ``feature_log_prob_`` for interpreting `MultinomialNB`
as a linear model.
.. deprecated:: 0.24
``coef_`` is deprecated in 0.24 and will be removed in 1.1
(renaming of 0.26).
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)``.
intercept_ : ndarray of shape (n_classes,)
Mirrors ``class_log_prior_`` for interpreting `MultinomialNB`
as a linear model.
.. deprecated:: 0.24
``intercept_`` is deprecated in 0.24 and will be removed in 1.1
(renaming of 0.26).
n_features_ : int
Number of features of each sample.
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]
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.
https://nlp.stanford.edu/IR-book/html/htmledition/naive-bayes-text-classification-1.html
"""
@_deprecate_positional_args
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 _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"""
return (safe_sparse_dot(X, self.feature_log_prob_.T) +
self.class_log_prior_)
class ComplementNB(_BaseDiscreteNB):
"""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, default=1.0
Additive (Laplace/Lidstone) smoothing parameter (0 for no smoothing).
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
coef_ : ndarray of shape (n_classes, n_features)
Mirrors ``feature_log_prob_`` for interpreting `ComplementNB`
as a linear model.
.. deprecated:: 0.24
``coef_`` is deprecated in 0.24 and will be removed in 1.1
(renaming of 0.26).
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.
intercept_ : ndarray of shape (n_classes,)
Mirrors ``class_log_prior_`` for interpreting `ComplementNB`
as a linear model.
.. deprecated:: 0.24
``coef_`` is deprecated in 0.24 and will be removed in 1.1
(renaming of 0.26).
n_features_ : int
Number of features of each sample.
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]
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
"""
@_deprecate_positional_args
def __init__(self, *, alpha=1.0, fit_prior=True, class_prior=None,
norm=False):
self.alpha = alpha
self.fit_prior = fit_prior
self.class_prior = class_prior
self.norm = norm
def _more_tags(self):
return {'requires_positive_X': True}
def _count(self, X, Y):
"""Count feature occurrences."""
check_non_negative(X, "ComplementNB (input X)")
self.feature_count_ += safe_sparse_dot(Y.T, X)
self.class_count_ += Y.sum(axis=0)
self.feature_all_ = self.feature_count_.sum(axis=0)
def _update_feature_log_prob(self, alpha):
"""Apply smoothing to raw counts and compute the weights."""
comp_count = self.feature_all_ + alpha - self.feature_count_
logged = np.log(comp_count / comp_count.sum(axis=1, keepdims=True))
# _BaseNB.predict uses argmax, but ComplementNB operates with argmin.
if self.norm:
summed = logged.sum(axis=1, keepdims=True)
feature_log_prob = logged / summed
else:
feature_log_prob = -logged
self.feature_log_prob_ = feature_log_prob
def _joint_log_likelihood(self, X):
"""Calculate the class scores for the samples in X."""
jll = safe_sparse_dot(X, self.feature_log_prob_.T)
if len(self.classes_) == 1:
jll += self.class_log_prior_
return jll
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, default=1.0
Additive (Laplace/Lidstone) smoothing parameter
(0 for no smoothing).
binarize : float or None, default=0.0
Threshold for binarizing (mapping to booleans) of sample features.
If None, input is presumed to already consist of binary vectors.
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)
Log probability of each class (smoothed).
classes_ : ndarray of shape (n_classes,)
Class labels known to the classifier
coef_ : ndarray of shape (n_classes, n_features)
Mirrors ``feature_log_prob_`` for interpreting `BernoulliNB`
as a linear model.
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).
intercept_ : ndarray of shape (n_classes,)
Mirrors ``class_log_prior_`` for interpreting `BernoulliNB`
as a linear model.
n_features_ : int
Number of features of each sample.
Examples
--------
>>> import numpy as np
>>> rng = np.random.RandomState(1)
>>> X = rng.randint(5, 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()
>>> print(clf.predict(X[2:3]))
[3]
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/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).
"""
@_deprecate_positional_args
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 _check_X(self, X):
X = super()._check_X(X)
if self.binarize is not None:
X = binarize(X, threshold=self.binarize)
return X
def _check_X_y(self, X, y):
X, y = super()._check_X_y(X, y)
if self.binarize is not None:
X = binarize(X, threshold=self.binarize)
return X, y
def _count(self, X, Y):
"""Count and smooth feature occurrences."""
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 = self.class_count_ + 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"""
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
class CategoricalNB(_BaseDiscreteNB):
"""Naive Bayes classifier for categorical features
The categorical Naive Bayes classifier is suitable for classification with
discrete features that are categorically distributed. The categories of
each feature are drawn from a categorical distribution.
Read more in the :ref:`User Guide <categorical_naive_bayes>`.
Parameters
----------
alpha : float, default=1.0
Additive (Laplace/Lidstone) smoothing parameter
(0 for no smoothing).
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.
min_categories : int or array-like of shape (n_features,), default=None
Minimum number of categories per feature.
- integer: Sets the minimum number of categories per feature to
`n_categories` for each features.
- array-like: shape (n_features,) where `n_categories[i]` holds the
minimum number of categories for the ith column of the input.
- None (default): Determines the number of categories automatically
from the training data.
.. versionadded:: 0.24
Attributes
----------
category_count_ : list of arrays of shape (n_features,)
Holds arrays of shape (n_classes, n_categories of respective feature)
for each feature. Each array provides the number of samples
encountered for each class and category of the specific feature.
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_log_prob_ : list of arrays of shape (n_features,)
Holds arrays of shape (n_classes, n_categories of respective feature)
for each feature. Each array provides the empirical log probability
of categories given the respective feature and class, ``P(x_i|y)``.
n_features_ : int
Number of features of each sample.
n_categories_ : ndarray of shape (n_features,), dtype=np.int64
Number of categories for each feature. This value is
inferred from the data or set by the minimum number of categories.
.. versionadded:: 0.24
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 CategoricalNB
>>> clf = CategoricalNB()
>>> clf.fit(X, y)
CategoricalNB()
>>> print(clf.predict(X[2:3]))
[3]
"""
@_deprecate_positional_args
def __init__(self, *, alpha=1.0, fit_prior=True, class_prior=None,
min_categories=None):
self.alpha = alpha
self.fit_prior = fit_prior
self.class_prior = class_prior
self.min_categories = min_categories
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. Here, each feature of X is
assumed to be from a different categorical distribution.
It is further assumed that all categories of each feature are
represented by the numbers 0, ..., n - 1, where n refers to the
total number of categories for the given feature. This can, for
instance, be achieved with the help of OrdinalEncoder.
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
"""
return super().fit(X, y, sample_weight=sample_weight)
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. Here, each feature of X is
assumed to be from a different categorical distribution.
It is further assumed that all categories of each feature are
represented by the numbers 0, ..., n - 1, where n refers to the
total number of categories for the given feature. This can, for
instance, be achieved with the help of OrdinalEncoder.
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
"""
return super().partial_fit(X, y, classes,
sample_weight=sample_weight)
def _more_tags(self):
return {'requires_positive_X': True}
def _check_X(self, X):
X = check_array(X, dtype='int', accept_sparse=False,
force_all_finite=True)
check_non_negative(X, "CategoricalNB (input X)")
return X
def _check_X_y(self, X, y):
X, y = self._validate_data(X, y, dtype='int', accept_sparse=False,
force_all_finite=True)
check_non_negative(X, "CategoricalNB (input X)")
return X, y
def _init_counters(self, n_effective_classes, n_features):
self.class_count_ = np.zeros(n_effective_classes, dtype=np.float64)
self.category_count_ = [np.zeros((n_effective_classes, 0))
for _ in range(n_features)]
@staticmethod
def _validate_n_categories(X, min_categories):
# rely on max for n_categories categories are encoded between 0...n-1
n_categories_X = X.max(axis=0) + 1
min_categories_ = np.array(min_categories)
if min_categories is not None:
if not np.issubdtype(min_categories_.dtype, np.signedinteger):
raise ValueError(
f"'min_categories' should have integral type. Got "
f"{min_categories_.dtype} instead."
)
n_categories_ = np.maximum(n_categories_X,
min_categories_,
dtype=np.int64)
if n_categories_.shape != n_categories_X.shape:
raise ValueError(
f"'min_categories' should have shape ({X.shape[1]},"
f") when an array-like is provided. Got"
f" {min_categories_.shape} instead."
)
return n_categories_
else:
return n_categories_X
def _count(self, X, Y):
def _update_cat_count_dims(cat_count, highest_feature):
diff = highest_feature + 1 - cat_count.shape[1]
if diff > 0:
# we append a column full of zeros for each new category
return np.pad(cat_count, [(0, 0), (0, diff)], 'constant')
return cat_count
def _update_cat_count(X_feature, Y, cat_count, n_classes):
for j in range(n_classes):
mask = Y[:, j].astype(bool)
if Y.dtype.type == np.int64:
weights = None
else:
weights = Y[mask, j]
counts = np.bincount(X_feature[mask], weights=weights)
indices = np.nonzero(counts)[0]
cat_count[j, indices] += counts[indices]
self.class_count_ += Y.sum(axis=0)
self.n_categories_ = self._validate_n_categories(
X, self.min_categories)
for i in range(self.n_features_):
X_feature = X[:, i]
self.category_count_[i] = _update_cat_count_dims(
self.category_count_[i], self.n_categories_[i] - 1)
_update_cat_count(X_feature, Y,
self.category_count_[i],
self.class_count_.shape[0])
def _update_feature_log_prob(self, alpha):
feature_log_prob = []
for i in range(self.n_features_):
smoothed_cat_count = self.category_count_[i] + alpha
smoothed_class_count = smoothed_cat_count.sum(axis=1)
feature_log_prob.append(
np.log(smoothed_cat_count) -
np.log(smoothed_class_count.reshape(-1, 1)))
self.feature_log_prob_ = feature_log_prob
def _joint_log_likelihood(self, X):
if not X.shape[1] == self.n_features_:
raise ValueError("Expected input with %d features, got %d instead"
% (self.n_features_, X.shape[1]))
jll = np.zeros((X.shape[0], self.class_count_.shape[0]))
for i in range(self.n_features_):
indices = X[:, i]
jll += self.feature_log_prob_[i][:, indices].T
total_ll = jll + self.class_log_prior_
return total_ll