# -*- 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 # Minor fixes by Fabian Pedregosa # Amit Aides # Yehuda Finkelstein # Lars Buitinck # Jan Hendrik Metzen # (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 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 from .utils.validation import _check_sample_weight __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. Only used in predict* methods. """ 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_`. """ 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 `. 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. 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 sigma_ : ndarray of shape (n_classes, n_features) Variance of each feature per class. .. deprecated:: 1.0 `sigma_` is deprecated in 1.0 and will be removed in 1.2. Use `var_` instead. 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] """ def __init__(self, *, priors=None, var_smoothing=1e-9): self.priors = priors self.var_smoothing = var_smoothing 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()) 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 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 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.var_[:, :] -= 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.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 return joint_log_likelihood @deprecated( # type: ignore "Attribute `sigma_` was deprecated in 1.0 and will be removed in" "1.2. Use `var_` instead." ) @property def sigma_(self): return self.var_ _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): """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): 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_in_: 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 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 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) # mypy error: Decorated property not supported @deprecated( # type: ignore "Attribute `coef_` was deprecated in " "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( # type: ignore "Attribute `intercept_` was deprecated in " "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} # TODO: Remove in 1.2 # mypy error: Decorated property not supported @deprecated( # type: ignore "Attribute `n_features_` was deprecated in version 1.0 and will be " "removed in 1.2. Use `n_features_in_` instead." ) @property def n_features_(self): return self.n_features_in_ 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 `. 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. .. deprecated:: 1.0 Attribute `n_features_` was deprecated in version 1.0 and will be removed in 1.2. Use `n_features_in_` instead. 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. 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 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, 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 `. .. 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. .. deprecated:: 1.0 Attribute `n_features_` was deprecated in version 1.0 and will be removed in 1.2. Use `n_features_in_` instead. 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] """ 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 `. 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. .. deprecated:: 1.0 Attribute `n_features_` was deprecated in version 1.0 and will be removed in 1.2. Use `n_features_in_` instead. 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 -------- CategoricalNB : Naive Bayes classifier for categorical features. ComplementNB : The Complement Naive Bayes classifier described in Rennie et al. (2003). GaussianNB : Gaussian Naive Bayes (GaussianNB). MultinomialNB : Naive Bayes classifier for multinomial models. 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). 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] """ def __init__(self, *, alpha=1.0, binarize=0.0, 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): """Validate X, used only in predict* methods.""" 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, reset=True): X, y = super()._check_X_y(X, y, reset=reset) 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_features = self.feature_log_prob_.shape[1] n_features_X = X.shape[1] 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 `. 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. .. deprecated:: 1.0 Attribute `n_features_` was deprecated in version 1.0 and will be removed in 1.2. Use `n_features_in_` instead. 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 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 See Also -------- BernoulliNB : Naive Bayes classifier for multivariate Bernoulli models. ComplementNB : Complement Naive Bayes classifier. GaussianNB : Gaussian Naive Bayes. MultinomialNB : Naive Bayes classifier for multinomial models. 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] """ 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 Returns the instance itself. """ 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 Returns the instance itself. """ 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): """Validate X, used only in predict* methods.""" X = self._validate_data( X, dtype="int", accept_sparse=False, force_all_finite=True, reset=False ) check_non_negative(X, "CategoricalNB (input X)") return X def _check_X_y(self, X, y, reset=True): X, y = self._validate_data( X, y, dtype="int", accept_sparse=False, force_all_finite=True, reset=reset ) check_non_negative(X, "CategoricalNB (input X)") return X, y def _init_counters(self, n_classes, n_features): self.class_count_ = np.zeros(n_classes, dtype=np.float64) self.category_count_ = [np.zeros((n_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( "'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]}," ") 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_in_): 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_in_): 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): self._check_n_features(X, reset=False) jll = np.zeros((X.shape[0], self.class_count_.shape[0])) for i in range(self.n_features_in_): indices = X[:, i] jll += self.feature_log_prob_[i][:, indices].T total_ll = jll + self.class_log_prior_ return total_ll