# -*- 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 # (parts based on earlier work by Mathieu Blondel) # # License: BSD Style. from abc import ABCMeta, abstractmethod import numpy as np from scipy.sparse import issparse from .base import BaseEstimator, ClassifierMixin from .preprocessing import binarize, LabelBinarizer from .utils import array2d, atleast2d_or_csr from .utils.extmath import safe_sparse_dot, logsumexp from .utils import deprecated class BaseNB(BaseEstimator, ClassifierMixin): """Abstract base class for naive Bayes estimators""" __metaclass__ = ABCMeta @abstractmethod def _joint_log_likelihood(self, X): """Compute the unnormalized posterior log probability of X I.e. ``log P(c) + log P(x|c)`` for all rows x of X, as an array-like of shape [n_classes, n_samples]. Input is passed to _joint_log_likelihood as-is by predict, predict_proba and predict_log_proba. """ def predict(self, X): """ Perform classification on an array of test vectors X. Parameters ---------- X : array-like, shape = [n_samples, n_features] Returns ------- C : array, shape = [n_samples] Predicted target values for X """ jll = self._joint_log_likelihood(X) return self.classes_[np.argmax(jll, axis=1)] def predict_log_proba(self, X): """ Return log-probability estimates for the test vector X. Parameters ---------- X : array-like, shape = [n_samples, n_features] Returns ------- C : array-like, shape = [n_samples, n_classes] Returns the log-probability of the sample for each class in the model, where classes are ordered arithmetically. """ jll = self._joint_log_likelihood(X) # normalize by P(x) = P(f_1, ..., f_n) log_prob_x = logsumexp(jll, axis=1) return jll - np.atleast_2d(log_prob_x).T def predict_proba(self, X): """ Return probability estimates for the test vector X. Parameters ---------- X : array-like, shape = [n_samples, n_features] Returns ------- C : array-like, shape = [n_samples, n_classes] Returns the probability of the sample for each class in the model, where classes are ordered arithmetically. """ return np.exp(self.predict_log_proba(X)) class GaussianNB(BaseNB): """ Gaussian Naive Bayes (GaussianNB) Parameters ---------- X : array-like, shape = [n_samples, n_features] Training vector, where n_samples in the number of samples and n_features is the number of features. y : array, shape = [n_samples] Target vector relative to X Attributes ---------- `class_prior_` : array, shape = [n_classes] probability of each class. `theta_` : array, shape = [n_classes, n_features] mean of each feature per class `sigma_` : array, shape = [n_classes, n_features] variance of each feature per class Examples -------- >>> import numpy as np >>> X = np.array([[-1, -1], [-2, -1], [-3, -2], [1, 1], [2, 1], [3, 2]]) >>> Y = np.array([1, 1, 1, 2, 2, 2]) >>> from sklearn.naive_bayes import GaussianNB >>> clf = GaussianNB() >>> clf.fit(X, Y) GaussianNB() >>> print clf.predict([[-0.8, -1]]) [1] """ def fit(self, X, y): """Fit Gaussian Naive Bayes according to X, y Parameters ---------- X : array-like, shape = [n_samples, n_features] Training vectors, where n_samples is the number of samples and n_features is the number of features. y : array-like, shape = [n_samples] Target values. Returns ------- self : object Returns self. """ X = np.asarray(X) y = np.asarray(y) n_samples, n_features = X.shape if n_samples != y.shape[0]: raise ValueError("X and y have incompatible shapes") self.classes_ = unique_y = np.unique(y) n_classes = unique_y.shape[0] self.theta_ = np.zeros((n_classes, n_features)) self.sigma_ = np.zeros((n_classes, n_features)) self.class_prior_ = np.zeros(n_classes) epsilon = 1e-9 for i, y_i in enumerate(unique_y): self.theta_[i, :] = np.mean(X[y == y_i, :], axis=0) self.sigma_[i, :] = np.var(X[y == y_i, :], axis=0) + epsilon self.class_prior_[i] = np.float(np.sum(y == y_i)) / n_samples return self def _joint_log_likelihood(self, X): X = array2d(X) joint_log_likelihood = [] for i in xrange(np.size(self.classes_)): jointi = np.log(self.class_prior_[i]) n_ij = - 0.5 * np.sum(np.log(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 @property @deprecated('GaussianNB.class_prior is deprecated' ' and will be removed in version 0.12.' ' Please use ``GaussianNB.class_prior_`` instead.') def class_prior(self): return self.class_prior_ @property @deprecated('GaussianNB.theta is deprecated' ' and will be removed in version 0.12.' ' Please use ``GaussianNB.theta_`` instead.') def theta(self): return self.theta_ @property @deprecated('GaussianNB.sigma is deprecated' ' and will be removed in version 0.12.' ' Please use ``GaussianNB.sigma_`` instead.') def sigma(self): return self.sigma_ 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 fit(self, X, y, sample_weight=None, class_prior=None): """Fit Naive Bayes classifier according to X, y Parameters ---------- X : {array-like, sparse matrix}, shape = [n_samples, n_features] Training vectors, where n_samples is the number of samples and n_features is the number of features. y : array-like, shape = [n_samples] Target values. sample_weight : array-like, shape = [n_samples], optional Weights applied to individual samples (1. for unweighted). class_prior : array, shape [n_classes] Custom prior probability per class. Overrides the fit_prior parameter. Returns ------- self : object Returns self. """ X = atleast2d_or_csr(X) labelbin = LabelBinarizer() Y = labelbin.fit_transform(y) self.classes_ = labelbin.classes_ n_classes = len(self.classes_) if Y.shape[1] == 1: Y = np.concatenate((1 - Y, Y), axis=1) if X.shape[0] != Y.shape[0]: msg = "X and y have incompatible shapes." if issparse(X): msg += "\nNote: Sparse matrices cannot be indexed w/ boolean \ masks (use `indices=True` in CV)." raise ValueError(msg) if sample_weight is not None: Y *= array2d(sample_weight).T if class_prior: if len(class_prior) != n_classes: raise ValueError( "Number of priors must match number of classes") self.class_log_prior_ = np.log(class_prior) elif self.fit_prior: # empirical prior, with sample_weight taken into account y_freq = Y.sum(axis=0) self.class_log_prior_ = np.log(y_freq) - np.log(y_freq.sum()) else: self.class_log_prior_ = np.zeros(n_classes) - np.log(n_classes) N_c, N_c_i = self._count(X, Y) self.feature_log_prob_ = (np.log(N_c_i + self.alpha) - np.log(N_c.reshape(-1, 1) + self.alpha * X.shape[1])) return self @staticmethod def _count(X, Y): """Count feature occurrences. Returns (N_c, N_c_i), where N_c is the count of all features in all samples of class c; N_c_i is the count of feature i in all samples of class c. """ N_c_i = safe_sparse_dot(Y.T, X) N_c = np.sum(N_c_i, axis=1) return N_c, N_c_i # XXX The following is a stopgap measure; we need to set the dimensions # of class_log_prior_ and feature_log_prob_ correctly. def _get_coef(self): return self.feature_log_prob_[1] if len(self.classes_) == 2 \ else self.feature_log_prob_ def _get_intercept(self): return self.class_log_prior_[1] if len(self.classes_) == 2 \ else self.class_log_prior_ coef_ = property(_get_coef) intercept_ = property(_get_intercept) class MultinomialNB(BaseDiscreteNB): """ Naive Bayes classifier for multinomial models The multinomial Naive Bayes classifier is suitable for classification with discrete features (e.g., word counts for text classification). The multinomial distribution normally requires integer feature counts. However, in practice, fractional counts such as tf-idf may also work. Parameters ---------- alpha: float, optional (default=1.0) Additive (Laplace/Lidstone) smoothing parameter (0 for no smoothing). fit_prior: boolean Whether to learn class prior probabilities or not. If false, a uniform prior will be used. Attributes ---------- `intercept_`, `class_log_prior_` : array, shape = [n_classes] Smoothed empirical log probability for each class. `feature_log_prob_`, `coef_` : array, shape = [n_classes, n_features] Empirical log probability of features given a class, P(x_i|y). (`intercept_` and `coef_` are properties referring to `class_log_prior_` and `feature_log_prob_`, respectively.) Examples -------- >>> import numpy as np >>> X = np.random.randint(5, size=(6, 100)) >>> Y = np.array([1, 2, 3, 4, 5, 6]) >>> from sklearn.naive_bayes import MultinomialNB >>> clf = MultinomialNB() >>> clf.fit(X, Y) MultinomialNB(alpha=1.0, fit_prior=True) >>> print clf.predict(X[2]) [3] Notes ----- For the rationale behind the names `coef_` and `intercept_`, i.e. naive Bayes as a linear classifier, see J. Rennie et al. (2003), Tackling the poor assumptions of naive Bayes text classifiers, ICML. """ def __init__(self, alpha=1.0, fit_prior=True): self.alpha = alpha self.fit_prior = fit_prior def _joint_log_likelihood(self, X): """Calculate the posterior log probability of the samples X""" X = atleast2d_or_csr(X) return (safe_sparse_dot(X, self.feature_log_prob_.T) + self.class_log_prior_) class BernoulliNB(BaseDiscreteNB): """Naive Bayes classifier for multivariate Bernoulli models. Like MultinomialNB, this classifier is suitable for discrete data. The difference is that while MultinomialNB works with occurrence counts, BernoulliNB is designed for binary/boolean features. Parameters ---------- alpha: float, optional (default=1.0) Additive (Laplace/Lidstone) smoothing parameter (0 for no smoothing). binarize: float or None, optional Threshold for binarizing (mapping to booleans) of sample features. If None, input is presumed to already consist of binary vectors. fit_prior: boolean Whether to learn class prior probabilities or not. If false, a uniform prior will be used. Attributes ---------- `class_log_prior_` : array, shape = [n_classes] Log probability of each class (smoothed). `feature_log_prob_` : array, shape = [n_classes, n_features] Empirical log probability of features given a class, P(x_i|y). Examples -------- >>> import numpy as np >>> X = np.random.randint(2, size=(6, 100)) >>> Y = np.array([1, 2, 3, 4, 4, 5]) >>> from sklearn.naive_bayes import BernoulliNB >>> clf = BernoulliNB() >>> clf.fit(X, Y) BernoulliNB(alpha=1.0, binarize=0.0, fit_prior=True) >>> print clf.predict(X[2]) [3] References ---------- C.D. Manning, P. Raghavan and H. Schütze (2008). Introduction to Information Retrieval. Cambridge University Press, pp. 234–265. A. McCallum and K. Nigam (1998). A comparison of event models for naive Bayes text classification. Proc. AAAI/ICML-98 Workshop on Learning for Text Categorization, pp. 41–48. V. Metsis, I. Androutsopoulos and G. Paliouras (2006). Spam filtering with naive Bayes -- Which naive Bayes? 3rd Conf. on Email and Anti-Spam (CEAS). """ def __init__(self, alpha=1.0, binarize=.0, fit_prior=True): self.alpha = alpha self.binarize = binarize self.fit_prior = fit_prior def _count(self, X, Y): if self.binarize is not None: X = binarize(X, threshold=self.binarize) return super(BernoulliNB, self)._count(X, Y) def _joint_log_likelihood(self, X): """Calculate the posterior log probability of the samples X""" X = atleast2d_or_csr(X) if self.binarize is not None: X = binarize(X, threshold=self.binarize) n_classes, n_features = self.feature_log_prob_.shape n_samples, n_features_X = X.shape if n_features_X != n_features: raise ValueError("Expected input with %d features, got %d instead" % (n_features, n_features_X)) neg_prob = np.log(1 - np.exp(self.feature_log_prob_)) # Compute neg_prob · (1 - X).T as ∑neg_prob - X · neg_prob X_neg_prob = (neg_prob.sum(axis=1) - safe_sparse_dot(X, neg_prob.T)) jll = safe_sparse_dot(X, self.feature_log_prob_.T) + X_neg_prob return jll + self.class_log_prior_