1.9.3. 3. The naïve Bayes classifier combines this model with a decision rule.

The corresponding classifier, a Bayes classifier, is the function that …

Bayes’ Theorem in Classification We have seen how Bayes’ theorem can be used for regression, by estimating the parameters of a linear model. The Model The goal of any probabilistic classifier is, with features x_0 through x_n and classes c_0 through c_k, to determine the probability of the features occurring in each class, and to return the most likely class. We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. Naive Bayes classifiers are a collection of classification algorithms based on Bayes’ Theorem.It is not a single algorithm but a family of algorithms where all of them share a common principle, i.e. every pair of features being classified is independent of each other. What’s learning, revisited Overfitting Bayes optimal classifier Naïve Bayes Machine Learning – 10701/15781 Carlos Guestrin Carnegie Mellon University January 24th, 2007 ©Carlos Guestrin 2005-2007 Bias-Variance Tradeoff Choice of hypothesis class introduces learning bias More complex class → less bias More complex class → more variance Now we will see how to use Bayes’ theorem for classification. You can change your ad preferences anytime. Now, note that the color fllled region deflnes the area with all those bases v producing the same sequence. Complement Naive Bayes¶ ComplementNB implements the complement naive Bayes (CNB) algorithm. Naive Bayes classifiers have been especially popular for text classification, and are a traditional solution for problems such as spam detection. The same reasoning could be applied to other kind of regression algorithms.

One common rule is to pick the hypothesis that is most probable; this is known as the maximum a posteriori or MAP decision rule. Classification results obtained by this Fisher's method (which bypasses extraction of discriminants engaged in the complex eigendecomposition) are identical with those obtained by Bayes' method only if pooled within-class covariance matrix is used with Bayes' method based on discriminants (see "Note" above) and all the discriminants are being used in the classification. This is known as Bayes’ optimal classifier. CNB is an adaptation of the standard multinomial naive Bayes (MNB) algorithm that is particularly suited for imbalanced data sets. Specifically, CNB uses statistics from the complement of each class to compute the model’s weights.