Generalized Naive Bayes

TL;DR

This paper introduces the Generalized Naive Bayes structure, providing algorithms that improve data fitting and feature selection over traditional methods, with proven optimality under certain conditions and demonstrated superior performance in experiments.

Contribution

The paper presents a new Generalized Naive Bayes structure and algorithms that find better data fits and optimal structures, advancing feature selection techniques.

Findings

Algorithms outperform related methods in many cases

Proven to fit data at least as well as classical Naive Bayes

Achieves optimal GNB distribution under certain conditions

Abstract

In this paper we introduce the so-called Generalized Naive Bayes structure as an extension of the Naive Bayes structure. We give a new greedy algorithm that finds a good fitting Generalized Naive Bayes (GNB) probability distribution. We prove that this fits the data at least as well as the probability distribution determined by the classical Naive Bayes (NB). Then, under a not very restrictive condition, we give a second algorithm for which we can prove that it finds the optimal GNB probability distribution, i.e. best fitting structure in the sense of KL divergence. Both algorithms are constructed to maximize the information content and aim to minimize redundancy. Based on these algorithms, new methods for feature selection are introduced. We discuss the similarities and differences to other related algorithms in terms of structure, methodology, and complexity. Experimental results show, that the algorithms introduced outperform the related algorithms in many cases.