Empirical Copula based Naive Bayes Classifier

Abstract

In this paper, we propose a Bayesian model with enhanced performance on statistical datasets by incorporating the concept of Empirical copulas to compute the joint probability distribution of features present in the data. Copulas are defined as cumulative distribution functions deemed popular in highdimensional statistical applications since they easily enable one to model and estimate the distribution of random vectors by estimating the marginals and copulae separately. The key idea of this method is to replace the joint probability, which is defined as the probability of occurrence of two or more simultaneous events, with the cumulative distribution generated by the nonparametric empirical copula function and utilize it on bivariate and multivariate data to assess the performance of the model thus generated. Through extensive research on the topic of nonparametric empirical copulas and tuning the model with various smoothing techniques, we have achieved significant accuracy with a more robust statistical hold in the predictive analysis of different datasets in comparison to the simple Gaussian Naïve Bayes technique.