Multinomial Naïve Bayes Classifier: Bayesian versus Nonparametric Classifier Approach

Abstract

This paper proposes a Naïve Bayes Classifier for Bayesian and nonparametric methods of analyzing multinomial regression. The Naïve Bayes classifier adopted Bayes’ rule for solving the posterior of the multinomial regression via its link function known as Logit link. The nonparametric adopted Gaussian, bi-weight kernels, Silverman’s rule of thumb bandwidth selector, and adjusted bandwidth as kernel density estimation. Three categorical responses of information on 78 people using one of three diets (Diet A, B, and C) that consist of scaled variables: age (in years), height (in cm), weight (in kg) before the diet (that is, pre-weight), weight (in kg) gained after 6 weeks of diet were subjected to the classifier multinomial regression of Naïve Bayes and nonparametric. The Gaussian and bi-weight kernel density estimation produced the minimum bandwidths across the three categorical responses for the four influencers. The Naïve Bayes classifier and nonparametric kernel density estimation for the multinomial regression produced the same prior probabilities of 0.3077, 0.3462, and 0.3462; and A prior probabilities of 0.3077, 0.3462, and 0.3462 for Diet A, Diet B, and Diet C at different smoothing bandwidths.

On Finite and Non-Finite Bayesian Mixture Models

“…The true weights for the three associated components are 0.5, 0.3, and 0.2 respectively. Their true means are (0,0), (5,5), and (-3,7) for the first, second and third components respectively for the simulated data of sample of size 120, such that their true sigma (variance) are (1,0), (2,0.9), and (1,-0.9) respectively. The starting guess value of the weights for each component was assigned to by equal weight of repetition (1,3)/3 via iteration of the sampler.…”

“…Consequently, it is not all the time that conjugate priors defined for certain likelihoods do give posterior forms of the likelihoods. In addition, the deduction that some non-informative priors usually accompany undefined posteriors irrespective of the sample size is a clear indicator of the complexity of Bayesian inference for some models [5].…”