Variational Bayesian Inference for Multinomial Dirichlet Gaussian Process Classification Model

Abstract

In this paper, we propose the variational Bayesian inference algorithm which can drive approximate posterior distributions of both three latent functions and two parameters needed to define the multinomial Dirichlet Gaussian process (GP) classification model. This model consists of three components: a latent function with GP prior, a response function with multiclass, and a link function that relates the latent function and response mean. Here, we consider the variational Bayesian estimation method to estimate the proposed model. This is performed in two parts: one is to derive the variational posterior distribution of auxiliary variables and latent function, another is to derive the variational posterior distribution for the various parameters. Moreover, we have proposed a classification rule that can predict a particular category for a new observation by using the trained model. Finally, we conducted experiment using a well-known Iris data in order to verify the performance of the proposed model. Experimental result reveals that the proposed model shows good performance on this data set.