Variational Bayesian multinomial probit model with Gaussian process classification on mice protein expression level data

Multinomial probit model is a popular model for multiclass classification and choice model. Markov chain Monte Carlo (MCMC) method is widely used for estimating multinomial probit model, but its computational cost is high. However, it is well known that variational Bayesian approximation is more computationally efficient than MCMC, because it uses subsets of samples. In this study, we describe multinomial probit model with Gaussian process classification and how to employ variational Bayesian approximation on the model. This study also compares the results of variational Bayesian multinomial probit model to the results of naive Bayes, K-nearest neighbors and support vector machine for the UCI mice protein expression level data.