Asymmetric Gaussian Mixtures with Reversible Jump MCMC

We propose a fully Bayesian learning approach using reversible jump Markov chain Monte Carlo (RJMCMC) for asymmetric Gaussian mixtures (AGM). Compared to classic Gaussian mixture model, AGM doesn't imply that target data is symmetric which brings flexibility and better fitting results. This paper also introduces a RJMCMC learning implementation based on Metropolis-Hastings (MH) within Gibbs sampling method. As an improvement of traditional sampling-based MCMC learning, RJMCMC has no assumption concerning the number of components and, therefore, the AGM model itself could be transferred between iterations. For better evaluating models with different mixture components numbers, the model selection is achieved by calculating integrated likelihood using Laplace approximation to figure out the best-fit components number. We selected both synthetic and challenging spam filtering dataset to show the merits of the proposed model.