Expectation-maximization algorithms for inference in Dirichlet processes mixture

Mixture models are ubiquitous in applied science. In many real-world applications, the number of mixture components needs to be estimated from the data. A popular approach consists of using information criteria to perform model selection. Another approach which has become very popular over the past few years consists of using Dirichlet processes mixture (DPM) models. Both approaches are computationally intensive. The use of information criteria requires computing the maximum likelihood parameter estimates for each candidate model whereas DPM are usually trained using Markov chain Monte Carlo (MCMC) or variational Bayes (VB) methods. We propose here original batch and recursive expectation-maximization algorithms to estimate the parameters of DPM. The performance of our algorithms is demonstrated on several applications including image segmentation and image classification tasks. Our algorithms are computationally much more efficient than MCMC and VB and outperform VB on an example.