A proximal method for stochastic EM algorithm

One of the most popular algorithm in latent data models is the EM algorithm. This algorithm is not proper for large data set as the first step of this algorithm is so expensive. To solve this problem, some practical method have been proposed one of them is an incremental method of the EM which is called iEM. Another version in which the E-step is a stochastic approximation. The two other versions are called the variance reduced versions. In latter they establish non-asymptotic convergence bounds for global convergence. In this paper we propose a proximal method which focus on the M-step. We use the method which is called sEM-VR for E-step and we propose new version for M-step. The proximal operator inspired us to apply it for M-step which is mentioned in Poximal SVRG. As the E-step is just the method that has been proposed in other paper and called sEM-VR the convergence rate would be the same.

Keywords:

EM Algorithm , Machine Learning , Minimization , Data Likelihood