Abstract

The Expectation-Maximisation (EM) algorithm is a popular algorithm for maximum likelihood estimation in the presence of missing data and/or latent variables. In its standard form, EM involves multiple runs through the data which renders it impractical in online settings, but recursive recastings are possible on the basis of Stochastic Approximation theory. In this talk, we will focus on two such schemes: the seminal work on recursive EM by D.Titterington (“Recursive parameter estimation using incomplete data”, JRSS -B 1984), as well as recent work by Cappe et al. (“Online EM for latent data models”, JRSS -B 2009). We will describe and compare these two algorithms, sketch their theoretical underpinnings, and discuss their applicability to challenging parameter estimation problems such as state-space and mixture modelling. To conclude, we will briefly point to important open problems.