Interacting Particle Systems for EM
Tim Johnston, University of Edinburgh and Francesca Crucinio, ENSAE, France
In this talk we discuss a new interacting particle system used for implementing an expectation maximization (EM) procedure (or more generally, to optimize over the parameters of a latent variable model). This continuous-time interacting particle system has the property that it can be seen as a Langevin diffusion over an extended state space, where the number of particles acts almost like an inverse parameter in classical settings for optimization. This then allow for use of the well-developed theory Langevin diffusions to prove non-asymptotic concentration bounds for the optimization error of the maximum marginal likelihood estimator. In this talk we shall place this new algorithm in the context of existing approaches, and also discuss the structure of our proof and how it naturally lends itself to generalisation.