Interacting Particle Langevin Algorithm for Maximum Marginal Likelihood Estimation

We study a class of interacting particle systems for implementing a marginal maximum likelihood estimation (MLE) procedure to optimize over the parameters of a latent variable model. To do so, we propose a continuous-time interacting particle system which can be seen as a Langevin diffusion over an extended state space, where the number of particles acts as the inverse temperature parameter in classical settings for optimisation. Using Langevin diffusions, we prove nonasymptotic concentration bounds for the optimisation error of the maximum marginal likelihood estimator in terms of the number of particles in the particle system, the number of iterations of the algorithm, and the step-size parameter for the time discretisation analysis.