Learning dynamical systems with particle stochastic approximation EM

Particle stochastic approximation EM (PSAEM) is an algorithm for learning of dynamical systems, combining stochastic approximation EM and particle Gibbs with ancestor sampling (PGAS). We provide a detailed derivation of the PSAEM algorithm, a theoretical analysis of its convergence properties, and show that PSAEM can be used for plain maximum likelihood inference as well as for empirical Bayes learning of hyperparameters. Specifically, the latter point means that existing PGAS implementations easily can be extended with PSAEM to estimate hyperparameters at almost no extra computational cost. We demonstrate that PSAEM obtains superior empirical performance compared to plain particle-smoothing-based approximations of the EM algorithm.