Approximation of hidden Markov models by mixtures of experts with application to particle filtering

Selecting conveniently the proposal kernel and the adjustment multiplier weights of the auxiliary particle filter may increase significantly the accuracy and computational efficiency of the method. However, in practice the optimal proposal kernel and multiplier weights are seldom known. In this paper we present a simulation-based method for constructing offline an approximation of these quantities that makes the filter close to fully adapted at a reasonable computational cost. The approximation is constructed as a mixture of experts optimised through an efficient stochastic approximation algorithm. The method is illustrated on two simulated examples.