Learning and Inference in Nonlinear State-Space Models

We present nonlinear state-space models (NSSMs) as a general method for the probabilistic modelling of sequences and time-series. NSSMs take the form of iterated maps on continuous state-spaces, and can have either discrete or continuous valued output functions. They are generalizations of the more well known state-space models such as Hidden Markov models (HMMs), and Kalman Filter Models (KFMs). In this paper, we describe the problems of inference and learning in NSSMs. We present a sequential Monte-Carlo method for inference of statespace trajectories given observed sequences, and present an expectationmaximization (EM) algorithm for maximum a posteriori estimation of the model’s parameter values. The method of inference used here leads to accurate approximations of the non-Gaussian and multi-modal posterior distributions that are typical in nonlinear state-space models.