Approximate Smoothing and Parameter Estimation in High-Dimensional State-Space Models

We present approximate algorithms for estimating additive smoothing functionals in a class of high-dimensional state-space models via sequential Monte Carlo methods ("particle filters"). In such high-dimensional settings, a prohibitively large number of particles, i.e. growing exponentially in the dimension of the state space, is usually required to obtain useful estimates of such smoothed quantities. Exploiting spatial ergodicity properties of the model, we circumvent this problem via a blocking strategy which leads to approximations that can be computed recursively in time and in parallel in space. In particular, our method enables us to perform maximum-likelihood estimation via stochastic gradient-ascent and stochastic expectation-maximisation algorithms. We demonstrate the methods on a high-dimensional state-space model.