Variational Bayesian inference of hidden stochastic processes with unknown parameters

Abstract

Estimating hidden processes from non-linear noisy observations is particularly difficult when the parameters of these processes are not known. This paper adopts a machine learning approach to devise variational Bayesian inference for such scenarios. In particular, a random process generated by the autoregressive moving average (ARMA) linear model is inferred from non-linearity noisy observations. The posterior distributions of hidden states are approximated by a set of weighted particles generated by the sequential Monte Carlo (SMC) algorithm involving sampling with importance samplingresampling (SISR). Numerical efficiency and estimation accuracy of the proposed inference method are evaluated by computer simulations. Furthermore, the proposed inference method is demonstrated on a practical problem of estimating the missing values in the gene expression time series assuming vector autoregressive (VAR) data model.