Variational Bayesian inference of hidden stochastic processes with unknown parameters

TL;DR

This paper introduces a variational Bayesian inference method for estimating hidden stochastic processes with unknown parameters from noisy, non-linear observations, using a combination of SMC algorithms and demonstrating its effectiveness through simulations and gene expression data application.

Contribution

It develops a novel variational Bayesian inference approach employing SMC techniques for hidden process estimation with unknown parameters in non-linear noisy settings.

Findings

The method achieves high estimation accuracy in simulations.

It demonstrates practical utility in gene expression time series analysis.

Numerical efficiency is validated through computational experiments.

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 noise observations. The posterior distribution of hidden states are approximated by a set of weighted particles generated by the sequential Monte carlo (SMC) algorithm involving sampling with importance sampling resampling (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.