Variational Bayesian inference of hidden stochastic processes with unknown parameters
This work addresses a specific challenge in statistical inference for hidden processes, but it appears incremental as it combines existing methods like variational Bayesian inference and SMC for a known bottleneck in parameter estimation.
The paper tackles the problem of estimating hidden stochastic processes from non-linear noisy observations when parameters are unknown, using a variational Bayesian inference approach with sequential Monte Carlo, and demonstrates its numerical efficiency and accuracy through simulations and a gene expression time series application.
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.