Explicitly Solvable Continuous-time Inference for Partially Observed Markov Processes
Abstract
Many natural and engineered systems can be modeled as discrete state Markov processes. Often, only a subset of states are directly observable. Inferring the conditional probability that a system occupies a particular hidden state, given the partial observation, is a problem with broad application. In this paper, we introduce a continuous-time formulation of the sum-product algorithm, which is a well-known discrete-time method for finding the hidden states' conditional probabilities, given a set of finite, discrete-time observations. From our new formulation, we can explicitly solve for the conditional probability of occupying any state, given the transition rates and observations within a finite time window. We apply our algorithm to a realistic model of the cystic fibrosis transmembrane conductance regulator (CFTR) protein for exact inference of the conditional occupancy probability, given a finite time series of partial observations.
Cite
@article{arxiv.2301.00843,
title = {Explicitly Solvable Continuous-time Inference for Partially Observed Markov Processes},
author = {Daniel Chen and Alexander G. Strang and Andrew W. Eckford and Peter J. Thomas},
journal= {arXiv preprint arXiv:2301.00843},
year = {2023}
}
Comments
Accepted for publication in IEEE Transactions on Signal Processing