Explicitly Solvable Continuous-time Inference for Partially Observed Markov Processes

TL;DR

This paper introduces an explicit continuous-time inference method for partially observed Markov processes, enabling exact calculation of hidden state probabilities from transition rates and partial observations within a finite time window.

Contribution

It presents a novel continuous-time formulation of the sum-product algorithm that allows explicit solutions for hidden state probabilities in Markov processes.

Findings

Successfully applied to a CFTR protein model for exact inference.

Provides explicit formulas for conditional probabilities based on transition rates.

Demonstrates broad applicability to systems with partial observations.

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.