An Efficient Forward-Reverse Expectation-Maximization Algorithm for Statistical Inference in Stochastic Reaction Networks

TL;DR

This paper introduces an efficient two-phase EM algorithm for statistical inference in stochastic reaction networks, combining deterministic ODE approximations with stochastic EM to improve parameter estimation from discrete data.

Contribution

It extends forward-reverse stochastic representations to SRNs and develops a novel two-phase inference method integrating ODE and Monte Carlo EM techniques.

Findings

Improved parameter estimation accuracy demonstrated in numerical examples.

Efficient approximation of expected functionals of SRN bridges achieved.

Parallel runs produce a cluster of approximate maximum likelihood estimates.

Abstract

In this work, we present an extension to the context of Stochastic Reaction Networks (SRNs) of the forward-reverse representation introduced in "Simulation of forward-reverse stochastic representations for conditional diffusions", a 2014 paper by Bayer and Schoenmakers. We apply this stochastic representation in the computation of efficient approximations of expected values of functionals of SNR bridges, i.e., SRNs conditioned to its values in the extremes of given time-intervals. We then employ this SNR bridge-generation technique to the statistical inference problem of approximating the reaction propensities based on discretely observed data. To this end, we introduce a two-phase iterative inference method in which, during phase I, we solve a set of deterministic optimization problems where the SRNs are replaced by their reaction-rate Ordinary Differential Equations (ODEs) approximation; then, during phase II, we apply the Monte Carlo version of the Expectation-Maximization (EM) algorithm starting from the phase I output. By selecting a set of over dispersed seeds as initial points for phase I, the output of parallel runs from our two-phase method is a cluster of approximate maximum likelihood estimates. Our results are illustrated by numerical examples.