A reaction network scheme which implements the EM algorithm

TL;DR

This paper introduces a novel reaction network scheme that implements a generalized EM algorithm, enabling chemical systems to perform complex statistical inference tasks akin to cellular information processing.

Contribution

It presents a new reaction network design that maps the EM algorithm onto biochemical reactions, bridging statistical inference and biological realism.

Findings

Reaction networks can implement the EM algorithm for statistical inference.

The scheme enables solving maximum likelihood estimation in biological contexts.

It connects statistical mechanics with biochemical computation.

Abstract

A detailed algorithmic explanation is required for how a network of chemical reactions can generate the sophisticated behavior displayed by living cells. Though several previous works have shown that reaction networks are computationally universal and can in principle implement any algorithm, there is scope for constructions that map well onto biological reality, make efficient use of the computational potential of the native dynamics of reaction networks, and make contact with statistical mechanics. We describe a new reaction network scheme for solving a large class of statistical problems including the problem of how a cell would infer its environment from receptor-ligand bindings. Specifically we show how reaction networks can implement information projection, and consequently a generalized Expectation-Maximization algorithm, to solve maximum likelihood estimation problems in partially-observed exponential families on categorical data. Our scheme can be thought of as an algorithmic interpretation of E. T. Jaynes's vision of statistical mechanics as statistical inference.