A Scheme for Molecular Computation of Maximum Likelihood Estimators for Log-Linear Models

TL;DR

This paper introduces a molecular computing scheme that uses reaction networks to efficiently compute maximum likelihood estimators for log-linear models by leveraging the connection between thermodynamic and statistical entropy.

Contribution

It presents a novel method mapping statistical inference problems onto chemical reaction systems, enabling efficient computation of estimators through equilibrium states.

Findings

Reaction networks can encode maximum likelihood estimators for log-linear models.

The scheme exploits the link between thermodynamic and statistical entropy.

Potential implications for understanding biochemical signaling pathways.

Abstract

We propose a novel molecular computing scheme for statistical inference. We focus on the much-studied statistical inference problem of computing maximum likelihood estimators for log-linear models. Our scheme takes log-linear models to reaction systems, and the observed data to initial conditions, so that the corresponding equilibrium of each reaction system encodes the corresponding maximum likelihood estimator. The main idea is to exploit the coincidence between thermodynamic entropy and statistical entropy. We map a Maximum Entropy characterization of the maximum likelihood estimator onto a Maximum Entropy characterization of the equilibrium concentrations for the reaction system. This allows for an efficient encoding of the problem, and reveals that reaction networks are superbly suited to statistical inference tasks. Such a scheme may also provide a template to understanding how in vivo biochemical signaling pathways integrate extensive information about their environment and history.