Generalized Glauber dynamics for inference in biology

TL;DR

This paper introduces generalized Glauber dynamics, a novel inference method for modeling the complex, multi-scale dynamics of biological systems, successfully capturing both steady states and long-tailed waiting time distributions.

Contribution

It develops a non-Markovian fluctuation dissipation-based approach to infer dynamical models that preserve steady states while reproducing observed temporal behaviors.

Findings

Successfully inferred social interaction dynamics in mice groups.

Reproduced long-tailed waiting time distributions in empirical data.

Validated method on simple Ising spin systems.

Abstract

Large interacting systems in biology often exhibit emergent dynamics, such as coexistence of multiple time scales, manifested by fat tails in the distribution of waiting times. While existing tools in statistical inference, such as maximum entropy models, reproduce the empirical steady state distributions, it remains challenging to learn dynamical models. We present a novel inference method, called generalized Glauber dynamics. Constructed through a non-Markovian fluctuation dissipation theorem, generalized Glauber dynamics tunes the dynamics of an interacting system, while keeping the steady state distribution fixed. We motivate the need for the method on real data from Eco-HAB, an automated habitat for testing behavior in groups of mice under semi-naturalistic conditions, and present it on simple Ising spin systems. We show its applicability for experimental data, by inferring dynamical models of social interactions in a group of mice that reproduce both its collective behavior and the long tails observed in individual dynamics.