Inverse modeling of time-delayed interactions via the dynamic-entropy formalism

TL;DR

This paper introduces a path integral maximum-entropy method to infer time-delayed interactions in collective systems, overcoming limitations of traditional equal-time correlation constraints, with applications to synthetic models and biological data.

Contribution

It develops a novel approach incorporating delays into maximum-entropy inference, enabling accurate estimation of coupling strengths and delay times in non-Markovian systems.

Findings

Accurately infers coupling strengths and delays in synthetic datasets.

Outperforms traditional methods by capturing non-instantaneous interactions.

Successfully applied to biological data showing improved modeling of dendritic migration.

Abstract

Although instantaneous interactions are unphysical, a large variety of maximum entropy statistical inference methods match the model-inferred and the empirically-measured equal-time correlation functions. Focusing on collective motion of active units, this constraint is reasonable when the interaction timescale is much faster than that of the interacting units, as in starling flocks, yet it fails in a number of counter examples, as in leukocyte coordination (where signalling proteins diffuse among two cells). Here, we relax this assumption and develop a path integral approach to maximum-entropy framework, which includes delay in signalling. Our method is able to infer the strength of couplings and fields, but also the time required by the couplings to completely transfer information among the units. We demonstrate the validity of our approach providing excellent results on synthetic datasets of non-Markovian trajectories generated by the Heisenberg-Kuramoto and Vicsek models equipped with delayed interactions. As a proof of concept, we also apply the method to experiments on dendritic migration, where matching equal-time correlations results in a significant information loss.