Decomposing Non-Markovian History Dependence

TL;DR

This paper introduces an information-theoretic framework to quantify and decompose historical dependencies in non-Markovian stochastic processes, with applications to biological systems like fly behavior.

Contribution

It provides a novel method to accurately capture and analyze non-Markovian dependencies, even when autocorrelations are absent, across multiple timescales.

Findings

Framework correctly captures historical dependencies in models.

Non-Markovian dependencies scale invariantly across timescales.

Overall non-Markovian information varies non-monotonically over time.

Abstract

Non-Markovian stochastic processes are ubiquitous in biology. Nevertheless, we lack a general framework for quantifying historical dependencies. In this Letter, we propose an information-theoretic approach to decompose history dependence in systems with non-Markovian dynamics, quantifying the information encoded in dependencies of each order. In minimal models of non-Markovian dynamics, we show that this framework correctly captures the underlying historical dependencies, even when autocorrelations do not. In prolonged recordings of fly behavior, we find that the scaling of non-Markovian dependencies is invariant across timescales from fractions of a second to minutes. Despite this invariance, the overall amount of non-Markovian information is non-monotonic, suggesting a unique timescale on which historical dependencies are strongest.