Learning non-stationary Langevin dynamics from stochastic observations of latent trajectories

TL;DR

This paper introduces a non-parametric method to infer non-stationary Langevin equations from stochastic observations, accounting for transient states and observation durations, with applications to neural decision-making dynamics.

Contribution

The authors develop a novel framework that explicitly models stochastic observation processes and non-stationary latent dynamics for accurate Langevin inference.

Findings

Framework accurately infers non-stationary Langevin dynamics

Corrects for non-stationary data to avoid erroneous features

Applied successfully to neural decision-making models

Abstract

Many complex systems operating far from the equilibrium exhibit stochastic dynamics that can be described by a Langevin equation. Inferring Langevin equations from data can reveal how transient dynamics of such systems give rise to their function. However, dynamics are often inaccessible directly and can be only gleaned through a stochastic observation process, which makes the inference challenging. Here we present a non-parametric framework for inferring the Langevin equation, which explicitly models the stochastic observation process and non-stationary latent dynamics. The framework accounts for the non-equilibrium initial and final states of the observed system and for the possibility that the system's dynamics define the duration of observations. Omitting any of these non-stationary components results in incorrect inference, in which erroneous features arise in the dynamics due to non-stationary data distribution. We illustrate the framework using models of neural dynamics underlying decision making in the brain.