Uncovering dynamical equations of stochastic decision models using data-driven SINDy algorithm

TL;DR

This paper applies the data-driven SINDy algorithm to uncover the underlying dynamical equations of stochastic decision models from neural activity data, improving understanding of perceptual decision formation.

Contribution

It demonstrates how SINDy can effectively identify deterministic components of stochastic decision models using neural activity data, especially with multi-trial approaches.

Findings

SINDy accurately estimates decision model dynamics across noise levels.

Multi-trial SINDy outperforms single-trial in model estimation.

Potential for real-time decision modeling using single-trial data.

Abstract

Decision formation in perceptual decision-making involves sensory evidence accumulation instantiated by the temporal integration of an internal decision variable towards some decision criterion or threshold, as described by sequential sampling theoretical models. The decision variable can be represented in the form of experimentally observable neural activities. Hence, elucidating the appropriate theoretical model becomes crucial to understanding the mechanisms underlying perceptual decision formation. Existing computational methods are limited to either fitting of choice behavioural data or linear model estimation from neural activity data. In this work, we made use of sparse identification of nonlinear dynamics (SINDy), a data-driven approach, to elucidate the deterministic linear and nonlinear components of often-used stochastic decision models within reaction time task paradigms. Based on the simulated decision variable activities of the models, SINDy, enhanced with approaches using multiple trials, could readily estimate the dynamical equations, choice accuracy and decision time of the models across a range of signal-to-noise ratio values. In particular, SINDy performed the best using the more memory intensive multi-trial approach while trial-averaging of parameters performed more moderately. The single-trial approach, although expectedly not performing as well, may be useful for real-time modelling. Taken together, our work offers alternative approaches for SINDy to uncover the dynamics in perceptual decision-making, and more generally, for first-passage time problems.