Modeling Neural Activity with Conditionally Linear Dynamical Systems

Victor Geadah, Amin Nejatbakhsh, David Lipshutz, Jonathan W. Pillow, Alex H Williams

Keywords: Linear Dynamical Systems, Gaussian Processes, Neural data analysis, Expectation-Maximization

TL;DR: We extended classical linear-Gaussian state space models of neural circuit dynamics to capture nonlinear dependencies on experimental conditions, while maintaining ease of fit and interpretability.

Abstract: Neural population activity exhibits complex, nonlinear dynamics, varying in time, over trials, and across experimental conditions. Here, we develop *Conditionally Linear Dynamical System* (CLDS) models as a general-purpose method to characterize these dynamics. These models use Gaussian Process priors to capture the nonlinear dependence of circuit dynamics on task and behavioral variables. Conditioned on these covariates, the data is modeled with linear dynamics. This allows for transparent interpretation and tractable Bayesian inference. We find that CLDS models can perform well even in severely data-limited regimes (e.g. one trial per condition) due to their Bayesian formulation and ability to share statistical power across nearby task conditions. In example applications, we apply CLDS to model thalamic neurons that nonlinearly encode heading direction and to model motor cortical neurons during a cued-reaching task.

Primary Area: Neuroscience and cognitive science (e.g., neural coding, brain-computer interfaces)

Submission Number: 10642