Modeling Latent Neural Dynamics with Gaussian Process Switching Linear Dynamical Systems.

Area of Science:

• Computational Neuroscience
• Statistical Modeling
• Machine Learning in Neuroscience

Background:

• Characterizing neural population activity is crucial for understanding brain computation and behavior.
• Low-dimensional latent dynamics models are essential for analyzing high-dimensional neural time series.
• Existing methods often struggle to balance model expressiveness for nonlinear dynamics with interpretability.

Purpose of the Study:

• To develop a novel statistical method, the Gaussian Process Switching Linear Dynamical System (gpSLDS), that balances expressiveness and interpretability.
• To address limitations of current models, such as artifactual oscillations and lack of uncertainty estimates.
• To improve the accuracy of estimating model parameters, particularly kernel hyperparameters.

Main Methods:

• Utilized Gaussian Process Stochastic Differential Equations (GP-SDEs) to model latent state evolution.
• Introduced a novel kernel function for smoothly interpolated locally linear dynamics.
• Employed a modified learning objective for improved kernel hyperparameter estimation.

Main Results:

• The gpSLDS method demonstrated flexible yet interpretable dynamics, overcoming limitations of recurrent switching linear dynamical systems (rSLDS).
• The approach successfully provided posterior uncertainty estimates for neural dynamics.
• Evaluations on synthetic and experimental neuroscience data showed favorable performance compared to rSLDS.

Conclusions:

• The gpSLDS offers a powerful new tool for analyzing complex neural population dynamics in neuroscience.
• This method provides a better balance between capturing intricate nonlinearities and maintaining model interpretability.
• The gpSLDS advances the statistical toolkit for uncovering the relationship between neural activity and behavior.