Determine latent dimensionality and number of regimes in real neural datasets

Determine the true latent dimensionality K and the optimal number of switching linear regimes J for the Gaussian Process Switching Linear Dynamical System when modeling a specific real neural dataset, given that these quantities are not known a priori and must be selected to balance model expressivity and interpretability.

Background

The Gaussian Process Switching Linear Dynamical System (gpSLDS) introduces a structured Gaussian process prior that yields smoothly switching locally linear dynamics, controlled by two key hyperparameters: the latent dimensionality K and the number of linear regimes J. In the paper’s experiments, these hyperparameters were set based on prior knowledge or true generative values for synthetic data.

For most real neural datasets, the true values of K and J are unknown beforehand, yet selecting them critically affects the model’s capacity to capture relevant dynamics while remaining interpretable. The authors suggest practical metrics such as forward simulation accuracy and co-smoothing performance for model comparison, highlighting the need to systematically determine K and J in applied settings.