Fast Multi-Group Gaussian Process Factor Models

TL;DR

This paper introduces two scalable methods for multi-group Gaussian process factor models, significantly reducing computational complexity and enabling analysis of large-scale neural recordings across multiple brain areas.

Contribution

The authors develop two approximate fitting approaches that reduce runtime from cubic to linear, facilitating large-scale multi-population neural data analysis.

Findings

Both methods achieved significant speed-ups with minimal statistical performance loss.

The frequency domain approach provided the best runtime improvements with few trade-offs.

Strategies to mitigate estimation biases in the frequency domain method were demonstrated.

Abstract

Gaussian processes are now commonly used in dimensionality reduction approaches tailored to neuroscience, especially to describe changes in high-dimensional neural activity over time. As recording capabilities expand to include neuronal populations across multiple brain areas, cortical layers, and cell types, interest in extending Gaussian process factor models to characterize multi-population interactions has grown. However, the cubic runtime scaling of current methods with the length of experimental trials and the number of recorded populations (groups) precludes their application to large-scale multi-population recordings. Here, we improve this scaling from cubic to linear in both trial length and group number. We present two approximate approaches to fitting multi-group Gaussian process factor models based on (1) inducing variables and (2) the frequency domain. Empirically, both methods achieved orders of magnitude speed-up with minimal impact on statistical performance, in simulation and on neural recordings of hundreds of neurons across three brain areas. The frequency domain approach, in particular, consistently provided the greatest runtime benefits with the fewest trade-offs in statistical performance. We further characterize the estimation biases introduced by the frequency domain approach and demonstrate effective strategies to mitigate them. This work enables a powerful class of analysis techniques to keep pace with the growing scale of multi-population recordings, opening new avenues for exploring brain function.