Latent Variable Models for Neuronal Spike Data

Modern large-scale recording techniques allow neuroscientists to simultaneously measure the spiking activity of tens to hundreds of neurons, yielding high- dimensional and noisy spike-train datasets. Latent variable models (LVMs) have become essential tools for visualizing and interpreting such data by extract- ing low-dimensional representations that capture underlying neural dynamics. Gaussian process factor analysis (GPFA), a widely used LVM, recovers smooth latent trajectories but suffers from intractable Bayesian inference due to the non-conjugate spike-train likelihood. To address this, we first develop a con- ditionally conjugate GPFA (ccGPFA) model using a novel data-augmentation strategy that renders the model analytically and computationally tractable, en- abling simple closed-form solutions.

Building on ccGPFA, we introduce Coupled Subspaces GPFA (CS-GPFA), a multi-condition extension designed for experiments in which neural responses are collected across structured condition spaces. Unlike standard GPFA methods that infer latent trajectories independently for each condition, CS-GPFA jointly models shared structure while capturing systematic variation across conditions, improving both accuracy and interpretability. We further incorporate an active- learning strategy that leverages the model’s uncertainty to adaptively select informative experimental conditions.

Experiments on synthetic, real-world datasets demonstrate that CS-GPFA outperforms existing approaches, and the active-learning procedure efficiently guides experimental design in practical neuroscience settings.

Committee: Chris Quinn (major professor), Hongyang Gao, Lin Yan, Wallapak Tavanapong and Mengdi Huai