  Gaussian process factor analysis (GPFA) is a latent variable modeling
technique commonly used to identify smooth, low-dimensional latent trajectories
underlying high-dimensional neural recordings. Specifically, researchers model
spiking rates as Gaussian observations, resulting in tractable inference.
Recently, GPFA has been extended to model spike count data. However, due to the
non-conjugacy of the likelihood, the inference becomes intractable. Prior works
rely on either black-box inference techniques, numerical integration or
polynomial approximations of the likelihood to handle intractability. To
overcome this challenge, we propose a conditionally-conjugate Gaussian process
factor analysis (ccGPFA) resulting in both analytically and computationally
tractable inference for modeling neural activity from spike count data. In
particular, we develop a novel data augmentation based method that renders the
model conditionally conjugate. Consequently, our model enjoys the advantage of
simple closed-form updates using a variational EM algorithm. Furthermore, due
to its conditional conjugacy, we show our model can be readily scaled using
sparse Gaussian Processes and accelerated inference via natural gradients. To
validate our method, we empirically demonstrate its efficacy through
experiments.
