# Conditionally-Conjugate Gaussian Process Factor Analysis for Spike Count Data via Data Augmentation

arXiv: https://arxiv.org/abs/2405.11683 · HTML: https://mlsanity.com/paper/2405.11683/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 42 references that are in the map.
- First posted on arXiv 19 May 2024.

## Builds on (most cited first, 7 of 7)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Machine learning for neural decoding](https://mlsanity.com/paper/1708.00909/) (2017)
- [Efficient Gaussian Process Classification Using Polya-Gamma Data Augmentation](https://mlsanity.com/paper/1802.06383/) (2018)
- [Boosting Black Box Variational Inference](https://mlsanity.com/paper/1806.02185/) (2018)
- [Efficient non-conjugate Gaussian process factor models for spike count data using polynomial approximations](https://mlsanity.com/paper/1906.03318/) (2019)
- [Linear Time GPs for Inferring Latent Trajectories from Neural Spike Trains](https://mlsanity.com/paper/2306.01802/) (2023)
- [Fast Bayesian Variable Selection in Binomial and Negative Binomial Regression](https://mlsanity.com/paper/2106.14981/) (2021)

## Built on by (most cited first, 1 of 1)

- [Learning Coupled Subspaces for Multi-Condition Spike Data](https://mlsanity.com/paper/2410.19153/) (2024)

## Abstract (arXiv)

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.