# Learning Coupled Subspaces for Multi-Condition Spike Data

arXiv: https://arxiv.org/abs/2410.19153 · HTML: https://mlsanity.com/paper/2410.19153/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 60 references that are in the map.
- First posted on arXiv 24 Oct 2024.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Latents Benchmark '21: Evaluating latent variable models of neural population activity](https://mlsanity.com/paper/2109.04463/) (2021)
- [Spatio-Temporal Variational Gaussian Processes](https://mlsanity.com/paper/2111.01732/) (2021)
- [Active Learning Using Uncertainty Information](https://mlsanity.com/paper/1702.08540/) (2017)
- [Bayes-Newton Methods for Approximate Bayesian Inference with PSD Guarantees](https://mlsanity.com/paper/2111.01721/) (2021)
- [State Space Expectation Propagation: Efficient Inference Schemes for Temporal Gaussian Processes](https://mlsanity.com/paper/2007.05994/) (2020)
- [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)
- [Multi-Region Markovian Gaussian Process: An Efficient Method to Discover Directional Communications Across Multiple Brain Regions](https://mlsanity.com/paper/2402.02686/) (2024)
- [Data Augementation with Polya Inverse Gamma](https://mlsanity.com/paper/1905.12141/) (2019)
- [Conditionally-Conjugate Gaussian Process Factor Analysis for Spike Count Data via Data Augmentation](https://mlsanity.com/paper/2405.11683/) (2024)

## Abstract (arXiv)

In neuroscience, numerous studies conduct sensory or behavioral experiments under multiple conditions to acquire neural responses in the form of high-dimensional spike train datasets. Analyzing high-dimensional spike data is a challenging statistical problem. To this end, Gaussian process factor analysis (GPFA), a popular class of latent variable models, has been proposed for data collected under a single experimental condition. GPFA extracts smooth, low-dimensional latent trajectories that summarize highdimensional spike datasets. However, standard GPFA infers these trajectories independently for each experimental condition, not accounting for how the underlying activity varies across the condition space. This poses limitations on both accuracy and the interpretability of the latent representation. To address these limitations, we propose Coupled Subspaces GPFA (CS-GPFA), a Bayesian model that jointly learns latent representations, characterizing how the neural activity varies over the condition space. Building on this, we further develop an active-learning algorithm for adaptively selecting conditions. Experiments on both synthetic and real neural datasets demonstrate that CS-GPFA achieves superior performance compared to existing approaches. Moreover, our active learning results show that CS-GPFA can efficiently guide experiment design in practical settings.