# Linear Time GPs for Inferring Latent Trajectories from Neural Spike Trains

arXiv: https://arxiv.org/abs/2306.01802 · HTML: https://mlsanity.com/paper/2306.01802/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 61 references that are in the map.
- First posted on arXiv 1 Jun 2023.

## Builds on (most cited first, 15 of 15)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Conjugate-Computation Variational Inference : Converting Variational Inference in Non-Conjugate Models to Inferences in Conjugate Models](https://mlsanity.com/paper/1703.04265/) (2017)
- [Neural Latents Benchmark '21: Evaluating latent variable models of neural population activity](https://mlsanity.com/paper/2109.04463/) (2021)
- [Variational Gaussian Process State-Space Models](https://mlsanity.com/paper/1406.4905/) (2014)
- [Natural Gradients in Practice: Non-Conjugate Variational Inference in Gaussian Process Models](https://mlsanity.com/paper/1803.09151/) (2018)
- [Fast yet Simple Natural-Gradient Descent for Variational Inference in Complex Models](https://mlsanity.com/paper/1807.04489/) (2018)
- [Spatio-Temporal Variational Gaussian Processes](https://mlsanity.com/paper/2111.01732/) (2021)
- [Variational Latent Gaussian Process for Recovering Single-Trial Dynamics from Population Spike Trains](https://mlsanity.com/paper/1604.03053/) (2016)
- [Fast Variational Learning in State-Space Gaussian Process Models](https://mlsanity.com/paper/2007.04731/) (2020)
- [Doubly Sparse Variational Gaussian Processes](https://mlsanity.com/paper/2001.05363/) (2020)
- [Streaming Variational Monte Carlo](https://mlsanity.com/paper/1906.01549/) (2019)
- [Linear-time inference for Gaussian Processes on one dimension](https://mlsanity.com/paper/2003.05554/) (2020)
- [State Space Expectation Propagation: Efficient Inference Schemes for Temporal Gaussian Processes](https://mlsanity.com/paper/2007.05994/) (2020)
- [Sparse Algorithms for Markovian Gaussian Processes](https://mlsanity.com/paper/2103.10710/) (2021)
- [Infinite-Horizon Gaussian Processes](https://mlsanity.com/paper/1811.06588/) (2018)

## Built on by (most cited first, 5 of 5)

- [SING: SDE Inference via Natural Gradients](https://mlsanity.com/paper/2506.17796/) (2025)
- [Learning Time-Varying Multi-Region Brain Communications via Scalable Markovian Gaussian Processes](https://mlsanity.com/paper/2407.00397/) (2024)
- [Conditionally-Conjugate Gaussian Process Factor Analysis for Spike Count Data via Data Augmentation](https://mlsanity.com/paper/2405.11683/) (2024)
- [Modeling Neural Activity with Conditionally Linear Dynamical Systems](https://mlsanity.com/paper/2502.18347/) (2025)
- [Learning Coupled Subspaces for Multi-Condition Spike Data](https://mlsanity.com/paper/2410.19153/) (2024)

## Abstract (arXiv)

Latent Gaussian process (GP) models are widely used in neuroscience to uncover hidden state evolutions from sequential observations, mainly in neural activity recordings. While latent GP models provide a principled and powerful solution in theory, the intractable posterior in non-conjugate settings necessitates approximate inference schemes, which may lack scalability. In this work, we propose cvHM, a general inference framework for latent GP models leveraging Hida-Mat'ern kernels and conjugate computation variational inference (CVI). With cvHM, we are able to perform variational inference of latent neural trajectories with linear time complexity for arbitrary likelihoods. The reparameterization of stationary kernels using Hida-Mat'ern GPs helps us connect the latent variable models that encode prior assumptions through dynamical systems to those that encode trajectory assumptions through GPs. In contrast to previous work, we use bidirectional information filtering, leading to a more concise implementation. Furthermore, we employ the Whittle approximate likelihood to achieve highly efficient hyperparameter learning.