# Towards Efficient Modeling and Inference in Multi-Dimensional Gaussian Process State-Space Models

arXiv: https://arxiv.org/abs/2309.01074 · HTML: https://mlsanity.com/paper/2309.01074/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 30 references that are in the map.
- First posted on arXiv 3 Sep 2023.

## Builds on (most cited first, 17 of 17)

- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Structured Inference Networks for Nonlinear State Space Models](https://mlsanity.com/paper/1609.09869/) (2016)
- [Probabilistic Recurrent State-Space Models](https://mlsanity.com/paper/1801.10395/) (2018)
- [Variational Gaussian Process State-Space Models](https://mlsanity.com/paper/1406.4905/) (2014)
- [Identification of Gaussian Process State Space Models](https://mlsanity.com/paper/1705.10888/) (2017)
- [Transforming Gaussian Processes With Normalizing Flows](https://mlsanity.com/paper/2011.01596/) (2020)
- [Bayesian Inference and Learning in Gaussian Process State-Space Models with Particle MCMC](https://mlsanity.com/paper/1306.2861/) (2013)
- [Overcoming Mean-Field Approximations in Recurrent Gaussian Process Models](https://mlsanity.com/paper/1906.05828/) (2019)
- [Compositionally-Warped Gaussian Processes](https://mlsanity.com/paper/1906.09665/) (2019)
- [Rethinking Bayesian Learning for Data Analysis: The Art of Prior and Inference in Sparsity-Aware Modeling](https://mlsanity.com/paper/2205.14283/) (2022)
- [Linear Multiple Low-Rank Kernel Based Stationary Gaussian Processes Regression for Time Series](https://mlsanity.com/paper/1904.09559/) (2019)
- [Efficient Transformed Gaussian Processes for Non-Stationary Dependent Multi-class Classification](https://mlsanity.com/paper/2205.15008/) (2022)
- [Free-Form Variational Inference for Gaussian Process State-Space Models](https://mlsanity.com/paper/2302.09921/) (2023)
- [Output-Dependent Gaussian Process State-Space Model](https://mlsanity.com/paper/2212.07608/) (2022)
- [Towards Flexibility and Interpretability of Gaussian Process State-Space Model](https://mlsanity.com/paper/2301.08843/) (2023)
- [Multitask Gaussian Process with Hierarchical Latent Interactions](https://mlsanity.com/paper/1808.01132/) (2018)

## Built on by (most cited first, 3 of 3)

- [Regularization-Based Efficient Continual Learning in Deep State-Space Models](https://mlsanity.com/paper/2403.10123/) (2024)
- [Efficient Transformed Gaussian Process State-Space Models for Non-Stationary High-Dimensional Dynamical Systems](https://mlsanity.com/paper/2503.18309/) (2025)
- [Simulation-Free Learning of GP-SDEs from Irregular Observations](https://mlsanity.com/paper/2609.33112/) (2026)

## Abstract (arXiv)

The Gaussian process state-space model (GPSSM) has attracted extensive attention for modeling complex nonlinear dynamical systems. However, the existing GPSSM employs separate Gaussian processes (GPs) for each latent state dimension, leading to escalating computational complexity and parameter proliferation, thus posing challenges for modeling dynamical systems with high-dimensional latent states. To surmount this obstacle, we propose to integrate the efficient transformed Gaussian process (ETGP) into the GPSSM, which involves pushing a shared GP through multiple normalizing flows to efficiently model the transition function in high-dimensional latent state space. Additionally, we develop a corresponding variational inference algorithm that surpasses existing methods in terms of parameter count and computational complexity. Experimental results on diverse synthetic and real-world datasets corroborate the efficiency of the proposed method, while also demonstrating its ability to achieve similar inference performance compared to existing methods. Code is available at urlhttps://github.com/zhidilin/gpssmProj.