# Output-Dependent Gaussian Process State-Space Model

arXiv: https://arxiv.org/abs/2212.07608 · HTML: https://mlsanity.com/paper/2212.07608/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 28 references that are in the map.
- First posted on arXiv 15 Dec 2022.

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

- [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)
- [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)
- [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)
- [Multitask Gaussian Process with Hierarchical Latent Interactions](https://mlsanity.com/paper/1808.01132/) (2018)
- [Deep Probabilistic Time Series Forecasting using Augmented Recurrent Input for Dynamic Systems](https://mlsanity.com/paper/2106.05848/) (2021)

## Built on by (most cited first, 6 of 6)

- [Towards Flexibility and Interpretability of Gaussian Process State-Space Model](https://mlsanity.com/paper/2301.08843/) (2023)
- [Ensemble Kalman Filtering Meets Gaussian Process SSM for Non-Mean-Field and Online Inference](https://mlsanity.com/paper/2312.05910/) (2023)
- [Regularization-Based Efficient Continual Learning in Deep State-Space Models](https://mlsanity.com/paper/2403.10123/) (2024)
- [Towards Efficient Modeling and Inference in Multi-Dimensional Gaussian Process State-Space Models](https://mlsanity.com/paper/2309.01074/) (2023)
- [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)

Gaussian process state-space model (GPSSM) is a fully probabilistic state-space model that has attracted much attention over the past decade. However, the outputs of the transition function in the existing GPSSMs are assumed to be independent, meaning that the GPSSMs cannot exploit the inductive biases between different outputs and lose certain model capacities. To address this issue, this paper proposes an output-dependent and more realistic GPSSM by utilizing the well-known, simple yet practical linear model of coregionalization (LMC) framework to represent the output dependency. To jointly learn the output-dependent GPSSM and infer the latent states, we propose a variational sparse GP-based learning method that only gently increases the computational complexity. Experiments on both synthetic and real datasets demonstrate the superiority of the output-dependent GPSSM in terms of learning and inference performance.