# The Gaussian Process Autoregressive Regression Model (GPAR)

arXiv: https://arxiv.org/abs/1802.07182 · HTML: https://mlsanity.com/paper/1802.07182/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2018.

## Built on by (most cited first, 12 of 12)

- [Fully Bayesian Autoencoders with Latent Sparse Gaussian Processes](https://mlsanity.com/paper/2302.04534/) (2023)
- [Learning Multi-Task Gaussian Process Over Heterogeneous Input Domains](https://mlsanity.com/paper/2202.12636/) (2022)
- [Multi-Fidelity Methods for Optimization: A Survey](https://mlsanity.com/paper/2402.09638/) (2024)
- [Scalable Multi-Task Gaussian Processes with Neural Embedding of Coregionalization](https://mlsanity.com/paper/2109.09261/) (2021)
- [GAR: Generalized Autoregression for Multi-Fidelity Fusion](https://mlsanity.com/paper/2301.05729/) (2023)
- [Federated Automatic Latent Variable Selection in Multi-output Gaussian Processes](https://mlsanity.com/paper/2407.16935/) (2024)
- [Scalable Multi-Output Gaussian Processes with Stochastic Variational Inference](https://mlsanity.com/paper/2407.02476/) (2024)
- [Evolving-Graph Gaussian Processes](https://mlsanity.com/paper/2106.15127/) (2021)
- [Volatility Based Kernels and Moving Average Means for Accurate Forecasting with Gaussian Processes](https://mlsanity.com/paper/2207.06544/) (2022)
- [Structured Recognition for Generative Models with Explaining Away](https://mlsanity.com/paper/2209.05212/) (2022)
- [Multi-task Neural Diffusion Processes](https://mlsanity.com/paper/2510.03419/) (2025)
- [Transformed Latent Variable Multi-Output Gaussian Processes](https://mlsanity.com/paper/2605.05133/) (2026)

## Abstract (arXiv)

Multi-output regression models must exploit dependencies between outputs to maximise predictive performance. The application of Gaussian processes (GPs) to this setting typically yields models that are computationally demanding and have limited representational power. We present the Gaussian Process Autoregressive Regression (GPAR) model, a scalable multi-output GP model that is able to capture nonlinear, possibly input-varying, dependencies between outputs in a simple and tractable way: the product rule is used to decompose the joint distribution over the outputs into a set of conditionals, each of which is modelled by a standard GP. GPAR's efficacy is demonstrated on a variety of synthetic and real-world problems, outperforming existing GP models and achieving state-of-the-art performance on established benchmarks.