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.

提出了 Gaussian Process Autoregressive Regression (GPAR) 模型， 是一种可伸缩的多输出高斯过程模型，能够简单而可行地捕获可能因输入变化而产生的非线性依赖关系，并在各种合成和真实世界问题上展示了 GPAR 的有效性，优于现有的 GP 模型并实现了在已有基准测试中的最先进性能。