Off-the-shelf Gaussian Process (GP) covariance functions encode smoothness assumptions on the structure of the function to be modeled. To model complex and non-differentiable functions, these smoothness assumptions are often too restrictive. One way to alleviate this limitation is to find a different representation of the data by introducing a feature space. This feature space is often learned in an unsupervised way, which might lead to data representations that are not useful for the overall regression task. In this paper, we propose Manifold Gaussian Processes, a novel supervised method that learns jointly a transformation of the data into a feature space and a GP regression from the feature space to observed space. The Manifold GP is a full GP, and it allows to learn data representations, which are useful for the overall regression task. As a proof-of-concept, we evaluate our approach on complex non-smooth functions where standard GPs perform poorly, such as step functions and effects of ground contacts in a robotics application.

本研究提出了一种新的监督学习方法，Manifold Gaussian Processes，该方法通过联合学习将数据转换为特征空间，并从特征空间到观测空间建立了GP回归模型，实验结果表明该方法适用于包括非光滑函数和机器人任务等不规则函数。

流形高斯过程回归