Multi-output Gaussian processes (MOGPs) have been introduced to deal with multiple tasks by exploiting the correlations between different outputs. Generally, MOGPs models assume a flat correlation structure between the outputs. However, such a formulation does not account for more elaborate relationships, for instance, if several replicates were observed for each output (which is a typical setting in biological experiments). This paper proposes an extension of MOGPs for hierarchical datasets (i.e. datasets for which the relationships between observations can be represented within a tree structure). Our model defines a tailored kernel function accounting for hierarchical structures in the data to capture different levels of correlations while leveraging the introduction of latent variables to express the underlying dependencies between outputs through a dedicated kernel. This latter feature is expected to significantly improve scalability as the number of tasks increases. An extensive experimental study involving both synthetic and real-world data from genomics and motion capture is proposed to support our claims.

该研究论文提出了一个扩展多输出高斯过程（MOGPs）用于分层数据集的方法，通过定义适合层次结构的核函数来捕捉不同层次的相关性，并通过引入潜在变量表达输出之间的潜在依赖关系，以提高可扩展性。通过合成数据和基因组学以及动作捕捉的真实世界数据进行了广泛的实验研究，以支持该方法。

层次数据的潜在变量多输出高斯过程