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

Latent Variable Multi-output Gaussian Processes for Hierarchical  Datasets

Scientific datasets often have hierarchical structure: for example, in
surveys, individual participants (samples) might be grouped at a higher level
(units) such as their geographical region. In these settings, the interest is
often in exploring the structure on the unit level rather than on the sample
level. Units can be compared based on the distance between their means, however
this ignores the within-unit distribution of samples. Here we develop an
approach for exploratory analysis of hierarchical datasets using the
Wasserstein distance metric that takes into account the shapes of within-unit
distributions. We use t-SNE to construct 2D embeddings of the units, based on
the matrix of pairwise Wasserstein distances between them. The distance matrix
can be efficiently computed by approximating each unit with a Gaussian
distribution, but we also provide a scalable method to compute exact
Wasserstein distances. We use synthetic data to demonstrate the effectiveness
of our Wasserstein t-SNE, and apply it to data from the 2017 German
parliamentary election, considering polling stations as samples and voting
districts as units. The resulting embedding uncovers meaningful structure in
the data.

本文介绍了一种使用 Wasserstein 距离度量内部分布形状的探索性层次数据集分析方法，并使用 t-SNE 构建了两维嵌入空间，以揭示 2017 年德国议会选举数据中分区与投票站之间的有意义结构。

Wasserstein t-SNE

In recent years, several models have improved the capacity to generate
synthetic tabular datasets. However, such models focus on synthesizing simple
columnar tables and are not useable on real-life data with complex structures.
This paper puts forward a generic framework to synthesize more complex data
structures with composite and nested types. It then proposes one practical
implementation, built with causal transformers, for struct (mappings of types)
and lists (repeated instances of a type). The results on standard benchmark
datasets show that such implementation consistently outperforms current
state-of-the-art models both in terms of machine learning utility and
statistical similarity. Moreover, it shows very strong results on two complex
hierarchical datasets with multiple nesting and sparse data, that were
previously out of reach.

这篇论文提出了一种通用框架来合成更复杂的数据结构，其中包括复合和嵌套类型，并通过因果变换器构建了一种实际的解决方案，用于结构（类型映射）和列表（类型的重复实例），在标准基准数据集上的结果表明，这种方式的实现在机器学习实用性和统计相似性方面均明显优于当前最先进的模型，并且对于以前无法解决的具有多重嵌套和稀疏数据的两个复杂层次数据集表现出非常强的结果。