Heterogeneous datasets emerge in various machine learning or optimization
applications that feature different data sources, various data types and
complex relationships between variables. In practice, heterogeneous datasets
are often partitioned into smaller well-behaved ones that are easier to
process. However, some applications involve expensive-to-generate or limited
size datasets, which motivates methods based on the whole dataset. The first
main contribution of this work is a modeling graph-structured framework that
generalizes state-of-the-art hierarchical, tree-structured, or variable-size
frameworks. This framework models domains that involve heterogeneous datasets
in which variables may be continuous, integer, or categorical, with some
identified as meta if their values determine the inclusion/exclusion or affect
the bounds of other so-called decreed variables. Excluded variables are
introduced to manage variables that are either included or excluded depending
on the given points. The second main contribution is the graph-structured
distance that compares extended points with any combination of included and
excluded variables: any pair of points can be compared, allowing to work
directly in heterogeneous datasets with meta variables. The contributions are
illustrated with some regression experiments, in which the performance of a
multilayer perceptron with respect to its hyperparameters is modeled with
inverse distance weighting and $K$-nearest neighbors models.

本文提出了一种图结构框架来建模涉及异构数据集的领域，该框架可以处理包含连续型、整数型或分类型变量以及一些被定义为元变量的复杂关系，同时提出了一种图结构距离来比较扩展数据点之间的任意组合，以便直接在异构数据集中处理元变量，并通过回归实验来验证其性能与超参数的模型关系。