A Graph-Structured Distance for Mixed-Variable Domains with Meta Variables

Heterogeneous datasets emerge in various machine learning and optimization applications that feature different input sources, types or formats. Most models or methods do not natively tackle heterogeneity. Hence, such datasets are often partitioned into smaller and simpler ones, which may limit the generalizability or performance, especially if data is limited. The first main contribution of this work is a modeling framework that generalizes hierarchical, tree-structured, variable-size or conditional search frameworks. The framework models mixed-variable domains in which variables may be continuous, integer, or categorical, with some identified as meta when they influence the structure of the problem. The second main contribution is a novel distance that compares any pair of mixed-variable points that do not share the same variables, allowing to use whole heterogeneous datasets that reside in mixed-variable domains with meta variables. The contributions are illustrated on several regression experiments, in which the performance of a multilayer perceptron with respect to its hyperparameters is modeled.