A distance for mixed-variable and hierarchical domains with meta variables

TL;DR

This paper introduces a new modeling framework and a novel distance measure for heterogeneous, hierarchical datasets with mixed variable types and meta variables, enhancing data utilization in machine learning tasks.

Contribution

It presents a generalized framework for hierarchical, mixed-variable domains and a new distance metric enabling comparison of heterogeneous data points, improving data integration.

Findings

Effective in regression and classification tasks

Allows use of entire heterogeneous datasets

Improves model performance with mixed-variable data

Abstract

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 when 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 and hierarchical 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 and hierarchical domains with meta variables. The contributions are illustrated through regression and classification experiments using simple distance-based models applied to datasets of hyperparameters with corresponding performance scores.