Density-based interpretable hypercube region partitioning for mixed numeric and categorical data

Abstract

Consider a structured dataset of features, such as $\{\textrm{SEX}, \textrm{INCOME}, \textrm{RACE}, \textrm{EXPERIENCE}\}$. A user may want to know where in the feature space observations are concentrated, and where it is sparse or empty. The existence of large sparse or empty regions can provide domain knowledge of soft or hard feature constraints (e.g., what is the typical income range, or that it may be unlikely to have a high income with few years of work experience). Also, these can suggest to the user that machine learning (ML) model predictions for data inputs in sparse or empty regions may be unreliable. An interpretable region is a hyper-rectangle, such as $\{\textrm{RACE} \in\{\textrm{Black}, \textrm{White}\}\}\:\&$ $\{10 \leq \:\textrm{EXPERIENCE} \:\leq 13\}$, containing all observations satisfying the constraints; typically, such regions are defined by a small number of features. Our method constructs an observation density-based partition of the observed feature space in the dataset into such regions. It has a number of advantages over others in that it works on features of mixed type (numeric or categorical) in the original domain, and can separate out empty regions as well. As can be seen from visualizations, the resulting partitions accord with spatial groupings that a human eye might identify; the results should thus extend to higher dimensions. We also show some applications of the partition to other data analysis tasks, such as inferring about ML model error, measuring high-dimensional density variability, and causal inference for treatment effect. Many of these applications are made possible by the hyper-rectangular form of the partition regions.