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Consider a structured dataset of features, such as $\{\textrm{SEX},\textrm{INCOME}, \textrm{RACE}, \textrm{EXPERIENCE}\}$. A user may want to knowwhere in the feature space observations are concentrated, and where it issparse or empty. The existence of large sparse or empty regions can providedomain knowledge of soft or hard feature constraints (e.g., what is the typicalincome range, or that it may be unlikely to have a high income with few yearsof work experience). Also, these can suggest to the user that machine learning(ML) model predictions for data inputs in sparse or empty regions may beunreliable.  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 methodconstructs an observation density-based partition of the observed feature spacein the dataset into such regions. It has a number of advantages over others inthat it works on features of mixed type (numeric or categorical) in theoriginal domain, and can separate out empty regions as well.  As can be seen from visualizations, the resulting partitions accord withspatial groupings that a human eye might identify; the results should thusextend to higher dimensions. We also show some applications of the partition toother data analysis tasks, such as inferring about ML model error, measuringhigh-dimensional density variability, and causal inference for treatmenteffect. Many of these applications are made possible by the hyper-rectangularform of the partition regions.

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