  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.
