An Interpretable Determinantal Choice Model for Subset Selection

TL;DR

This paper introduces an interpretable determinantal choice model that unifies random utility models and determinantal point processes, enabling better understanding and modeling of subset selection with dependencies.

Contribution

It establishes that all DPPs are random utility models and proposes a new determinantal choice model that combines interpretability with the tractability of DPPs.

Findings

Model can learn a range of negative dependencies from data.

The model subsumes logistic regression and MNL as special cases.

Applied study provides new insights into wireless interference.

Abstract

Understanding how subsets of items are chosen from offered sets is critical to assortment planning, wireless network planning, and many other applications. There are two seemingly unrelated subset choice models that capture dependencies between items: intuitive and interpretable random utility models; and tractable determinantal point processes (DPPs). This paper connects the two. First, all DPPs are shown to be random utility models. Next, a determinantal choice model that enjoys the best of both worlds is specified; the model is shown to subsume logistic regression when dependence is minimal, and MNL when dependence is maximally negative. This makes the model interpretable, while retaining the tractability of DPPs. A simulation study verifies that the model can learn a continuum of negative dependencies from data, and an applied study using original experimental data produces novel insights on wireless interference in LoRa networks.