Short Boolean Formulas as Explanations in Practice

TL;DR

This paper explores the use of short Boolean formulas as interpretable explanations for data, providing theoretical bounds and practical methods to balance accuracy and interpretability through length control.

Contribution

It introduces novel bounds for expected error of Boolean explanations and demonstrates practical encoding and validation techniques for selecting interpretable explanations.

Findings

Short Boolean formulas can achieve accuracy comparable to other methods.

Limiting formula length reduces overfitting and enhances interpretability.

Cross validation helps select optimal explanation length.

Abstract

We investigate explainability via short Boolean formulas in the data model based on unary relations. As an explanation of length k, we take a Boolean formula of length k that minimizes the error with respect to the target attribute to be explained. We first provide novel quantitative bounds for the expected error in this scenario. We then also demonstrate how the setting works in practice by studying three concrete data sets. In each case, we calculate explanation formulas of different lengths using an encoding in Answer Set Programming. The most accurate formulas we obtain achieve errors similar to other methods on the same data sets. However, due to overfitting, these formulas are not necessarily ideal explanations, so we use cross validation to identify a suitable length for explanations. By limiting to shorter formulas, we obtain explanations that avoid overfitting but are still reasonably accurate and also, importantly, human interpretable.