Axiomatic Characterization of Data-Driven Influence Measures for Classification

TL;DR

This paper introduces a family of influence measures for classification that are derived axiomatically, based solely on data, providing a principled way to assess feature importance without querying the classifier.

Contribution

The paper defines and characterizes monotone influence measures (MIM) using axioms, establishing a novel, data-driven framework for feature influence assessment in classification.

Findings

MIM measures are uniquely determined by axioms.

MIM provides reliable feature influence scores from data alone.

Effectiveness demonstrated on real datasets.

Abstract

We study the following problem: given a labeled dataset and a specific datapoint x, how did the i-th feature influence the classification for x? We identify a family of numerical influence measures - functions that, given a datapoint x, assign a numeric value phi_i(x) to every feature i, corresponding to how altering i's value would influence the outcome for x. This family, which we term monotone influence measures (MIM), is uniquely derived from a set of desirable properties, or axioms. The MIM family constitutes a provably sound methodology for measuring feature influence in classification domains; the values generated by MIM are based on the dataset alone, and do not make any queries to the classifier. While this requirement naturally limits the scope of our framework, we demonstrate its effectiveness on data.