What makes you unique?

TL;DR

This paper introduces a uniqueness Shapley measure to quantify how effectively different variables identify subjects, leveraging information theory and efficient computation methods to analyze data like voter rolls and solar flares.

Contribution

It proposes a novel uniqueness Shapley measure based on variable reduction effects, enabling detailed analysis of variable importance in identification tasks.

Findings

The measure effectively quantifies variable uniqueness in identification.

Significant computational speedups are achieved using all dimension trees.

Applications include voter registration data and solar flare detection.

Abstract

This paper proposes a uniqueness Shapley measure to compare the extent to which different variables are able to identify a subject. Revealing the value of a variable on subject $t$ shrinks the set of possible subjects that $t$ could be. The extent of the shrinkage depends on which other variables have also been revealed. We use Shapley value to combine all of the reductions in log cardinality due to revealing a variable after some subset of the other variables has been revealed. This uniqueness Shapley measure can be aggregated over subjects where it becomes a weighted sum of conditional entropies. Aggregation over subsets of subjects can address questions like how identifying is age for people of a given zip code. Such aggregates have a corresponding expression in terms of cross entropies. We use uniqueness Shapley to investigate the differential effects of revealing variables from the North Carolina voter registration rolls and in identifying anomalous solar flares. An enormous speedup (approaching 2000 fold in one example) is obtained by using the all dimension trees of Moore and Lee (1998) to store the cardinalities we need.