What makes you unique?
This addresses the problem of variable importance in identification tasks for researchers in fields like data analysis and anomaly detection, though it is incremental as it builds on existing Shapley value and entropy concepts.
The paper introduces a uniqueness Shapley measure to quantify how well different variables identify subjects, such as in voter registration or solar flare data, achieving speedups of up to 2000-fold using efficient data structures.
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.