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The Shapley Value in Database Management

Leopoldo Bertossi

Teacher at SKEMA Canada

Attribution scores can be applied in data management to quantify the contribution of individual items to con- clusions from the data, as part of the explanation of what led to these conclusions. In Artificial Intelligence, Machine Learning, and Data Management, some of the common scores are deployments of the Shapley value, a formula for profit sharing in cooperative game theory. Since its invention in the 1950s, the Shapley value has been used for contribution measurement in many fields, from economics to law, with its latest researched ap- plications in modern machine learning. Recent stud- ies investigated the application of the Shapley value to database management. This article gives an overview of recent results on the computational complexity of the Shapley value for measuring the contribution of tuples to query answers and to the extent of inconsistency with respect to integrity constraints. More specifically, the article highlights lower and upper bounds on the com- plexity of calculating the Shapley value, either exactly or approximately, as well as solutions for realizing the calculation in practice.


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