Computing the Shapley Value of Facts in Query Answering

Daniel Deutch, Nave Frost, Benny Kimelfeld, Mikaël Monet

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

6 Scopus citations


The Shapley value is a game-theoretic notion for wealth distribution that is nowadays extensively used to explain complex data-intensive computation, for instance, in network analysis or machine learning. Recent theoretical works show that query evaluation over relational databases fits well in this explanation paradigm. Yet, these works fall short of providing practical solutions to the computational challenge inherent to the Shapley computation. We present in this paper two practically effective solutions for computing Shapley values in query answering. We start by establishing a tight theoretical connection to the extensively studied problem of query evaluation over probabilistic databases, which allows us to obtain a polynomial-time algorithm for the class of queries for which probability computation is tractable. We then propose a first practical solution for computing Shapley values that adopts tools from probabilistic query evaluation. In particular, we capture the dependence of query answers on input database facts using Boolean expressions (data provenance), and then transform it, via Knowledge Compilation, into a particular circuit form for which we devise an algorithm for computing the Shapley values. Our second practical solution is a faster yet inexact approach that transforms the provenance to a Conjunctive Normal Form and uses a heuristic to compute the Shapley values. Our experiments on TPC-H and IMDB demonstrate the practical effectiveness of our solutions.

Original languageEnglish
Title of host publicationSIGMOD 2022 - Proceedings of the 2022 International Conference on Management of Data
PublisherAssociation for Computing Machinery
Number of pages14
ISBN (Electronic)9781450392495
StatePublished - 10 Jun 2022
Externally publishedYes
Event2022 ACM SIGMOD International Conference on the Management of Data, SIGMOD 2022 - Virtual, Online, United States
Duration: 12 Jun 202217 Jun 2022

Publication series

NameProceedings of the ACM SIGMOD International Conference on Management of Data
ISSN (Print)0730-8078


Conference2022 ACM SIGMOD International Conference on the Management of Data, SIGMOD 2022
Country/TerritoryUnited States
CityVirtual, Online


  • knowledge compilation
  • provenance
  • shapley value

ASJC Scopus subject areas

  • Software
  • Information Systems


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