Computing the Shapley Value of Facts in Query Answering

TL;DR

This paper introduces practical methods for computing the Shapley value in query answering, leveraging probabilistic databases and data provenance, with proven efficiency on real datasets.

Contribution

It presents the first practical algorithms for Shapley value computation in query answering, connecting it to probabilistic query evaluation and using knowledge compilation techniques.

Findings

Polynomial-time algorithm for tractable query classes

Effective inexact heuristic for faster Shapley computation

Demonstrated success on TPC-H and IMDB datasets

Abstract

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.