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Shapley values, originating in game theory and increasingly prominent inexplainable AI, have been proposed to assess the contribution of facts in queryanswering over databases, along with other similar power indices such asBanzhaf values. In this work we adapt these Shapley-like scores toprobabilistic settings, the objective being to compute their expected value. Weshow that the computations of expected Shapley values and of the expectedvalues of Boolean functions are interreducible in polynomial time, thusobtaining the same tractability landscape. We investigate the specifictractable case where Boolean functions are represented as deterministicdecomposable circuits, designing a polynomial-time algorithm for this setting.We present applications to probabilistic databases through database provenance,and an effective implementation of this algorithm within the ProvSQL system,which experimentally validates its feasibility over a standard benchmark.

Expected Shapley-Like Scores of Boolean Functions: Complexity and Applications to Probabilistic Databases