Shapley values, originating in game theory and increasingly prominent in explainable AI, have been proposed to assess the contribution of facts in query answering over databases, along with other similar power indices such as Banzhaf values. In this work we adapt these Shapley-like scores to probabilistic settings, the objective being to compute their expected value. We show that the computations of expected Shapley values and of the expected values of Boolean functions are interreducible in polynomial time, thus obtaining the same tractability landscape. We investigate the specific tractable case where Boolean functions are represented as deterministic decomposable 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.

通过适应Shapley值以及类似的权力指数，本研究在概率设置下计算其期望值，研究了将布尔函数作为确定的可分解电路表示的可计算情况，并在ProvSQL系统中实现了这一算法，通过数据库来源验证了其可行性。

布尔函数期望Shapley-Like得分：复杂性及其对概率数据库的应用