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.

翻译：沙普利值源于博弈论，在可解释人工智能中日益重要，已被用于评估数据库查询回答中事实的贡献，其他类似权力指数如班扎夫值亦然。本研究将这些沙普利类分数适配至概率场景，目标在于计算其期望值。我们证明期望沙普利值计算与布尔函数期望值计算可在多项式时间内相互归约，从而获得相同的可解性图景。我们研究了布尔函数表示为确定性可分解电路时的特定可解情况，为此场景设计了多项式时间算法。通过数据库溯源展示了在概率数据库中的应用，并在ProvSQL系统中实现了该算法的有效部署，实验验证了其在标准基准测试中的可行性。