The Shapley Value of Tuples in Query Answering

We investigate the application of the Shapley value to quantifying the contribution of a tuple to a query answer. The Shapley value is a widely known numerical measure in cooperative game theory and in many applications of game theory for assessing the contribution of a player to a coalition game. It has been established already in the 1950s, and is theoretically justified by being the very single wealth-distribution measure that satisfies some natural axioms. While this value has been investigated in several areas, it received little attention in data management. We study this measure in the context of conjunctive and aggregate queries by defining corresponding coalition games. We provide algorithmic and complexity-theoretic results on the computation of Shapley-based contributions to query answers; and for the hard cases we present approximation algorithms

Counterfactuals and Causability in Explainable Artificial Intelligence: Theory, Algorithms, and Applications

There has been a growing interest in model-agnostic methods that can make deep learning models more transparent and explainable to a user. Some researchers recently argued that for a machine to achieve a certain degree of human-level explainability, this machine needs to provide human causally understandable explanations, also known as causability. A specific class of algorithms that have the potential to provide causability are counterfactuals. This paper presents an in-depth systematic review of the diverse existing body of literature on counterfactuals and causability for explainable artificial intelligence. We performed an LDA topic modelling analysis under a PRISMA framework to find the most relevant literature articles. This analysis resulted in a novel taxonomy that considers the grounding theories of the surveyed algorithms, together with their underlying properties and applications in real-world data. This research suggests that current model-agnostic counterfactual algorithms for explainable AI are not grounded on a causal theoretical formalism and, consequently, cannot promote causability to a human decision-maker. Our findings suggest that the explanations derived from major algorithms in the literature provide spurious correlations rather than cause/effects relationships, leading to sub-optimal, erroneous or even biased explanations. This paper also advances the literature with new directions and challenges on promoting causability in model-agnostic approaches for explainable artificial intelligence

The Tractability of SHAP-Score-Based Explanations over Deterministic and Decomposable Boolean Circuits

International audienceScores based on Shapley values are widely used for providing explanations to classification results over machine learning models. A prime example of this is the influential SHAPscore, a version of the Shapley value that can help explain the result of a learned model on a specific entity by assigning a score to every feature. While in general computing Shapley values is a computationally intractable problem, it has recently been claimed that the SHAP-score can be computed in polynomial time over the class of decision trees. In this paper, we provide a proof of a stronger result over Boolean models: the SHAP-score can be computed in polynomial time over deterministic and decomposable Boolean circuits. Such circuits, also known as tractable Boolean circuits, generalize a wide range of Boolean circuits and binary decision diagrams classes, including binary decision trees, Ordered Binary Decision Diagrams (OBDDs) and Free Binary Decision Diagrams (FBDDs). We also establish the computational limits of the notion of SHAP-score by observing that, under a mild condition, computing it over a class of Boolean models is always polynomially as hard as the model counting problem for that class. This implies that both determinism and decomposability are essential properties for the circuits that we consider, as removing one or the other renders the problem of computing the SHAP-score intractable (namely, #P-hard)

The Shapley Value of Tuples in Query Answering

We investigate the application of the Shapley value to quantifying the contribution of a tuple to a query answer. The Shapley value is a widely known numerical measure in cooperative game theory and in many applications of game theory for assessing the contribution of a player to a coalition game. It has been established already in the 1950s, and is theoretically justified by being the very single wealth-distribution measure that satisfies some natural axioms. While this value has been investigated in several areas, it received little attention in data management. We study this measure in the context of conjunctive and aggregate queries by defining corresponding coalition games. We provide algorithmic and complexity-theoretic results on the computation of Shapley-based contributions to query answers; and for the hard cases we present approximation algorithms