Related papers: A Quantum Algorithm for Shapley Value Estimation
We investigate the distribution of the well-studied Shapley--Shubik values in weighted voting games where the agents are stochastically determined. The Shapley--Shubik value measures the voting power of an agent, in typical collective…
Following the work of Lloyd Shapley on the Shapley value, and tangentially the work of Guillermo Owen, we offer an alternative non-probabilistic formulation of part of the work of Robert J. Weber in his 1978 paper "Probabilistic values for…
For reinforcement learning systems to be widely adopted, their users must understand and trust them. We present a theoretical analysis of explaining reinforcement learning using Shapley values, following a principled approach from game…
The Shapley value is a conventional and well-studied function for determining the contribution of a player to the coalition in a cooperative game. Among its applications in a plethora of domains, it has recently been proposed to use the…
Feature attributions based on the Shapley value are popular for explaining machine learning models; however, their estimation is complex from both a theoretical and computational standpoint. We disentangle this complexity into two factors:…
The Shapley value is commonly illustrated by roll call votes in which players support or reject a proposal in sequence. If all sequences are equiprobable, a voter's Shapley value can be interpreted as the probability of being pivotal, i.e.,…
We propose a novel definition of Shapley values with uncertain value functions based on first principles using probability theory. Such uncertain value functions can arise in the context of explainable machine learning as a result of…
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…
According to Shapley's game-theoretical result, there exists a unique game value of finite cooperative games that satisfies axioms on additivity, efficiency, null-player property and symmetry. The original setting requires symmetry with…
Value factorisation is a useful technique for multi-agent reinforcement learning (MARL) in global reward game, however its underlying mechanism is not yet fully understood. This paper studies a theoretical framework for value factorisation…
Lloyd Shapley's cooperative value allocation theory stands as a central concept in game theory, extensively utilized across various domains to distribute resources, evaluate individual contributions, and ensure fairness. The Shapley value…
This paper proposes a novel approach to explain the predictions made by data-driven methods. Since such predictions rely heavily on the data used for training, explanations that convey information about how the training data affects the…
The Shapley value is a common tool in game theory to evaluate the importance of a player in a cooperative setting. In a geometric context, it provides a way to measure the contribution of a geometric object in a set towards some function on…
Shapley value is a concept from game theory. Recently, it has been used for explaining complex models produced by machine learning techniques. Although the mathematical definition of Shapley value is straight-forward, the implication of…
Shapley values have become increasingly popular in the machine learning literature thanks to their attractive axiomatisation, flexibility, and uniqueness in satisfying certain notions of `fairness'. The flexibility arises from the myriad…
The computation of a solution concept of a cooperative game usually employs values of all coalitions. However, in some applications, the values of some of the coalitions might be unknown due to high costs associated with their determination…
Explaining complex or seemingly simple machine learning models is an important practical problem. We want to explain individual predictions from a complex machine learning model by learning simple, interpretable explanations. Shapley values…
We introduce a class of cooperative games induced by weighted directed graphs. Specifically, the coalitional value combines an internal interaction term given by the induced subgraph game with an external component based on minimal incoming…
Shapley values underlie one of the most popular model-agnostic methods within explainable artificial intelligence. These values are designed to attribute the difference between a model's prediction and an average baseline to the different…
The latest developments in AI focus on agentic systems where artificial and human agents cooperate to realize global goals. An example is collaborative learning, which aims to train a global model based on data from individual agents. A…