A novel sparsity-based deterministic method for Shapley value approximation, with applications

Abstract

The Shapley value, a concept from cooperative game theory, plays a crucial role in fair distribution of payoffs among participants based on their individual contributions. However, the exact computation of the Shapley values is often impractical due to the exponential complexity. The currently available approximation methods offer some benefits but come with significant drawbacks, such as high computational overhead, variability in accuracy, and reliance on heuristics that may compromise fairness. Given these limitations, there is a pressing need for approaches that ensure consistent and reliable results. A deterministic method could not only improve computational efficiency but also ensure reproducibility and fairness. Leveraging principles from the so-called compressed sensing, techniques which exploit data sparsity, and elementary results from the matrix theory, this paper introduces a novel algorithm for approximating Shapley values, emphasizing deterministic computations that ensure reproducible data valuation and lessen computational demands. We illustrate the efficiency of this algorithm within the framework of data valuation in the two-settlement electricity market. The simulations convincingly indicate essential advantages of the proposed method over the existing ones. In particular, our method achieved an average increase of 33.8% in approximation accuracy, as measured by relative error, while maintaining consistent performance across multiple trials.