Fairness Analysis with Shapley-Owen Effects

TL;DR

This paper introduces a spectral decomposition method for efficiently computing Shapley-Owen effects, which are used to measure fairness in model attribution, by leveraging polynomial chaos expansion for reusable and accurate calculations.

Contribution

It develops a spectral decomposition of Shapley-Owen effects that separates model-specific and model-independent parts, enabling efficient and precise fairness analysis.

Findings

Spectral decomposition reduces computation time for Shapley-Owen effects.

Polynomial chaos expansion allows reuse of model-specific calculations.

Proposed algorithms ensure convergence and control approximation errors.

Abstract

We argue that relative importance and its equitable attribution in terms of Shapley-Owen effects is an appropriate one, and, if we accept a small number of reasonable imperatives for equitable attribution, the only way to measure fairness. On the other hand, the computation of Shapley-Owen effects can be very demanding. Our main technical result is a spectral decomposition of the Shapley-Owen effects, which decomposes the computation of these indices into a model-specific and a model-independent part. The model-independent part is precomputed once and for all, and the model-specific computation of Shapley-Owen effects is expressed analytically in terms of the coefficients of the model's \emph{polynomial chaos expansion} (PCE), which can now be reused to compute different Shapley-Owen effects. We also propose an algorithm for computing precise and sparse truncations of the PCE of the model and the spectral decomposition of the Shapley-Owen effects, together with upper bounds on the accumulated approximation errors. The approximations of both the PCE and the Shapley-Owen effects converge to their true values.