用谱分解加速公平性归因计算，提升效率与精度。
Fairness Analysis with Shapley-Owen Effects
- 提出谱分解方法，分离模型无关与特定部分计算
- 通过多项式混沌展开实现高效近似，误差可量化
- 适合需要高精度公平性分析的机器学习研究者
我们认为，基于Shapley-Owen效应的相对重要性及其公平分配是恰当的衡量方式，若接受若干合理公平分配前提，则为唯一可行路径。然而，Shapley-Owen效应的计算极为耗时。本文的主要技术成果是其谱分解，将计算拆分为模型无关与模型相关两部分：前者可预先一次性计算，后者则通过模型的多项式混沌展开（PCE）系数解析表达，支持复用。我们还提出了精确且稀疏截断PCE的算法，以及对累加近似误差的上界估计，确保PCE和Shapley-Owen效应的近似值均收敛至真实值。
原文摘要 · Abstract (English)
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.
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