arXiv:2605.02827cs.AIstat.ME2026-05被引 1

提出新方法提升概率值估计效率,显著降低误差。

First-Order Efficiency for Probabilistic Value Estimation via A Statistical Viewpoint

论文配图:First-Order Efficiency for Probabilistic Value Estimation via A Statistical Viewpoint
图 1 · 摘自论文原文
  • 基于采样策略与代理函数的首阶展开,统一现有估算方法
  • 新方法在多种概率值估计中均实现更低均方误差
  • 适合需要高精度解释性分析的机器学习应用

概率值(如谢帕利值和半值)为黑箱模型的行为归因提供了模型无关框架,广泛应用于可解释人工智能与数据估值。然而其精确计算需对指数级数量的联盟进行效用评估,因此蒙特卡洛近似在现代机器学习中至关重要。现有估计器通过加权平均、自归一化加权、回归校正和加权最小二乘等不同表示策略构建。我们发现这些看似不同的构造共享一个共同的首阶展开,其中主导项由采样分布和一个工作代理函数决定。该首阶表达式给出了主导均方误差的显式形式,揭示了采样分布与代理函数如何共同影响统计效率。基于此准则,我们提出效率感知的代理调整估计器(EASE),直接优化采样分布与代理函数以最小化首阶均方误差。实证表明,EASE在多种概率值估计任务中始终优于现有方法。

原文摘要 · Abstract (English)

Probabilistic values, including Shapley values and semivalues, provide a model-agnostic framework to attribute the behavior of a black-box model to data points or features, with a wide range of applications including explainable artificial intelligence and data valuation. However, their exact computation requires utility evaluations over exponentially many coalitions, making Monte Carlo approximation essential in modern machine learning applications. Existing estimators are often developed through different representation strategies, including weighted averages, self-normalized weighting, regression adjustment, and weighted least squares. Our key observation is that these seemingly distinct constructions share a common first-order expansion, in which the leading term is determined by the sampling law and a working surrogate function. This first-order representation yields an explicit expression for the leading mean squared error (MSE), which characterizes how the sampling law and the surrogate jointly determine statistical efficiency. Guided by this criterion, we propose an Efficiency-Aware Surrogate-adjusted Estimator (EASE) that directly chooses the sampling law and surrogate to minimize the first-order MSE. We demonstrate that EASE consistently outperforms existing estimators for various probabilistic values.

概率值估计解释性AI蒙特卡洛高效算法

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