Attribution scores reflect how important the feature values in an input
entity are for the output of a machine learning model. One of the most popular
attribution scores is the SHAP score, which is an instantiation of the general
Shapley value used in coalition game theory. The definition of this score
relies on a probability distribution on the entity population. Since the exact
distribution is generally unknown, it needs to be assigned subjectively or be
estimated from data, which may lead to misleading feature scores. In this
paper, we propose a principled framework for reasoning on SHAP scores under
unknown entity population distributions. In our framework, we consider an
uncertainty region that contains the potential distributions, and the SHAP
score of a feature becomes a function defined over this region. We study the
basic problems of finding maxima and minima of this function, which allows us
to determine tight ranges for the SHAP scores of all features. In particular,
we pinpoint the complexity of these problems, and other related ones, showing
them to be NP-complete. Finally, we present experiments on a real-world
dataset, showing that our framework may contribute to a more robust feature
scoring.

本文提出了一个基于不明实体群体分布的 SHAP 得分推理的原则性框架，并通过研究函数最大值和最小值的基本问题来确定所有特征的 SHAP 得分的紧密范围，最终通过实验显示我们的框架可以为更稳健的特征评分做出贡献。

可解释机器学习中 SHAP 评分的分布性不确定性

The Distributional Uncertainty of the SHAP score in Explainable Machine  Learning

While several feature scoring methods are proposed to explain the output of
complex machine learning models, most of them lack formal mathematical
definitions. In this study, we propose a novel definition of the feature score
using the maximally invariant data perturbation, which is inspired from the
idea of adversarial example. In adversarial example, one seeks the smallest
data perturbation that changes the model's output. In our proposed approach, we
consider the opposite: we seek the maximally invariant data perturbation that
does not change the model's output. In this way, we can identify important
input features as the ones with small allowable data perturbations. To find the
maximally invariant data perturbation, we formulate the problem as linear
programming. The experiment on the image classification with VGG16 shows that
the proposed method could identify relevant parts of the images effectively.

本研究提出了一种新的特征分数定义方法，使用最大不变数据扰动，将问题转化为线性规划，可有效识别重要输入特征，实验表明该方法在图像分类中能够有效识别图像的相关部件。