Researchers in explainable artificial intelligence have developed numerous methods for helping users understand the predictions of complex supervised learning models. By contrast, explaining the $\textit{uncertainty}$ of model outputs has received relatively little attention. We adapt the popular Shapley value framework to explain various types of predictive uncertainty, quantifying each feature's contribution to the conditional entropy of individual model outputs. We consider games with modified characteristic functions and find deep connections between the resulting Shapley values and fundamental quantities from information theory and conditional independence testing. We outline inference procedures for finite sample error rate control with provable guarantees, and implement efficient algorithms that perform well in a range of experiments on real and simulated data. Our method has applications to covariate shift detection, active learning, feature selection, and active feature-value acquisition.

翻译：可解释人工智能领域的研究人员已开发出诸多方法，帮助用户理解复杂监督学习模型的预测结果。相比之下，对模型输出$\textit{不确定性}$的解释却鲜有关注。我们改编了经典的Shapley值框架，以解释各类预测不确定性，量化每个特征对单个模型输出条件熵的贡献。我们考虑了具有修正特征函数的博弈，并发现由此产生的Shapley值与信息论及条件独立性检验中的基本量之间存在深刻联系。我们提出了有限样本错误率可控的推理程序，并实现了高效的算法，在真实与模拟数据的多项实验中表现优异。该方法可应用于协变量偏移检测、主动学习、特征选择及主动特征值获取。