有界树宽的多项式阈值函数：若干可解释性与复杂度方面的研究
Polynomial Threshold Functions of Bounded Tree-Width: Some Explainability and Complexity Aspects
AI总结：
本研究针对布尔变量，探讨有界树宽多项式阈值函数，给出其在贝叶斯网络分类器中的两个XAI应用，并证明正与一般多项式阈值函数的表示能力存在分离。
摘要：
多元多项式的树宽是指其超图的树宽，该超图的超边对应多项式的各项。有界树宽的多元多项式已被Makowsky和Meer研究过，作为一种新的稀疏性条件，能让通常难以求解的问题可以在多项式时间内解决。我们针对布尔变量研究了这一主题的一个变体。将布尔函数表示为多项式符号的形式被称为多项式阈值表示。我们讨论了可表示为有界树宽多项式阈值函数的布尔函数，并提出了其在贝叶斯网络分类器（一种概率图模型）中的两个应用。这两个应用都属于可解释人工智能（XAI）领域，该领域研究的是解决许多近期机器学习模型的黑箱特性问题。我们还给出了正多项式阈值函数与一般多项式阈值函数之间表示能力的一个分离结果。
英文摘要：
The tree-width of a multivariate polynomial is the tree-width of the hypergraph with hyperedges corresponding to its terms. Multivariate polynomials of bounded tree-width have been studied by Makowsky and Meer as a new sparsity condition that allows for polynomial solvability of problems which are intractable in general. We consider a variation on this theme for Boolean variables. A representation of a Boolean function as the sign of a polynomial is called a polynomial threshold representation. We discuss Boolean functions representable as polynomial threshold functions of bounded tree-width and present two applications to Bayesian network classifiers, a probabilistic graphical model. Both applications are in Explainable Artificial Intelligence (XAI), the research area dealing with the black-box nature of many recent machine learning models. We also give a separation result between the representational power of positive and general polynomial threshold functions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
