标题： 线性模型的概率解释 显示英文标题

标题： Probabilistic Explanations for Linear Models

摘要： 形式化XAI是一个新兴领域，专注于为机器学习模型做出的决策提供具有数学保证的解释。 这一领域的大量工作集中在计算“充分原因”上。 给定一个模型$M$和一个输入实例$\vec{x}$，决策$M(\vec{x})$的充分原因为特征集$S$，该特征集是$\vec{x}$的特征的子集，使得对于任何实例$\vec{z}$，其在$S$中的每个特征上的值与$\vec{x}$相同，均满足$M(\vec{x}) = M(\vec{z})$。 直观地，这表示$S$中的特征足以完全证明$\vec{x}$由$M$进行分类的合理性。 为了在实践中足够有用，它们应该尽可能小，一种自然的方法是考虑概率松弛；对于与$\vec{x}$在$S$中的特征一致的随机实例$\vec{z}$，$M(\vec{x}) = M(\vec{z})$的概率必须至少为某个值$\delta \in (0,1]$。 计算小$\delta$-充分原因 ($\delta$-SRs) 被认为是一个理论上的难题；即使在决策树上——传统上被认为简单且可解释的模型——强大的不可近似性结果使得高效计算小$\delta$-SRs 不太可能。我们提出了$(\delta, \epsilon)$-SR 的概念，这是$\delta$-SRs 的一种简单松弛，并证明这种解释可以在线性模型上高效计算。 显示英文摘要

摘要： Formal XAI is an emerging field that focuses on providing explanations with mathematical guarantees for the decisions made by machine learning models. A significant amount of work in this area is centered on the computation of "sufficient reasons". Given a model $M$ and an input instance $\vec{x}$, a sufficient reason for the decision $M(\vec{x})$ is a subset $S$ of the features of $\vec{x}$ such that for any instance $\vec{z}$ that has the same values as $\vec{x}$ for every feature in $S$, it holds that $M(\vec{x}) = M(\vec{z})$. Intuitively, this means that the features in $S$ are sufficient to fully justify the classification of $\vec{x}$ by $M$. For sufficient reasons to be useful in practice, they should be as small as possible, and a natural way to reduce the size of sufficient reasons is to consider a probabilistic relaxation; the probability of $M(\vec{x}) = M(\vec{z})$ must be at least some value $\delta \in (0,1]$, for a random instance $\vec{z}$ that coincides with $\vec{x}$ on the features in $S$. Computing small $\delta$-sufficient reasons ($\delta$-SRs) is known to be a theoretically hard problem; even over decision trees--traditionally deemed simple and interpretable models--strong inapproximability results make the efficient computation of small $\delta$-SRs unlikely. We propose the notion of $(\delta, \epsilon)$-SR, a simple relaxation of $\delta$-SRs, and show that this kind of explanation can be computed efficiently over linear models.