arXiv 2206.087582022-06cs.AI

纠正单标号布尔分类器

Rectifying Mono-Label Boolean Classifiers

Univ. Artois（阿尔图瓦大学）；CNRS（法国国家科学研究中心）；CRIL（计算机科学与基础信息实验室）；Institut Universitaire de France（法国大学研究院）

Sylvie Coste-Marquis, Pierre Marquis

备注：: 8 pages, rewriting of motivations in the Introduction section and of Example 3 and Example 4 explanations, typo corrected in Example 4 and captions of Figure 4 and Figure 5 rectified

摘要：

我们详细阐述了一个布尔分类器$Σ$的整流的概念。给定$Σ$和一些背景知识$T$，已经提出了表征必须将$Σ$改变为符合$T$的新分类器$Σ\star T$的方式的假设。我们在这里集中在单标签布尔分类器的特定情况下，即，存在单个目标概念，并且任何实例被分类为肯定的（概念的元素）或否定的（补充概念的元素）。在这种特殊情况下，我们的主要贡献是两方面的：（1）我们证明了存在唯一的整流算子$\star$满足这些假设，（2）当$Σ$和$T$是布尔电路时，我们证明了如何在$Σ$和$T$的大小上按时间线性计算等价于$Σ\star T$的分类电路;当$Σ$和$T$是决策树时，可以在$Σ$和$T$大小的时间多项式中计算与$Σ\star T$等效的决策树。

英文摘要：

We elaborate on the notion of rectification of a Boolean classifier $Σ$. Given $Σ$ and some background knowledge $T$, postulates characterizing the way $Σ$ must be changed into a new classifier $Σ\star T$ that complies with $T$ have already been presented. We focus here on the specific case of mono-label Boolean classifiers, i.e., there is a single target concept and any instance is classified either as positive (an element of the concept), or as negative (an element of the complementary concept). In this specific case, our main contribution is twofold: (1) we show that there is a unique rectification operator $\star$ satisfying the postulates, and (2) when $Σ$ and $T$ are Boolean circuits, we show how a classification circuit equivalent to $Σ\star T$ can be computed in time linear in the size of $Σ$ and $T$; when $Σ$ and $T$ are decision trees, a decision tree equivalent to $Σ\star T$ can be computed in time polynomial in the size of $Σ$ and $T$.

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。