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arXiv 2004.12734cs.LOcs.AIcs.CRcs.LGcs.SE
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统计机器学习形式化规约的认知方法

An Epistemic Approach to the Formal Specification of Statistical Machine Learning

AIST(产业技术综合研究所)

Yusuke Kawamoto

AI总结:

本文提出基于 Kripke 模型与扩展 StatEL 的认知逻辑框架,以形式化监督分类器的性能、鲁棒性和公平性,并揭示其属性关系。

摘要:

我们提出一种用于形式化机器学习统计属性的认知方法。具体而言,我们引入了一个基于 Kripke 模型的监督学习形式模型,其中每个可能世界对应一个可能数据集,模态算子被解释为对数据集的转换与测试。随后,我们利用对统计认知逻辑(StatEL)的扩展,将统计分类器的分类性能、鲁棒性和公平性的各种概念加以形式化。在此形式化中,我们展示了分类器各属性之间的关系,以及分类性能与鲁棒性之间的相关性。据我们所知,这是首个使用认知模型和逻辑公式表达机器学习统计属性的工作,并将成为发展机器学习形式化规约理论的起点。

英文摘要:

We propose an epistemic approach to formalizing statistical properties of machine learning. Specifically, we introduce a formal model for supervised learning based on a Kripke model where each possible world corresponds to a possible dataset and modal operators are interpreted as transformation and testing on datasets. Then we formalize various notions of the classification performance, robustness, and fairness of statistical classifiers by using our extension of statistical epistemic logic (StatEL). In this formalization, we show relationships among properties of classifiers, and relevance between classification performance and robustness. As far as we know, this is the first work that uses epistemic models and logical formulas to express statistical properties of machine learning, and would be a starting point to develop theories of formal specification of machine learning.

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。

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