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      Towards Logical Specification of Statistical Machine Learning

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          Abstract

          We introduce a logical approach to formalizing statistical properties of machine learning. Specifically, we propose a formal model for statistical classification based on a Kripke model, and formalize various notions of classification performance, robustness, and fairness of classifiers by using epistemic logic. Then we show some relationships among properties of classifiers and those between classification performance and robustness, which suggests robustness-related properties that have not been formalized in the literature as far as we know. To formalize fairness properties, we define a notion of counterfactual knowledge and show techniques to formalize conditional indistinguishability by using counterfactual epistemic operators. As far as we know, this is the first work that uses logical formulas to express statistical properties of machine learning, and that provides epistemic (resp. counterfactually epistemic) views on robustness (resp. fairness) of classifiers.

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          Towards Evaluating the Robustness of Neural Networks

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            DeepFool: A Simple and Accurate Method to Fool Deep Neural Networks

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              Differential Privacy

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                Author and article information

                Journal
                24 July 2019
                Article
                1907.10327
                3c3a923e-9af4-4650-90c8-e099a24277d5

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                SEFM'19 conference paper
                cs.LO cs.AI cs.CR cs.LG cs.SE

                Software engineering,Theoretical computer science,Security & Cryptology,Artificial intelligence

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