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Register a new userAn Epistemic Approach to the Formal Specification of Statistical Machine Learning
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Added by
Yusuke Kawamoto
Publication date
2020
fields
Informatics Engineering
and research's language is
English
Authors
Yusuke Kawamoto
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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.
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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.
We introduce a modal logic for describing statistical knowledge, which we call statistical epistemic logic. We propose a Kripke model dealing with probability distributions and stochastic assignments, and show a stochastic semantics for the logic. To our knowledge, this is the first semantics for modal logic that can express the statistical knowledge dependent on non-deterministic inputs and the statistical significance of observed results. By using statistical epistemic logic, we express a notion of statistical secrecy with a confidence level. We also show that this logic is useful to formalize statistical hypothesis testing and differential privacy in a simple and abstract manner.
RISC-V is a relatively new, open instruction set architecture with a mature ecosystem and an official formal machine-readable specification. It is therefore a promising playground for formal-methods research. However, we observe that different formal-methods research projects are interested in different aspects of RISC-V and want to simplify, abstract, approximate, or ignore the other aspects. Often, they also require different encoding styles, resulting in each project starting a new formalization from-scratch. We set out to identify the commonalities between projects and to represent the RISC-V specification as a program with holes that can be instantiated differently by different projects. Our formalization of the RISC-V specification is written in Haskell and leverages existing tools rather than requiring new domain-specific tools, contrary to other approaches. To our knowledge, it is the first RISC-V specification able to serve as the interface between a processor-correctness proof and a compiler-correctness proof, while supporting several other projects with diverging requirements as well.
(To appear in Theory and Practice of Logic Programming (TPLP)) ESmodels is designed and implemented as an experiment platform to investigate the semantics, language, related reasoning algorithms, and possible applications of epistemic specifications.We first give the epistemic specification language of ESmodels and its semantics. The language employs only one modal operator K but we prove that it is able to represent luxuriant modal operators by presenting transformation rules. Then, we describe basic algorithms and optimization approaches used in ESmodels. After that, we discuss possible applications of ESmodels in conformant planning and constraint satisfaction. Finally, we conclude with perspectives.
This paper presents two formal models of the Data Encryption Standard (DES), a first using the international standard LOTOS, and a second using the more recent process calculus LNT. Both models encode the DES in the style of asynchronous circuits, i.e., the data-flow blocks of the DES algorithm are represented by processes communicating via rendezvous. To ensure correctness of the models, several techniques have been applied, including model checking, equivalence checking, and comparing the results produced by a prototype automatically generated from the formal model with those of existing implementations of the DES. The complete code of the models is provided as appendices and also available on the website of the CADP verification toolbox.
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