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- W3197599704 abstract "Suppose that we have two training sequences generated by parametrized distributions <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$P_{theta}$</tex> and <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$P_{varepsilon^{*}}$</tex> , where <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$theta$</tex> * and <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$xi^{*}$</tex> are unknown true parameters. Given training sequences, we study the problem of classifying whether a test sequence was generated according to <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$P_{theta}$</tex> * or <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$P_{xi^{*}}$</tex> . This problem can be thought of as a hypothesis testing problem and our aim is to analyze the weighted sum of type-I and type-II error probabilities. Utilizing the analysis of the codeword lengths of the Bayes code, our previous study derived more refined bounds on the error probability than known previously. However, our previous study had the following deficiencies: i) the prior distributions of <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$theta$</tex> and <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$xi$</tex> are the same; ii) the prior distributions of two hypotheses are uniform; iii) no numerical calculation at finite blocklength. This study solves these problems. We remove the restrictions i) and ii) and derive more general results than obtained previously. To deal with problem iii), we perform a numerical calculation for a concrete model." @default.
- W3197599704 created "2021-09-13" @default.
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- W3197599704 date "2021-07-12" @default.
- W3197599704 modified "2023-09-24" @default.
- W3197599704 title "Evaluation of Error Probability of Classification Based on the Analysis of the Bayes Code: Extension and Example" @default.
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- W3197599704 doi "https://doi.org/10.1109/isit45174.2021.9517718" @default.
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