TY - GEN

T1 - Evaluation of Error Probability of Classification Based on the Analysis of the Bayes Code

T2 - 2021 IEEE International Symposium on Information Theory, ISIT 2021

AU - Saito, Shota

AU - Matsushima, Toshiyasu

N1 - Funding Information:
This work was supported in part by JSPS KAKENHI Grant Numbers JP17K06446, JP19K04914, and JP19K14989.
Publisher Copyright:
© 2021 IEEE.

PY - 2021/7/12

Y1 - 2021/7/12

N2 - Suppose that we have two training sequences generated by parametrized distributions P_{\theta} and P_{\varepsilon^{*}}, where \theta ∗ and \xi^{*} are unknown true parameters. Given training sequences, we study the problem of classifying whether a test sequence was generated according to P_{\theta} ∗ or P_{\xi^{*}}. 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 \theta and \xi 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.

AB - Suppose that we have two training sequences generated by parametrized distributions P_{\theta} and P_{\varepsilon^{*}}, where \theta ∗ and \xi^{*} are unknown true parameters. Given training sequences, we study the problem of classifying whether a test sequence was generated according to P_{\theta} ∗ or P_{\xi^{*}}. 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 \theta and \xi 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.

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U2 - 10.1109/ISIT45174.2021.9517718

DO - 10.1109/ISIT45174.2021.9517718

M3 - Conference contribution

AN - SCOPUS:85115095064

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1445

EP - 1450

BT - 2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

Y2 - 12 July 2021 through 20 July 2021

ER -