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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 王奕翔(I-Hsiang Wang) | |
| dc.contributor.author | Chia-Yu Hsu | en |
| dc.contributor.author | 許嘉喻 | zh_TW |
| dc.date.accessioned | 2022-11-25T07:48:58Z | - |
| dc.date.available | 2023-12-31 | |
| dc.date.copyright | 2021-10-04 | |
| dc.date.issued | 2021 | |
| dc.date.submitted | 2021-09-29 | |
| dc.identifier.citation | [1] R. Blahut. Hypothesis testing and information theory. IEEE Transactions on Information Theory, 20(4):405–417, 1974. [2] G. Casella and R. L. Berger. Statistical inference. Cengage Learning, 2021. [3] I. Csiszar. The method of types [information theory]. IEEE Transactions on Information Theory, 44(6):2505–2523, 1998. [4] M. Gutman. Asymptotically optimal classification for multiple tests with empirically observed statistics. IEEE Transactions on Information Theory, 35(2):401–408, 1989. [5] M. Haghifam, V. Y. F. Tan, and A. Khisti. Sequential classification with empirically observed statistics. IEEE Transactions on Information Theory, 67(5):3095–3113, 2021. [6] W. Hoeffding. Asymptotically optimal tests for multinomial distributions. The Annals of Mathematical Statistics, pages 369–401, 1965. [7] H.-W. Hsu and I.-H. Wang. On binary statistical classification from mismatched empirically observed statistics. In 2020 IEEE International Symposium on Information Theory (ISIT), pages 2533–2538, 2020. [8] S. B. Kotsiantis, I. Zaharakis, P. Pintelas, et al. Supervised machine learning: A review of classification techniques. Emerging artificial intelligence applications in computer engineering, 160(1):3–24, 2007. [9] X. Li, J. Liu, and Z. Ying. Generalized sequential probability ratio test for separate families of hypotheses. Sequential analysis, 33(4):539–563, 2014. [10] Y. Li, S. Nitinawarat, Y. Su, and V. V. Veeravalli. Universal outlier hypothesis testing: Application to anomaly detection. In 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 5595–5599, 2015. [11] Y. Li, S. Nitinawarat, and V. V. Veeravalli. Universal sequential outlier hypothesis testing. In 2014 48th Asilomar Conference on Signals, Systems and Computers, pages 281–285, 2014. [12] Y. Li and V. Y. F. Tan. Second-order asymptotics of sequential hypothesis testing. IEEE Transactions on Information Theory, 66(11):7222–7230, 2020. [13] J. Lin. Divergence measures based on the shannon entropy. IEEE Transactions on Information Theory, 37(1):145–151, 1991. [14] G. Lu and B. Li. A class of new metrics based on triangular discrimination. Information, 6(3):361–374, 2015. [15] Y. Polyanskiy and Y. Wu. Lecture notes on information theory. [16] A. Wald and J. Wolfowitz. Optimum character of the sequential probability ratio test. The Annals of Mathematical Statistics, pages 326–339, 1948. [17] Y. Xu and Q. Wang. Asymptotical optimality of sequential universal hypothesis testing based on the method of types. IEEE Signal Processing Letters, 21(11):1316– 1320, 2014. [18] O. Zeitouni, J. Ziv, and N. Merhav. When is the generalized likelihood ratio test optimal? IEEE Transactions on Information Theory, 38(5):1597–1602, 1992. [19] L. Zhou, V. Y. F. Tan, and M. Motani. Second-order asymptotically optimal statistical classification. In 2019 IEEE International Symposium on Information Theory (ISIT), pages 231–235, 2019. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/82666 | - |
| dc.description.abstract | 本論文研究在廣用平均停止時間要求下之資料導向逐次假說檢定問題。我們首先考慮二元假說的設定，其中，決策者可以收到逐次輸入的兩組訓練資料串，且他們分別是由兩個未知分佈P0 和P1 以獨立且相同的方式逐次取樣產生。決策者之目標是以這兩組訓練序列分類目前收到的測試序列，其中測試序列是由P0 和P1 其中一個未知分佈以獨立且相同的方式逐次取樣產生。本論文提出一種基於測試序列和訓練序列的統計經驗分布之方法，稱為逐次類型匹配檢定(STMT)，其和 Gutman [4] 所提出之檢定相比，在錯誤指數上有很大的進步。此外，我們也證明了在所有滿足廣用停止時間要求以及類型一和類型二錯誤率指數遞減之方法中，STMT 有漸進最佳性。最後，我們將二元假說設定下所得到的結果延伸至多元(超過兩個假說)假說的設定。 | zh_TW |
| dc.description.provenance | Made available in DSpace on 2022-11-25T07:48:58Z (GMT). No. of bitstreams: 1 U0001-2909202110102600.pdf: 643705 bytes, checksum: e4701e357bd84e2f9d7308c52cbb770d (MD5) Previous issue date: 2021 | en |
| dc.description.tableofcontents | Verification Letter from the Oral Examination Committee i Acknowledgements iii 摘要 v Abstract vii Contents ix List of Figures xiii List of Tables xv Chapter 1 Introduction 1 1.1 Related Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Chapter 2 Background 9 2.1 Sequential Binary Hypothesis Testing . . . . . . . . . . . . . . . . . 9 2.1.1 Single-Sided SPRT . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2 Fixed-Length Data-driven Hypothesis Testing . . . . . . . . . . . . . 14 2.3 Data-driven Semi-sequential Hypothesis Testing . . . . . . . . . . . 16 Chapter 3 Data-driven Sequential Hypothesis Testing 19 3.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.2 Main Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.3 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.3.1 On Error Exponents: STMT vs. The Modified Haghifam’s Test . . . 25 3.3.2 On Bayesian Error Exponents: STMT vs. Gutman’s Test . . . . . . 27 3.3.3 On Number of Samples . . . . . . . . . . . . . . . . . . . . . . . . 28 3.4 Extension: Multiple Hypotheses . . . . . . . . . . . . . . . . . . . . 29 Chapter 4 Proof of Achievability 35 4.1 Achievability in Two Hypotheses . . . . . . . . . . . . . . . . . . . 35 4.2 Achievability in Multiple Hypotheses . . . . . . . . . . . . . . . . . 38 Chapter 5 Proof of Converse 41 5.1 Transform Randomized Test to Deterministic Test . . . . . . . . . . 41 5.2 Transform Deterministic Test to Deterministic Type-Based Test . . . 45 5.3 Converse in Two Hypotheses . . . . . . . . . . . . . . . . . . . . . . 49 5.4 Converse in Multiple Hypotheses . . . . . . . . . . . . . . . . . . . 54 Chapter 6 Discussion and Conclusion 63 6.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 6.1.1 Semi-sequential Setting with The Decision Concept of STMT . . . . 63 6.1.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 6.2 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 References 67 Appendix A — Proofs in Chapter 2 71 A.1 Proof of Theorem 2.1.2 . . . . . . . . . . . . . . . . . . . . . . . . . 71 A.2 Proof of Theorem 2.1.3 . . . . . . . . . . . . . . . . . . . . . . . . . 75 A.3 Proof of Theorem 2.1.4 . . . . . . . . . . . . . . . . . . . . . . . . . 76 Appendix B — Additional Proofs 79 B.1 Proof of Theorem 3.3.1 . . . . . . . . . . . . . . . . . . . . . . . . . 79 B.2 Special Case of The Conjecture . . . . . . . . . . . . . . . . . . . . 80 | |
| dc.language.iso | en | |
| dc.subject | 漸進最佳性 | zh_TW |
| dc.subject | 資料導向 | zh_TW |
| dc.subject | 假說檢定 | zh_TW |
| dc.subject | 廣用性 | zh_TW |
| dc.subject | Asymptotic Optimality | en |
| dc.subject | Data-driven | en |
| dc.subject | Hypothesis Testing | en |
| dc.subject | Universality | en |
| dc.title | 資料導向之逐次假說檢定：廣用性與漸進最佳性 | zh_TW |
| dc.title | Data-driven Sequential Hypothesis Testing: Universality and Asymptotic Optimality | en |
| dc.date.schoolyear | 109-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 黃昱智(Hsin-Tsai Liu),林士駿(Chih-Yang Tseng) | |
| dc.subject.keyword | 資料導向,假說檢定,廣用性,漸進最佳性, | zh_TW |
| dc.subject.keyword | Data-driven,Hypothesis Testing,Universality,Asymptotic Optimality, | en |
| dc.relation.page | 81 | |
| dc.identifier.doi | 10.6342/NTU202103449 | |
| dc.rights.note | 同意授權(限校園內公開) | |
| dc.date.accepted | 2021-10-01 | |
| dc.contributor.author-college | 電機資訊學院 | zh_TW |
| dc.contributor.author-dept | 電信工程學研究所 | zh_TW |
| dc.date.embargo-lift | 2023-12-31 | - |
| 顯示於系所單位： | 電信工程學研究所 | |
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