請用此 Handle URI 來引用此文件:
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/56317
完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 陳素雲(Su-Yun Huang) | |
dc.contributor.author | Yi-Ting Ma | en |
dc.contributor.author | 馬翊庭 | zh_TW |
dc.date.accessioned | 2021-06-16T05:23:13Z | - |
dc.date.available | 2020-08-06 | |
dc.date.copyright | 2020-08-06 | |
dc.date.issued | 2020 | |
dc.date.submitted | 2020-07-30 | |
dc.identifier.citation | A. Basu, I. R. Harris, N. L. Hjort, and M. Jones. Robust and efficient estimationby minimising a density power divergence.Biometrika, 85(3):549–559, 1998. A. Christmann and I. Steinwart. On robustness properties of convex risk min-imization methods for pattern recognition.Journal of Machine Learning Re-search, 5(Aug):1007–1034, 2004. C. Croux. Limit behavior of the empirical influence function of the median.Statistics probability letters, 37(4):331–340, 1998. C. Croux and C. Dehon. Robust linear discriminant analysis using s-estimators.Canadian Journal of Statistics, 29(3):473–493, 2001. C. Croux, G. Haesbroeck, and K. Joossens. Logistic discrimination using robustestimators: an influence function approach.Canadian Journal of Statistics,36(1):157–174, 2008. H. Fujisawa and S. Eguchi. Robust parameter estimation with a small biasagainst heavy contamination.Journal of Multivariate Analysis, 99(9):2053–2081, 2008. A. Ghosh and A. Basu. Robust estimation in generalized linear models: thedensity power divergence approach.Test, 25(2):269–290, 2016. F. R. Hampel, E. M. Ronchetti, P. J. Rousseeuw, and W. A. Stahel.Robuststatistics: the approach based on influence functions, volume 196. John Wiley Sons, 2011. P. J. Huber.Robust statistics, volume 523. John Wiley Sons, 2004. H. Hung, Z.-Y. Jou, and S.-Y. Huang. Robust mislabel logistic regressionwithout modeling mislabel probabilities.Biometrics, 74(1):145–154, 2018. M. Jones, N. L. Hjort, I. R. Harris, and A. Basu. A comparison of relateddensity-based minimum divergence estimators.Biometrika, 88(3):865–873,2001. T. Kanamori and H. Fujisawa. Robust estimation under heavy contaminationusing unnormalized models.Biometrika, 102(3):559–572, 2015.31 M. Nasser and M. M. Alam. Estimators of influence function.Communicationsin Statistics—Theory and Methods, 35:21–32, 02 2006. A. M. Pires and J. A. Branco. Partial influence functions.Journal of Multi-variate Analysis, 83(2):451–468, 2002.[ M. P. Windham. Robustifying model fitting.Journal of the Royal StatisticalSociety. Series B (Methodological), pages 599–609, 1995. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/56317 | - |
dc.description.abstract | 不管是人為或是非人為所產生的離群值都會對模型造成嚴重的影響,也因此我們利用影響函數去計算支援向量機、邏輯式回歸和費雪線性判別分析之間對離群值的影響,來藉此研究不同模型之間的穩健性。在論文中,我們特別針對在參數估計以及分類錯誤率的影響函數來研究。 | zh_TW |
dc.description.abstract | In literature there are quite some renowned classical linear methods for discriminant analysis. Their performance may heavily depend on the quality of the training data. However, in practice, the training data might not be clean enough. There might be outliers due to some unexpected error, or heavy-tail distribution, or data contamination, etc. With the contaminated data, the resulting inference might not go well, or might even fail. Thus, the ability to be resistant to outliers becomes an important issue in statistical inference. Linear methods are fundamental for data analysis. In this thesis, we will focus on three types of linear classifiers, namely, logistic regression, support vector machine and Fisher linear discriminant analysis. Their influence functions for parameter estimation and error rate will be discussed and several numerical examples will be presented. | en |
dc.description.provenance | Made available in DSpace on 2021-06-16T05:23:13Z (GMT). No. of bitstreams: 1 U0001-2707202014372300.pdf: 3501197 bytes, checksum: dff0b08678eb97ce5e6ddf44c6613528 (MD5) Previous issue date: 2020 | en |
dc.description.tableofcontents | Contents目錄 口試委員審定書i 誌謝ii 中文摘要iii Abstract英文摘要iv 1 Introduction1 2 Influence Function3 2.1 Logistic Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 2.1.1Influence function for parameter estimation . . . . . . . . . .5 2.1.2Influence function for classification error rate . . . . . . . . . .6 2.2 Linear SVM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.1Influence function for parameter estimation . . . . . . . . . . 10 2.3 Fisher LDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3.1Influence function for error rate . . . . . . . . . . . . . . . . . 13 2.4γ-Logistic Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4.1Influence function for parameter estimation . . . . . . . . . . 16 2.4.2Influence function for error rate . . . . . . . . . . . . . . . . . 16 2.5 Partial Influence Function . . . . . . . . . . . . . . . . . . . . . . . . 18 3 Numerical Examples19 4 Concluding Discussions 30 Reference 31 | |
dc.language.iso | en | |
dc.title | 支援向量機、邏輯式迴歸和費雪線性判別分析之影響函數與穩健性的比較 | zh_TW |
dc.title | Influence Function and Robustness Comparison for Support Vector Machine, Logistic Regression and Fisher Linear Discriminant Analysis | en |
dc.type | Thesis | |
dc.date.schoolyear | 108-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 洪弘(Hung Hung),黃子銘(Tzee-Ming Huang) | |
dc.subject.keyword | 影響函數,支援向量機,邏輯式回歸,線性判別分析, | zh_TW |
dc.subject.keyword | Robustness,Influence fucntion,SVM,logistic regression,LDA, | en |
dc.relation.page | 32 | |
dc.identifier.doi | 10.6342/NTU202001907 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2020-07-31 | |
dc.contributor.author-college | 理學院 | zh_TW |
dc.contributor.author-dept | 應用數學科學研究所 | zh_TW |
顯示於系所單位: | 應用數學科學研究所 |
文件中的檔案:
檔案 | 大小 | 格式 | |
---|---|---|---|
U0001-2707202014372300.pdf 目前未授權公開取用 | 3.42 MB | Adobe PDF |
系統中的文件,除了特別指名其著作權條款之外,均受到著作權保護,並且保留所有的權利。