Please use this identifier to cite or link to this item:
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/65625
Full metadata record
???org.dspace.app.webui.jsptag.ItemTag.dcfield??? | Value | Language |
---|---|---|
dc.contributor.advisor | 陳素雲(Su-Yun Huang) | |
dc.contributor.author | Yu-Tin Lin | en |
dc.contributor.author | 林昱廷 | zh_TW |
dc.date.accessioned | 2021-06-16T23:54:41Z | - |
dc.date.available | 2014-07-20 | |
dc.date.copyright | 2012-07-20 | |
dc.date.issued | 2012 | |
dc.date.submitted | 2012-07-18 | |
dc.identifier.citation | [1] B‥uhlmann, P. and van de Geer, S. (2011). Statistics for High-Dimensional Data:
Methods, Theory and Applications. Springer Series in Statistics. [2] Cand`es, E. J., Li, X., Ma, Y. andWright, J. (2011). Robust principal component analysis? Journal of the ACM, 58(3), Article 11. [3] Cook, R. D. and Ni, L. (2005). Sufficient dimension reduction via inverse regression: a minimum discrepancy approach. Journal of American Statistical Association, 100(470), 410-428. [4] Fan, J. and Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of American Statistical Association, 96(456), 1348-1360. [5] Henderson, H. V. and Searle, S. R. (1979). Vec and vech operators for matrices, with some uses in Jacobians and multivariate statistics. Canadian Journal of Statistics, 7(1), 65-81. [6] Kolda, T.G. and Bader, B.W. (2009). Tensor decompositions and applications. SIAM Review, 51(3), 455-500. [7] Liu, H., Roeder, K. and Wasserman, L. (2010). Stability approach to regularization selection (StARS) for high dimensional graphical models. arXiv:1006.3316v1 Screen and Clean software http://wpicr.wpic.pitt.edu/WPICCompGen/ [8] Magnus, J. R. and Neudecker, H. (1979). The commutation matrix: some properties and applications. Annals of Statistics, 7(2), 381-394. [9] Shapiro, A. (1986). Asymptotic theory of overparameterized structural models. Journal of American Statistical Association, 81(393), 142-149. [10] Tusher, V. G., Tibshirani, R., and Chu, G. (2001). Significance analysis of micro-arrays applied to the ionizing radiation response. Proceedings of the Na- tional Academy of Sciences, 98(9), 5116-5121. [11] Wasserman, L. and Roeder, K. (2009). High-dimensional variable selection. Annals of Statistics, 37(5A), 2178-2201. [12] Wu, J., Devlin, B., Ringquist, S., Trucco, M. and Roeder, K. (2010). Screen and clean: a tool for identifying interactions in genome-wide association studies. Genetic Epidemiology, 34(3), 275-285. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/65625 | - |
dc.description.abstract | Researchers in biological sciences nowadays often encounter the curse of
high-dimensionality. A serious consequence is that many traditional statistical methods fail to fit for high-dimensional models. The problem becomes even more severe when the interest is in interactions between variables, as there will be p(p−1)/2 interaction terms with p variables. To improve the performance, in this thesis we model the interaction effects utilizing its matrix form with a low-rank structure. A low-rank model for symmetric matrix then greatly reduces the number of parameters required, and hence, increases the stability and quality of statistical analysis. Individual hypothesis tests are then carried out on each interaction effect to wash out insignificant interactions. A low- rank matrix, however, is not necessarily sparse. We thus impose a sparsity constraint in the second stage to select interactions. Due to the extremely high-dimensionality for gene×gene interactions, a single-stage method is not adequately flexible enough for variable selection. Our sparse low-rank approach for interactions is a modification of a multi- stage screen-and-clean procedure byWasserman and Roeder (2009) andWu et al. (2010). We replace their mere sparsity constraint by combining a low-rank structure and a sparsity constraint to the interactions. In simulation studies, we show that the proposed low-rank approximation-aided screen and clean procedure often can achieve higher power and higher selection-consistency probability. | en |
dc.description.provenance | Made available in DSpace on 2021-06-16T23:54:41Z (GMT). No. of bitstreams: 1 ntu-101-R99221021-1.pdf: 2976818 bytes, checksum: 46c9fdfca827293f8a66b496e723c484 (MD5) Previous issue date: 2012 | en |
dc.description.tableofcontents | Contents
Acknowledgements i Abstract (in Chinese) ii Abstract (in English) iii Contests iv Figures v Tables vi 1 Introduction and model specification 1 2 Estimation procedure for sparse low-rank interaction model 4 2.1 Estimation for low-rank model with 2-norm penalty . . . . . . . . . . 5 2.1.1 Rank-2r model implementation . . . . . . . . . . . . . . . . . 5 2.1.2 Rank-1 model implementation . . . . . . . . . . . . . . . . . . 7 2.2 Estimation for sparse model with 1-norm penalty . . . . . . . . . . . 8 2.3 Why a sparse low-rank model, why not a direct sparse model? . . . . 8 3 Low-rank screening by hypothesis testing 10 3.1 Asymptotic properties . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.2 Asymptotic testing procedure . . . . . . . . . . . . . . . . . . . . . . 11 4 Multistage variable selection for detecting gene×gene interactions 13 4.1 Review of screen-and-clean method . . . . . . . . . . . . . . . . . . . 13 4.2 Low-rank aided screen-and-clean method . . . . . . . . . . . . . . . . 14 5 Simulation studies 16 5.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 5.2 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 6 Conclusion discussion 33 Appendix 33 References 37 | |
dc.language.iso | en | |
dc.title | 利用多層稀疏低秩迴歸探測基因與基因的交互作用 | zh_TW |
dc.title | Detection of Gene×Gene Interactions by Multistage Sparse Low-Rank Regression | en |
dc.type | Thesis | |
dc.date.schoolyear | 100-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 陳宏(Hung Chen),陳鵬文(Peng-Wen Chen),洪弘(Hung Hung),蕭朱杏(Chuh-Sing Hsiao) | |
dc.subject.keyword | 漸近常態,交互作用,低秩估計,過度參數化,稀疏性, | zh_TW |
dc.subject.keyword | Asymptotic normality,Interaction,Low-rank approximation,Over-parameterized,Screen and clean,Sparsity, | en |
dc.relation.page | 38 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2012-07-19 | |
dc.contributor.author-college | 理學院 | zh_TW |
dc.contributor.author-dept | 數學研究所 | zh_TW |
Appears in Collections: | 數學系 |
Files in This Item:
File | Size | Format | |
---|---|---|---|
ntu-101-1.pdf Restricted Access | 2.91 MB | Adobe PDF |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.