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標題: | 利用多層稀疏低秩迴歸探測基因與基因的交互作用 Detection of Gene×Gene Interactions by Multistage Sparse Low-Rank Regression |
作者: | Yu-Tin Lin 林昱廷 |
指導教授: | 陳素雲(Su-Yun Huang) |
關鍵字: | 漸近常態,交互作用,低秩估計,過度參數化,稀疏性, Asymptotic normality,Interaction,Low-rank approximation,Over-parameterized,Screen and clean,Sparsity, |
出版年 : | 2012 |
學位: | 碩士 |
摘要: | 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. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/65625 |
全文授權: | 有償授權 |
顯示於系所單位: | 數學系 |
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