利用多層稀疏低秩迴歸探測基因與基因的交互作用

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.