Grad Student Seminar: Siliang Gong & Leo Liu

Siliang Gong
(Joint work with Kai Zhang and Yufeng Liu)

Penalized linear regression with high-dimensional pairwise screening

In variable selection, most existing screening methods focus on marginal e ects and ignore dependence between covariates. To improve the performance of selection, we incorporate pairwise e ects in covariates for screening and penalization. We achieve this by studying the asymptotic distribution of the maximal absolute pairwise sample correlation among independent covariates. The novelty of the theory is in that the convergence is with respect to the dimensionality p, and is uniform with respect to the sample size n. Moreover, we obtain an upper bound for the maximal pairwise R squares when regressing the response onto two di erent covariates. Based on these extreme value results, we propose a screening procedure to detect covariates pairs that are potentially correlated and associated with the response. We further combine the pairwise screening with Sure Independence Screening (?) and develop a new regularized variable selection procedure. Numerical studies show that our method is very competitive in terms of both prediction accuracy and variable selection accuracy.

Leo Yufeng Liu

Subject Variant Scalar-on-Image Regression

The use of imaging biomarkers to predict clinical outcomes is of great impact in public health. Many studies have demonstrated that medical images deliver clinically important information, which has been widely used to explore the pathophysiology of certain diseases and assist diagnosis and treatments. A popular approach for these studies is through Scalar-on-Image regressions. These methods directly regress the clinical outcomes on the medical images. Despite the rapid development in this field, most methods in the literature still cannot handle the heterogeneity of the imaging features, which is very common for medical images. We proposed a Subject Variant Scalar-on-Image Regression (SVSIR) model, by imposing an individual level Potts prior and applying the Reproducing Kernel-based method. Both the heterogeneity structure and the desired imaging features can be achieved. Extensive numerical studies demonstrate the usefulness of the proposed SVSIR.