A0695
Title: Linear shrinkage convexification of penalized linear regression with missing data
Authors: Johan Lim - Seoul National University (Korea, South) [presenting]
Abstract: One of the common challenges faced by researchers in recent data analysis is missing values. In the context of penalized linear regression, which has been extensively explored over several decades, missing values introduce bias and yield a non-positive definite covariance matrix of the covariates, rendering the least square loss function non-convex. A novel procedure called the linear shrinkage positive definite (LPD) modification is proposed to address this issue. The LPD modification aims to modify the covariance matrix of the covariates to ensure consistency and positive definiteness. Employing the new covariance estimator, the penalized regression problem can be transformed into a convex one, thereby facilitating the identification of sparse solutions. Notably, the LPD modification is computationally efficient and can be expressed analytically. In the presence of missing values, the selection consistency is established, and the convergence rate of the l1-penalized regression estimator is proven with LPD, showing an optimal l2-error convergence rate. To further evaluate the effectiveness of the approach, real data is analyzed from the genomics of drug sensitivity in cancer (GDSC) dataset. This dataset provides incomplete measurements of drug sensitivities of cell lines and their protein expressions. A series of penalized linear regression models are conducted, with each sensitivity value serving as a response variable and protein expressions as explanatory variables.
