Biostatistics Seminar Series - Hongzhe Li, PhD

Title: Transfer learning in high-dimensional linear regression and graphical models Abstract: This talk considers the estimation and prediction of a high-dimensional linear regression and Gaussian graphical models in the setting of transfer learning, using samples from the target model as well as auxiliary samples from different but possibly related models. When the set of "informative" auxiliary samples is known, an estimator and a predictor are proposed and their optimality is established. The optimal rates of convergence for prediction and estimation are faster than the corresponding rates without using the auxiliary samples. This implies that knowledge from the informative auxiliary samples can be transferred to improve the learning performance of the target problem. In the case that the set of informative auxiliary samples is unknown, we propose a data-driven procedure for transfer learning, called Trans-Lasso, and reveal its robustness to non-informative auxiliary samples and its efficiency in knowledge transfer. We also present a Trans-CLIME method for estimation and inference of high-dimensional Gaussian graphical models with transfer learning. The proposed procedures are demonstrated in numerical studies and are applied to a dataset concerning the associations among gene expressions. It is shown that Trans-Lasso and Trans-CLIME lead to improved performance in gene expression prediction in a target tissue by incorporating the data from multiple different tissues as auxiliary samples.