A1010
Title: Residual importance weighted transfer learning For high-dimensional linear regression
Authors: Junlong Zhao - Beijing Normal University (China) [presenting]
Abstract: Transfer learning is an emerging paradigm for leveraging multiple sources to improve the statistical inference on a single target. A novel approach named residual importance weighted transfer learning (RIW-TL) is proposed for high-dimensional linear models built on penalized likelihood. Compared to existing methods, such as trans-Lasso, which selects sources in an all-in-all-out manner, RIW-TL includes samples via importance weighting and thus may permit more effective sample use. To determine the weights, remarkably, RIW-TL only requires the knowledge of one-dimensional densities dependent on residuals, thus overcoming the curse of dimensionality of having to estimate high-dimensional densities in naive importance weighting. It is shown that the oracle RIW-TL provides a faster rate than its competitors and develops a cross-fitting procedure to estimate this oracle. Variants of RIW-TL by adopting different choices for residual weighting are discussed. The theoretical properties of RIW-TL and variants are established and compared with those of Lasso and trans-Lasso. Extensive simulation and real data analysis confirm its advantages.
