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arXiv · 2311.07972

Residual Importance Weighted Transfer Learning For High-dimensional Linear Regression

Junlong Zhao·Shengbin Zheng·Chenlei Leng
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Abstract

Transfer learning is an emerging paradigm for leveraging multiple sources to improve the statistical inference on a single target. In this paper, we propose a novel approach named residual importance weighted transfer learning (RIW-TL) for high-dimensional linear models built on penalized likelihood. Compared to existing methods such as Trans-Lasso that 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. We show that the oracle RIW-TL provides a faster rate than its competitors and develop a cross-fitting procedure to estimate this oracle. We discuss variants of RIW-TL by adopting different choices for residual weighting. The theoretical properties of RIW-TL and its variants are established and compared with those of LASSO and Trans-Lasso. Extensive simulation and a real data analysis confirm its advantages.

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Junlong Zhao, Shengbin Zheng, Chenlei Leng. 2023-11-14. Residual Importance Weighted Transfer Learning For High-dimensional Linear Regression. https://arxiv.org/abs/2311.07972

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