Problem
Research questions and friction points this paper is trying to address.
Transfer learning
High-dimensional quantile regression
Sample-level transfer
Heterogeneous source domains
Limited target samples
Beyond Source-Level Transfer: Sample-Level Learning for High-Dimensional Quantile Regression
🤖 AI Summary
This study addresses the transfer learning challenges in high-dimensional quantile regression arising from scarce target samples and source domain heterogeneity. We propose a fine-grained, sample-level transfer learning method that adaptively computes sample weights via one-dimensional density estimation to identify transferable data. This approach effectively circumvents the bottleneck of high-dimensional density ratio estimation and overcomes the limitations of conventional methods that treat entire source domains as indivisible units. By incorporating sample splitting and cross-fitting techniques, the computational complexity is substantially reduced. Theoretically, we establish that the proposed estimator achieves faster convergence rates than existing methods. Simulation studies and empirical applications further demonstrate the effectiveness and robustness of the algorithm.
📝 Abstract
This paper studies transfer learning for high-dimensional quantile regression with limited target samples and heterogeneous source domains. We propose a sample-level transfer learning method (SL-TL) that combines sample selection and importance weighting. Unlike existing source-level approaches that include or exclude entire source domains, SL-TL identifies transferable samples within each source domain and incorporates them through adaptive importance weights. The proposed weights rely only on one-dimensional densities associated with the quantile loss, avoiding the estimation of high-dimensional density ratios. We establish error bounds for SL-TL estimators and characterize the effective sample size contributed by source domains. In the oracle setting, we show that SL-TL achieves faster $\ell_2$-convergence rates than existing competitors under the considered regimes. For the unknown setting, we develop an implementable algorithm based on sample splitting and cross-fitting procedures. Extensive simulations and a real data analysis demonstrate the finite-sample performance and robustness of SL-TL.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Sample-level transfer learning
High-dimensional quantile regression
Importance weighting
Cross-fitting
Convergence rate
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