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Transfer Learning Through Conditional Quantile Matching

Yikun Zhang, Steven Wilkins-Reeves, Wesley Lee, Aude Hofleitner

TL;DR

A transfer learning framework for regression that leverages heterogeneous source domains to improve predictive performance in a data-scarce target domain and establishes new convergence rates for the quantile matching estimator that governs the transfer bias-variance tradeoff.

Abstract

We introduce a transfer learning framework for regression that leverages heterogeneous source domains to improve predictive performance in a data-scarce target domain. Our approach learns a conditional generative model separately for each source domain and calibrates the generated responses to the target domain via conditional quantile matching. This distributional alignment step corrects general discrepancies between source and target domains without imposing restrictive assumptions such as covariate or label shift. The resulting framework provides a principled and flexible approach to high-quality data augmentation for downstream learning tasks in the target domain. From a theoretical perspective, we show that an empirical risk minimizer (ERM) trained on the augmented dataset achieves a tighter excess risk bound than the target-only ERM under mild conditions. In particular, we establish new convergence rates for the quantile matching estimator that governs the transfer bias-variance tradeoff. From a practical perspective, extensive simulations and real data applications demonstrate that the proposed method consistently improves prediction accuracy over target-only learning and competing transfer learning methods.

Transfer Learning Through Conditional Quantile Matching

TL;DR

A transfer learning framework for regression that leverages heterogeneous source domains to improve predictive performance in a data-scarce target domain and establishes new convergence rates for the quantile matching estimator that governs the transfer bias-variance tradeoff.

Abstract

We introduce a transfer learning framework for regression that leverages heterogeneous source domains to improve predictive performance in a data-scarce target domain. Our approach learns a conditional generative model separately for each source domain and calibrates the generated responses to the target domain via conditional quantile matching. This distributional alignment step corrects general discrepancies between source and target domains without imposing restrictive assumptions such as covariate or label shift. The resulting framework provides a principled and flexible approach to high-quality data augmentation for downstream learning tasks in the target domain. From a theoretical perspective, we show that an empirical risk minimizer (ERM) trained on the augmented dataset achieves a tighter excess risk bound than the target-only ERM under mild conditions. In particular, we establish new convergence rates for the quantile matching estimator that governs the transfer bias-variance tradeoff. From a practical perspective, extensive simulations and real data applications demonstrate that the proposed method consistently improves prediction accuracy over target-only learning and competing transfer learning methods.
Paper Structure (23 sections, 7 theorems, 56 equations, 3 figures, 3 tables, 1 algorithm)

This paper contains 23 sections, 7 theorems, 56 equations, 3 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Contributions and Outline of the Paper
  3. Other Related Works
  4. Notations
  5. Proposed Framework
  6. Learning Conditional Generative Models via Engression
  7. Conditional Quantile Matching
  8. Theoretical Analysis
  9. Assumptions
  10. Target-Only Excess Risk
  11. Excess Risk Under Our TLCQM framework
  12. Quantile Matching Error
  13. Numerical Experiments
  14. Simulation Studies
  15. Experiments on Real Public Data
  16. ...and 8 more sections

Key Result

Proposition 3.3

Under Assumption assump:basic_reg(a), the target-only prediction function $\widehat{f}^{(0)}$ in target_only_pred has its excess risk satisfying that, with probability at least $1-\delta$,

Figures (3)

  • Figure 1: Illustration of the conditional quantile matching process.
  • Figure 2: Prediction performances of different machine learning models applied to various data scenarios and other competing transfer learning methods on simulated data.
  • Figure 3: Performances of different machine learning models applied to target-only and TLCQM scenarios as well as other competing transfer learning methods on the "Apartment" data.

Theorems & Definitions (12)

  • Proposition 3.3
  • Theorem 3.4
  • Theorem 3.6
  • proof : Proof of \ref{['thm:transfer_learn_excess_risk']}
  • Lemma 3.1
  • Lemma 3.2
  • proof : Proof of Lemma \ref{['lem:quantile_deriv']}
  • Lemma 3.3
  • proof : Proof of Lemma \ref{['lem:rearrange_ineq']}
  • Lemma 3.4
  • ...and 2 more