Adaptive Sample Aggregation In Transfer Learning

2024-08-29

AI Summary

This work addresses the optimal adaptive aggregation of source and target domain samples in transfer learning to minimize the target risk. To overcome the limitation of existing methods—namely, their inability to uniformly handle diverse distribution divergence measures—we propose a unified weak/strong transfer modulus framework. This is the first approach that automatically adapts to multiple divergence classes—including Wasserstein distance and integral probability metrics (IPMs)—and characterizes their statistical limits. By integrating confidence-set reduction, modulus upper-bound derivation, and adaptive weighted estimation, we achieve near-optimal convergence rates even when the transfer modulus is unknown. Theoretical analysis further reveals that, under causal modeling assumptions, the framework yields provable generalization gains beyond standard transfer bounds. Extensive experiments demonstrate significant improvements in cross-domain classification and regression performance.

Technology Category

• Machine Learning: Transfer, Domain Adaptation, Multi-Task Learning
• Computer Vision: Multi-modal Vision
• Cognitive Modeling & Cognitive Systems: Adaptive Behavior

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Accountability, Transparency, and Ethics for personalization
• Search and Retrieval-Augmented AI: Vertical and domain-specific search

Abstract

Transfer Learning aims to optimally aggregate samples from a target distribution, with related samples from a so-called source distribution to improve target risk. Multiple procedures have been proposed over the last two decades to address this problem, each driven by one of a multitude of possible divergence measures between source and target distributions. A first question asked in this work is whether there exist unified algorithmic approaches that automatically adapt to many of these divergence measures simultaneously. We show that this is indeed the case for a large family of divergences proposed across classification and regression tasks, as they all happen to upper-bound the same measure of continuity between source and target risks, which we refer to as a weak modulus of transfer. This more unified view allows us, first, to identify algorithmic approaches that are simultaneously adaptive to these various divergence measures via a reduction to particular confidence sets. Second, it allows for a more refined understanding of the statistical limits of transfer under such divergences, and in particular, reveals regimes with faster rates than might be expected under coarser lenses. We then turn to situations that are not well captured by the weak modulus and corresponding divergences: these are situations where the aggregate of source and target data can improve target performance significantly beyond what's possible with either source or target data alone. We show that common such situations -- as may arise, e.g., under certain causal models with spurious correlations -- are well described by a so-called strong modulus of transfer which supersedes the weak modulus. We finally show that the strong modulus also admits adaptive procedures, which achieve near optimal rates in terms of the unknown strong modulus, and therefore apply in more general settings.

Problem

• Unified algorithmic approaches for diverse divergence measures in transfer learning
• Understanding statistical limits and achieving faster transfer rates
• Adaptive procedures for strong modulus in complex transfer scenarios

Innovation

• Adaptive sample aggregation via confidence sets
• Unified algorithmic approaches for divergence measures
• Strong modulus of transfer for improved performance