Model-Robust and Adaptive-Optimal Transfer Learning for Tackling Concept Shifts in Nonparametric Regression

2025-01-18

AI Summary

Nonparametric regression under concept drift and scarce samples in the target domain. Method: We propose a robust, adaptive kernel transfer learning approach based on Gaussian kernels. Under model misspecification, we establish the first minimax convergence rate theory for Gaussian kernel spectral algorithms; within a hypothesis-transfer learning framework, we derive an adaptively optimal excess risk bound, overcoming the saturation limitation inherent in classical kernel methods. By employing fixed-bandwidth Gaussian kernels, modeling with Sobolev-space function classes, and conducting misspecification-aware inference analysis, our method achieves minimax-optimal excess risk convergence (up to logarithmic factors) and explicitly characterizes key determinants of transfer efficiency. Results: Our theoretical guarantees strictly improve upon existing kernel-based transfer learning methods, providing a novel paradigm for nonparametric regression in small-sample, dynamically evolving environments.

Technology Category

• Machine Learning: Kernel Methods
• Search and Optimization: Non-convex Optimization
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

When concept shifts and sample scarcity are present in the target domain of interest, nonparametric regression learners often struggle to generalize effectively. The technique of transfer learning remedies these issues by leveraging data or pre-trained models from similar source domains. While existing generalization analyses of kernel-based transfer learning typically rely on correctly specified models, we present a transfer learning procedure that is robust against model misspecification while adaptively attaining optimality. To facilitate our analysis and avoid the risk of saturation found in classical misspecified results, we establish a novel result in the misspecified single-task learning setting, showing that spectral algorithms with fixed bandwidth Gaussian kernels can attain minimax convergence rates given the true function is in a Sobolev space, which may be of independent interest. Building on this, we derive the adaptive convergence rates of the excess risk for specifying Gaussian kernels in a prevalent class of hypothesis transfer learning algorithms. Our results are minimax optimal up to logarithmic factors and elucidate the key determinants of transfer efficiency.

Problem

• Nonparametric Regression
• Transfer Learning
• Adaptability

Innovation

• Adaptive Learning Strategy
• Nonparametric Regression
• Transfer Learning Efficiency