Wasserstein Transfer Learning

TL;DR

This paper introduces a transfer learning framework for regression models with outputs as probability distributions in Wasserstein space, providing theoretical guarantees and practical algorithms to improve transfer efficiency.

Contribution

It presents a novel Wasserstein space-based transfer learning method with asymptotic convergence analysis and a data-driven approach to handle unknown source domain relevance.

Findings

The estimator achieves provable asymptotic convergence rates.

The data-driven procedure effectively reduces negative transfer.

Validated through simulations and real-world applications.

Abstract

Transfer learning is a powerful paradigm for leveraging knowledge from source domains to enhance learning in a target domain. However, traditional transfer learning approaches often focus on scalar or multivariate data within Euclidean spaces, limiting their applicability to complex data structures such as probability distributions. To address this limitation, we introduce a novel transfer learning framework for regression models whose outputs are probability distributions residing in the Wasserstein space. When the informative subset of transferable source domains is known, we propose an estimator with provable asymptotic convergence rates, quantifying the impact of domain similarity on transfer efficiency. For cases where the informative subset is unknown, we develop a data-driven transfer learning procedure designed to mitigate negative transfer. The proposed methods are supported by rigorous theoretical analysis and are validated through extensive simulations and real-world applications. The code is available at https://github.com/h7nian/WaTL