Wasserstein Transfer Learning
This work addresses a gap in transfer learning for complex data structures like probability distributions, offering theoretical and practical solutions for domain adaptation in such settings.
The paper tackles the problem of transfer learning for regression models with probability distribution outputs in Wasserstein space, introducing a framework with provable asymptotic convergence rates and a data-driven procedure to mitigate negative transfer.
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