Zhang, X., Blanchet, J., Ghosh, S. & Squillante, M.S.. (2022). A Class of Geometric Structures in Transfer Learning: Minimax Bounds and Optimality . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:3794-3820 Available from https://proceedings.mlr.press/v151/zhang22a.html.
Abstract
We study the problem of transfer learning, observing that previous efforts to understand its information-theoretic limits do not fully exploit the geometric structure of the source and target domains. In contrast, our study first illustrates the benefits of incorporating a natural geometric structure within a linear regression model, which corresponds to the generalized eigenvalue problem formed by the Gram matrices of both domains. We next establish a finite-sample minimax lower bound, propose a refined model interpolation estimator that enjoys a matching upper bound, and then extend our framework to multiple source domains and generalized linear models. Surprisingly, as long as information is available on the distance between the source and target parameters, negative-transfer does not occur. Simulation studies show that our proposed interpolation estimator outperforms state-of-the-art transfer learning methods in both moderate-and high-dimensional settings.
Authors
Xuhui Zhang, Jose Blanchet, Soumyadip Ghosh, Mark S Squillante
Publication date
2022/5/3
Conference
International Conference on Artificial Intelligence and Statistics
Pages
3794-3820
Publisher
PMLR
