Adaptive transfer learning
This work addresses the challenge of making inferences in target populations using related source data, with potential applications in domains where data from different distributions are available, though it appears incremental as it builds on existing transfer learning concepts.
The paper tackles the problem of transfer learning for binary classification by introducing a framework that allows for flexible, covariate-dependent relationships between source and target distributions without requiring preservation of the Bayes decision boundary. It derives minimax optimal convergence rates (up to poly-logarithmic factors) and presents an algorithm that adapts to unknown transfer relationships and distributional parameters, achieving these rates through decision tree-based calibration of local nearest-neighbor procedures.
In transfer learning, we wish to make inference about a target population when we have access to data both from the distribution itself, and from a different but related source distribution. We introduce a flexible framework for transfer learning in the context of binary classification, allowing for covariate-dependent relationships between the source and target distributions that are not required to preserve the Bayes decision boundary. Our main contributions are to derive the minimax optimal rates of convergence (up to poly-logarithmic factors) in this problem, and show that the optimal rate can be achieved by an algorithm that adapts to key aspects of the unknown transfer relationship, as well as the smoothness and tail parameters of our distributional classes. This optimal rate turns out to have several regimes, depending on the interplay between the relative sample sizes and the strength of the transfer relationship, and our algorithm achieves optimality by careful, decision tree-based calibration of local nearest-neighbour procedures.