Adaptive transfer learning

In transfer learning, we wish to make inference about a target population when have access data both from the distribution itself, and different but related source distribution. We introduce flexible framework for learning in context of binary classification, allowing covariate-dependent relationships between distributions that are not required preserve Bayes decision boundary. Our main contributions derive minimax optimal rates convergence (up poly-logarithmic factors) this problem, show rate can be achieved by an algorithm adapts key aspects unknown relationship, as well smoothness tail parameters our distributional classes. This turns out several regimes, depending on interplay relative sample sizes strength achieves optimality careful, tree-based calibration local nearest-neighbour procedures.