Transfer Learning for Nonparametric Regression: Non-asymptotic Minimax
  Analysis and Adaptive Procedure
T. Tony Cai Hongming Pu
Transfer learning for nonparametric regression is considered. We first study
the non-asymptotic minimax risk for this problem and develop a novel estimator
called the confidence thresholding estimator, which is shown to achieve the
minimax optimal risk up to a logarithmic factor. Our results demonstrate two
unique phenomena in transfer learning: auto-smoothing and super-acceleration,
which differentiate it from nonparametric regression in a traditional setting.
We then propose a data-driven algorithm that adaptively achieves the minimax
risk up to a logarithmic factor across a wide range of parameter spaces.
Simulation studies are conducted to evaluate the numerical performance of the
adaptive transfer learning algorithm, and a real-world example is provided to
demonstrate the benefits of the proposed method.