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Transfer Learning for Nonparametric Regression: Non-asymptotic Minimax Analysis and Adaptive Procedure

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arxiv 2401.12272 v1 pith:C6MWKGM4 submitted 2024-01-22 stat.ML cs.LG

T. Tony Cai , Hongming Pu This is my paper
classification stat.MLcs.LG
keywords learningminimaxtransfernonparametricregressionriskadaptivealgorithm
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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.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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  5. Multi-Environment GLAMP: Approximate Message Passing for Transfer Learning with Applications to Lasso-based Estimators

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    A two-step framework combining block-wise imputation with shared and task-specific multi-task learning improves prediction under distribution and posterior shift.

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