Transfer Learning in Nonparametric Regression with Deep ReLU Networks

Junpeng Ren, Carlos Misael Madrid Padilla, Yanzhen Chen, Oscar Hernan Madrid Padilla
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:104563-104609, 2026.

Abstract

This paper develops a general transfer learning framework for nonparametric regression with data consisting of multiple groups. Under the assumption that groups share a common structure along with group-specific deviations in additive form, the proposed method employs a two-stage offset learning procedure: the first stage pools data from all groups to estimate an overall mean function, and the second stage estimates offsets for each group, yielding final group-level estimators through additive combination. Upper bounds on the $\mathcal L_2$ error are established for the proposed framework, covering a broad class of nonparametric estimators under mild complexity and noise conditions. When instantiated with deep ReLU networks, explicit convergence rates are derived under hierarchical composition models, demonstrating the ability to overcome the curse of dimensionality. Conditions that enable positive transfer with faster rates are considered, including learning with simpler functions and data augmentation through pooling samples across groups. Various simulations and real-data experiments further validate the effectiveness of the proposed method.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-ren26k, title = {Transfer Learning in Nonparametric Regression with Deep {R}e{LU} Networks}, author = {Ren, Junpeng and Madrid Padilla, Carlos Misael and Chen, Yanzhen and Madrid Padilla, Oscar Hernan}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {104563--104609}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/ren26k/ren26k.pdf}, url = {https://proceedings.mlr.press/v306/ren26k.html}, abstract = {This paper develops a general transfer learning framework for nonparametric regression with data consisting of multiple groups. Under the assumption that groups share a common structure along with group-specific deviations in additive form, the proposed method employs a two-stage offset learning procedure: the first stage pools data from all groups to estimate an overall mean function, and the second stage estimates offsets for each group, yielding final group-level estimators through additive combination. Upper bounds on the $\mathcal L_2$ error are established for the proposed framework, covering a broad class of nonparametric estimators under mild complexity and noise conditions. When instantiated with deep ReLU networks, explicit convergence rates are derived under hierarchical composition models, demonstrating the ability to overcome the curse of dimensionality. Conditions that enable positive transfer with faster rates are considered, including learning with simpler functions and data augmentation through pooling samples across groups. Various simulations and real-data experiments further validate the effectiveness of the proposed method.} }
Endnote
%0 Conference Paper %T Transfer Learning in Nonparametric Regression with Deep ReLU Networks %A Junpeng Ren %A Carlos Misael Madrid Padilla %A Yanzhen Chen %A Oscar Hernan Madrid Padilla %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-ren26k %I PMLR %P 104563--104609 %U https://proceedings.mlr.press/v306/ren26k.html %V 306 %X This paper develops a general transfer learning framework for nonparametric regression with data consisting of multiple groups. Under the assumption that groups share a common structure along with group-specific deviations in additive form, the proposed method employs a two-stage offset learning procedure: the first stage pools data from all groups to estimate an overall mean function, and the second stage estimates offsets for each group, yielding final group-level estimators through additive combination. Upper bounds on the $\mathcal L_2$ error are established for the proposed framework, covering a broad class of nonparametric estimators under mild complexity and noise conditions. When instantiated with deep ReLU networks, explicit convergence rates are derived under hierarchical composition models, demonstrating the ability to overcome the curse of dimensionality. Conditions that enable positive transfer with faster rates are considered, including learning with simpler functions and data augmentation through pooling samples across groups. Various simulations and real-data experiments further validate the effectiveness of the proposed method.
APA
Ren, J., Madrid Padilla, C.M., Chen, Y. & Madrid Padilla, O.H.. (2026). Transfer Learning in Nonparametric Regression with Deep ReLU Networks. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:104563-104609 Available from https://proceedings.mlr.press/v306/ren26k.html.

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