AKORN: Adaptive Knots generated Online for RegressioN splines

Sunil Madhow, Dheeraj Baby, Yu-Xiang Wang
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:42394-42420, 2025.

Abstract

In order to attain optimal rates, state-of-the-art algorithms for non-parametric regression require that a hyperparameter be tuned according to the smoothness of the ground truth (Tibshirani, 2014). This amounts to an assumption of oracle access to certain features of the data-generating process. We present a parameter-free algorithm for offline non-parametric regression over $TV_1$-bounded functions. By feeding offline data into an optimal online denoising algorithm styled after (Baby et al., 2021), we are able to use change-points to adaptively select knots that respect the geometry of the underlying ground truth. We call this procedure AKORN (Adaptive Knots gener- ated Online for RegressioN splines). By combining forward and backward passes over the data, we obtain an estimator whose empirical performance is close to Trend Filtering (Kim et al., 2009; Tibshirani, 2014), even when we provide the latter with oracle knowledge of the ground truth’s smoothness.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-madhow25a, title = {{AKORN}: Adaptive Knots generated Online for {R}egressio{N} splines}, author = {Madhow, Sunil and Baby, Dheeraj and Wang, Yu-Xiang}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {42394--42420}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/madhow25a/madhow25a.pdf}, url = {https://proceedings.mlr.press/v267/madhow25a.html}, abstract = {In order to attain optimal rates, state-of-the-art algorithms for non-parametric regression require that a hyperparameter be tuned according to the smoothness of the ground truth (Tibshirani, 2014). This amounts to an assumption of oracle access to certain features of the data-generating process. We present a parameter-free algorithm for offline non-parametric regression over $TV_1$-bounded functions. By feeding offline data into an optimal online denoising algorithm styled after (Baby et al., 2021), we are able to use change-points to adaptively select knots that respect the geometry of the underlying ground truth. We call this procedure AKORN (Adaptive Knots gener- ated Online for RegressioN splines). By combining forward and backward passes over the data, we obtain an estimator whose empirical performance is close to Trend Filtering (Kim et al., 2009; Tibshirani, 2014), even when we provide the latter with oracle knowledge of the ground truth’s smoothness.} }
Endnote
%0 Conference Paper %T AKORN: Adaptive Knots generated Online for RegressioN splines %A Sunil Madhow %A Dheeraj Baby %A Yu-Xiang Wang %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-madhow25a %I PMLR %P 42394--42420 %U https://proceedings.mlr.press/v267/madhow25a.html %V 267 %X In order to attain optimal rates, state-of-the-art algorithms for non-parametric regression require that a hyperparameter be tuned according to the smoothness of the ground truth (Tibshirani, 2014). This amounts to an assumption of oracle access to certain features of the data-generating process. We present a parameter-free algorithm for offline non-parametric regression over $TV_1$-bounded functions. By feeding offline data into an optimal online denoising algorithm styled after (Baby et al., 2021), we are able to use change-points to adaptively select knots that respect the geometry of the underlying ground truth. We call this procedure AKORN (Adaptive Knots gener- ated Online for RegressioN splines). By combining forward and backward passes over the data, we obtain an estimator whose empirical performance is close to Trend Filtering (Kim et al., 2009; Tibshirani, 2014), even when we provide the latter with oracle knowledge of the ground truth’s smoothness.
APA
Madhow, S., Baby, D. & Wang, Y.. (2025). AKORN: Adaptive Knots generated Online for RegressioN splines. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:42394-42420 Available from https://proceedings.mlr.press/v267/madhow25a.html.

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