Adaptive Estimation and Learning under Temporal Distribution Shift

Dheeraj Baby, Yifei Tang, Hieu Duy Nguyen, Yu-Xiang Wang, Rohit Pyati
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:2176-2202, 2025.

Abstract

In this paper, we study the problem of estimation and learning under temporal distribution shift. Consider an observation sequence of length $n$, which is a noisy realization of a time-varying ground-truth sequence. Our focus is to develop methods to estimate the groundtruth at the final time-step while providing sharp point-wise estimation error rates. We show that, without prior knowledge on the level of temporal shift, a wavelet soft-thresholding estimator provides an optimal estimation error bound for the groundtruth. Our proposed estimation method generalizes existing researches (Mazetto and Upfal, 2023) by establishing a connection between the sequence’s non-stationarity level and the sparsity in the wavelet-transformed domain. Our theoretical findings are validated by numerical experiments. Additionally, we applied the estimator to derive sparsity-aware excess risk bounds for binary classification under distribution shift and to develop computationally efficient training objectives. As a final contribution, we draw parallels between our results and the classical signal processing problem of total-variation denoising (Mammen and van de Geer 1997; Tibshirani 2014 ), uncovering novel optimal algorithms for such task.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-baby25a, title = {Adaptive Estimation and Learning under Temporal Distribution Shift}, author = {Baby, Dheeraj and Tang, Yifei and Nguyen, Hieu Duy and Wang, Yu-Xiang and Pyati, Rohit}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {2176--2202}, 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/baby25a/baby25a.pdf}, url = {https://proceedings.mlr.press/v267/baby25a.html}, abstract = {In this paper, we study the problem of estimation and learning under temporal distribution shift. Consider an observation sequence of length $n$, which is a noisy realization of a time-varying ground-truth sequence. Our focus is to develop methods to estimate the groundtruth at the final time-step while providing sharp point-wise estimation error rates. We show that, without prior knowledge on the level of temporal shift, a wavelet soft-thresholding estimator provides an optimal estimation error bound for the groundtruth. Our proposed estimation method generalizes existing researches (Mazetto and Upfal, 2023) by establishing a connection between the sequence’s non-stationarity level and the sparsity in the wavelet-transformed domain. Our theoretical findings are validated by numerical experiments. Additionally, we applied the estimator to derive sparsity-aware excess risk bounds for binary classification under distribution shift and to develop computationally efficient training objectives. As a final contribution, we draw parallels between our results and the classical signal processing problem of total-variation denoising (Mammen and van de Geer 1997; Tibshirani 2014 ), uncovering novel optimal algorithms for such task.} }
Endnote
%0 Conference Paper %T Adaptive Estimation and Learning under Temporal Distribution Shift %A Dheeraj Baby %A Yifei Tang %A Hieu Duy Nguyen %A Yu-Xiang Wang %A Rohit Pyati %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-baby25a %I PMLR %P 2176--2202 %U https://proceedings.mlr.press/v267/baby25a.html %V 267 %X In this paper, we study the problem of estimation and learning under temporal distribution shift. Consider an observation sequence of length $n$, which is a noisy realization of a time-varying ground-truth sequence. Our focus is to develop methods to estimate the groundtruth at the final time-step while providing sharp point-wise estimation error rates. We show that, without prior knowledge on the level of temporal shift, a wavelet soft-thresholding estimator provides an optimal estimation error bound for the groundtruth. Our proposed estimation method generalizes existing researches (Mazetto and Upfal, 2023) by establishing a connection between the sequence’s non-stationarity level and the sparsity in the wavelet-transformed domain. Our theoretical findings are validated by numerical experiments. Additionally, we applied the estimator to derive sparsity-aware excess risk bounds for binary classification under distribution shift and to develop computationally efficient training objectives. As a final contribution, we draw parallels between our results and the classical signal processing problem of total-variation denoising (Mammen and van de Geer 1997; Tibshirani 2014 ), uncovering novel optimal algorithms for such task.
APA
Baby, D., Tang, Y., Nguyen, H.D., Wang, Y. & Pyati, R.. (2025). Adaptive Estimation and Learning under Temporal Distribution Shift. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:2176-2202 Available from https://proceedings.mlr.press/v267/baby25a.html.

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