Adaptive Estimation and Learning under Temporal Distribution Shift

• URL: http://arxiv.org/abs/2505.15803v1
• Date: Wed, 21 May 2025 17:56:07 GMT
• Title: Adaptive Estimation and Learning under Temporal Distribution Shift
• Authors: Dheeraj Baby, Yifei Tang, Hieu Duy Nguyen, Yu-Xiang Wang, Rohit Pyati,
• Abstract summary: We study the problem of estimation and learning under temporal distribution shift.<n>Consider an observation sequence of length $n$, which is a noisy realization of a time-varying groundtruth sequence.<n>We show that a wavelet soft-thresholding estimator provides an optimal estimation error bound for the groundtruth.
• Score: 17.82448143883071
• License: http://creativecommons.org/licenses/by/4.0/
• 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 groundtruth 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 Mazzetto 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.

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