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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2505.15803 |
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| _version_ | 1866912386035744768 |
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| author | Baby, Dheeraj Tang, Yifei Nguyen, Hieu Duy Wang, Yu-Xiang Pyati, Rohit |
| author_facet | Baby, Dheeraj Tang, Yifei Nguyen, Hieu Duy Wang, Yu-Xiang Pyati, Rohit |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15803 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adaptive Estimation and Learning under Temporal Distribution Shift Baby, Dheeraj Tang, Yifei Nguyen, Hieu Duy Wang, Yu-Xiang Pyati, Rohit Machine Learning 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. |
| title | Adaptive Estimation and Learning under Temporal Distribution Shift |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2505.15803 |