AISTATS 2021poster15 citations
An Optimal Reduction of TV-Denoising to Adaptive Online Learning
Dheeraj Baby, Xuandong Zhao, Yu-Xiang Wang
Abstract
We consider the problem of estimating a function from $n$ noisy samples whose discrete Total Variation (TV) is bounded by $C_n$. We reveal a deep connection to the seemingly disparate problem of \emph{Strongly Adaptive} online learning [Daniely et al 2015] and provide an $O(n \log n)$ time algorithm that attains the near minimax optimal rate of $\tilde O (n^{1/3}C_n^{2/3})$ under squared error loss. The resulting algorithm runs online and optimally \emph{adapts} to the \emph{unknown} smoothness parameter $C_n$. This leads to a new and more versatile alternative to wavelets-based methods for (1) adaptively estimating TV bounded functions; (2) online forecasting of TV bounded trends in time series.
BibTeX
@InProceedings{pmlr-v130-baby21a,
title = { An Optimal Reduction of TV-Denoising to Adaptive Online Learning },
author = {Baby, Dheeraj and Zhao, Xuandong and Wang, Yu-Xiang},
booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics},
pages = {2899--2907},
year = {2021},
editor = {Banerjee, Arindam and Fukumizu, Kenji},
volume = {130},
series = {Proceedings of Machine Learning Research},
month = {13--15 Apr},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v130/baby21a/baby21a.pdf},
url = {https://proceedings.mlr.press/v130/baby21a.html},
abstract = { We consider the problem of estimating a function from $n$ noisy samples whose discrete Total Variation (TV) is bounded by $C_n$. We reveal a deep connection to the seemingly disparate problem of \emph{Strongly Adaptive} online learning [Daniely et al 2015] and provide an $O(n \log n)$ time algorithm that attains the near minimax optimal rate of $\tilde O (n^{1/3}C_n^{2/3})$ under squared error loss. The resulting algorithm runs online and optimally \emph{adapts} to the \emph{unknown} smoothness parameter $C_n$. This leads to a new and more versatile alternative to wavelets-based methods for (1) adaptively estimating TV bounded functions; (2) online forecasting of TV bounded trends in time series. }
}