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arXiv 2101.09438cs.LGmath.OCstat.ML
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TV去噪到自适应在线学习的最优约简

An Optimal Reduction of TV-Denoising to Adaptive Online Learning

UC Santa Barbara(加州大学圣巴巴拉分校)

Dheeraj Baby, Xuandong Zhao, Yu-Xiang Wang

摘要:

我们考虑从$n$噪声样本中估计一个函数的问题,该样本的离散全变差(TV)由$C_n$限定。我们揭示了与强自适应在线学习(Daniely et al,2015)的看似不同的问题的深层联系,并提供了一种$O(n \log n)$时间算法,该算法在平方误差损失下获得了$\tilde O (n^{1/3}C_n^{2/3})$的近极小极大最优速率。所得到的算法在线运行,并最佳地适应未知的平滑参数$C_n$。这导致了一个新的和更通用的替代小波为基础的方法(1)自适应估计电视有界函数;(2)在线预测电视有界的趋势,在时间序列。

英文摘要:

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 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 adapts to the 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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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