改进的噪声种群恢复和稀疏函数的逆Bonami-Beckner不等式

Shachar Lovett, Jiapeng Zhang
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引用次数: 19

摘要

噪声种群恢复问题是一个基本的统计推理问题。给定支持大小为k的{0,1}n中的未知分布,并且只能访问其中的噪声样本,其中每个比特以(1-μ)/2的概率独立翻转,估计原始概率直至加性误差ε。给出了一种求解该问题的时间多项式算法(klog log k, n, 1/ε)。这是对Wigderson和Yehudayoff [FOCS 2012]之前的算法的改进,该算法在(klog k, n, 1/ε)的时间多项式中解决问题。我们的主要技术贡献是简化了算法,为稀疏函数的L1范数提供了一个新的反向Bonami-Beckner不等式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Improved Noisy Population Recovery, and Reverse Bonami-Beckner Inequality for Sparse Functions
The noisy population recovery problem is a basic statistical inference problem. Given an unknown distribution in {0,1}n with support of size k, and given access only to noisy samples from it, where each bit is flipped independently with probability (1-μ)/2, estimate the original probability up to an additive error of ε. We give an algorithm which solves this problem in time polynomial in (klog log k, n, 1/ε). This improves on the previous algorithm of Wigderson and Yehudayoff [FOCS 2012] which solves the problem in time polynomial in (klog k, n, 1/ε). Our main technical contribution, which facilitates the algorithm, is a new reverse Bonami-Beckner inequality for the L1 norm of sparse functions.
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