Recovering Structure of Noisy Data through Hypothesis Testing
Recovering Structure of Noisy Data through Hypothesis Testing
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DOI：
10.1109/isit44484.2020.9174229
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发表时间：
2020-06
期刊：
影响因子：
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通讯作者：
Minoh Jeong;Alex Dytso;Martina Cardone;H. V. Poor
中科院分区：
文献类型：
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作者：
Minoh Jeong;Alex Dytso;Martina Cardone;H. V. Poor
本文研究了一个噪声数据结构的恢复问题。具体来说，目标是研究以下问题：给定对数据的嘈杂观察，原始数据按照哪种排列排序？主要关注数据根据各向同性高斯分布生成的场景，并且扰动包括添加具有对角标量协方差矩阵的高斯噪声。这个问题是在假设检验框架内提出的。首先，对最优决策准则进行表征，并证明其与观测的假设相同。然后，利用最优决策准则的结构，对误差概率进行表征。最后，在数据维数趋于无穷大的情况下，推导出误差概率的对数行为（即指数）。
This paper considers a noisy data structure recovery problem. Specifically, the goal is to investigate the following question: Given a noisy observation of the data, according to which permutation was the original data sorted? The main focus is on scenarios where data is generated according to an isotropic Gaussian distribution, and the perturbation consists of adding Gaussian noise with diagonal scalar covariance matrix. This problem is posed within a hypothesis testing framework. First, the optimal decision criterion is characterized and shown to be identical to the hypothesis of the observation. Then, by leveraging the structure of the optimal decision criterion, the probability of error is characterized. Finally, the logarithmic behavior (i.e., the exponent) of the probability of error is derived in the regime where the dimension of the data goes to infinity.