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Weak Detection in the Spiked Wigner Model with General Rank
arXiv - CS - Machine Learning Pub Date : 2020-01-16 , DOI: arxiv-2001.05676 Ji Hyung Jung, Hye Won Chung, and Ji Oon Lee
arXiv - CS - Machine Learning Pub Date : 2020-01-16 , DOI: arxiv-2001.05676 Ji Hyung Jung, Hye Won Chung, and Ji Oon Lee
We study the statistical decision process of detecting the presence of signal
from a 'signal+noise' type matrix model with an additive Wigner noise. We
derive the error of the likelihood ratio test, which minimizes the sum of the
Type-I and Type-II errors, under the Gaussian noise for the signal matrix with
arbitrary finite rank. We propose a hypothesis test based on the linear
spectral statistics of the data matrix, which is optimal and does not depend on
the distribution of the signal or the noise. We also introduce a test for rank
estimation that does not require the prior information on the rank of the
signal.
中文翻译:
具有一般等级的 Spiked Wigner 模型中的弱检测
我们研究了从带有加性 Wigner 噪声的“信号+噪声”类型矩阵模型中检测信号存在的统计决策过程。我们推导出似然比检验的误差,它在具有任意有限秩的信号矩阵的高斯噪声下最小化了 I 型和 II 型误差的总和。我们提出了一种基于数据矩阵的线性谱统计的假设检验,这是最优的并且不依赖于信号或噪声的分布。我们还引入了一种秩估计检验,它不需要信号秩的先验信息。
更新日期:2020-05-11
中文翻译:
具有一般等级的 Spiked Wigner 模型中的弱检测
我们研究了从带有加性 Wigner 噪声的“信号+噪声”类型矩阵模型中检测信号存在的统计决策过程。我们推导出似然比检验的误差,它在具有任意有限秩的信号矩阵的高斯噪声下最小化了 I 型和 II 型误差的总和。我们提出了一种基于数据矩阵的线性谱统计的假设检验,这是最优的并且不依赖于信号或噪声的分布。我们还引入了一种秩估计检验,它不需要信号秩的先验信息。