不均匀子矩阵检测
Inhomogeneous Submatrix Detection
AI总结：
本文提出了一种在大规模高斯随机矩阵中检测多个不均匀子矩阵的方法，通过均值和方差偏移模型，设计算法以达到信息论下界。
摘要：
本文研究了在大规模高斯随机矩阵中检测多个隐藏子矩阵的问题，当所植信号在不同位置不均匀时。在原假设下，观察到的矩阵具有独立同分布的标准正态 entries。在备择假设下，存在几个所植的子矩阵，其 entries 以两种方式偏离背景：在均值偏移模型中，所植 entries（模板）具有非零且可能变化的均值；在方差偏移模型中，所植 entries 具有放大且可能变化的方差。我们考虑了两种所植子矩阵的放置模式。在第一种模式中，行和列的索引集是任意的。受科学应用启发，在第二种模式中，行和列的索引被限制为连续的。对于两种备择假设和两种放置模式，我们通过证明信息论下界并设计算法来分析检测的统计极限，这些算法在广泛模板家族中达到下界，仅在对数因子上有所差异。
英文摘要：
In this paper, we study the problem of detecting multiple hidden submatrices in a large Gaussian random matrix when the planted signal is inhomogeneous across entries. Under the null hypothesis, the observed matrix has independent and identically distributed standard normal entries. Under the alternative, there exist several planted submatrices whose entries deviate from the background in one of two ways: in the mean-shift model, planted entries (templates) have nonzero and possibly varying means; in the variance-shift model, planted entries have inflated and possibly varying variances. We consider two placement regimes for the planted submatrices. In the first, the row and column index sets are arbitrary. Motivated by scientific applications, in the second regime the row and column indices are restricted to be consecutive. For both alternatives and both placement regimes, we analyze the statistical limits of detection by proving information-theoretic lower bounds and by designing algorithms that match these bounds up to logarithmic factors, for a wide family of templates.
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。
