Sharp Variable Selection of a Sparse Submatrix in a High-Dimensional Noisy Matrix
Sharp Variable Selection of a Sparse Submatrix in a High-Dimensional Noisy Matrix
复制标题
高维噪声矩阵中稀疏子矩阵的锐变量选择
DOI：
10.1051/ps/2014017
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
I. Suslina
中科院分区：
文献类型：
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作者：
C. Butucea;Yu. I. Ingster;I. Suslina
我们观察到一个由独立的同分布高斯随机变量组成的$N\乘以M$矩阵，除了一些大小为$N\乘以M$的子矩阵的元素外，这些子矩阵的平均值大于一些$a>0$。子矩阵是稀疏的，因为$n/ n $和$m/ m $趋向于0，而$n,\, m, \, n $和$m $趋向于无穷。
We observe a $N\times M$ matrix of independent, identically distributed Gaussian random variables which are centered except for elements of some submatrix of size $n\times m$ where the mean is larger than some $a>0$. The submatrix is sparse in the sense that $n/N$ and $m/M$ tend to 0, whereas $n,\, m, \, N$ and $M$ tend to infinity.
We consider the problem of selecting the random variables with significantly large mean values. We give sufficient conditions on $a$ as a function of $n,\, m,\,N$ and $M$ and construct a uniformly consistent procedure in order to do sharp variable selection. We also prove the minimax lower bounds under necessary conditions which are complementary to the previous conditions. The critical values $a^*$ separating the necessary and sufficient conditions are sharp (we show exact constants).
We note a gap between the critical values $a^*$ for selection of variables and that of detecting that such a submatrix exists given by Butucea and Ingster (2012). When $a^*$ is in this gap, consistent detection is possible but no consistent selector of the corresponding variables can be found.
关于高斯随机矩阵中大平均和方差分析拟合子矩阵的最大尺寸。
DOI：
10.3150/11-bej394
发表时间：
2013
期刊：
Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability
影响因子：
--
作者：
Sun,Xing;Nobel,AndrewB
通讯作者：
Nobel,AndrewB