论文标题
在多个网络推断和PCA中不变子空间的分布式估计的限制结果
Limit results for distributed estimation of invariant subspaces in multiple networks inference and PCA
论文作者
论文摘要
我们研究了具有共享不变子空间的矩阵集合的主要奇异向量的分布式估计问题。特别是，我们考虑了一种算法，该算法首先估算了与每个单独矩阵的领先单数向量相对应的投影矩阵，然后计算投影矩阵的平均值，并最终返回样品平均值的领先特征向量。 We show that the algorithm, when applied to (1) parameters estimation for a collection of independent edge random graphs with shared singular vectors but possibly heterogeneous edge probabilities or (2) distributed PCA for independent sub-Gaussian random vectors with spiked covariance structure, yields estimates whose row-wise fluctuations are normally distributed around the rows of the true singular vectors.利用这些结果，我们还考虑了一对随机图具有相同的边缘概率的零假设的两样本测试，并且我们提出了一个测试统计量，其限制分布会收敛到中心（无中心）$χ^2 $下的null（null（分别）局部替代性）假设。
We study the problem of distributed estimation of the leading singular vectors for a collection of matrices with shared invariant subspaces. In particular we consider an algorithm that first estimates the projection matrices corresponding to the leading singular vectors for each individual matrix, then computes the average of the projection matrices, and finally returns the leading eigenvectors of the sample averages. We show that the algorithm, when applied to (1) parameters estimation for a collection of independent edge random graphs with shared singular vectors but possibly heterogeneous edge probabilities or (2) distributed PCA for independent sub-Gaussian random vectors with spiked covariance structure, yields estimates whose row-wise fluctuations are normally distributed around the rows of the true singular vectors. Leveraging these results we also consider a two-sample test for the null hypothesis that a pair of random graphs have the same edge probabilities and we present a test statistic whose limiting distribution converges to a central (resp. non-central) $χ^2$ under the null (resp. local alternative) hypothesis.
