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作者：Bao, Zhigang; Pan, Guangming; Zhou, Wang
作者单位：Zhejiang University; Nanyang Technological University; National University of Singapore
摘要：This paper is aimed at deriving the universality of the largest eigenvalue of a class of high-dimensional real or complex sample covariance matrices of the form W-N = Sigma(XX)-X-1/2*E-1/2. Here, X = (xij)(M,N) is an M x N random matrix with independent entries x(ij), 1 <= i <= M, 1 <= j <= N such that Ex(ij) = 0, E vertical bar x(ij)vertical bar(2) = 1/N. On dimensionality, we assume that M = M(N) and N/M -> d is an element of(0, infinity) as N -> infinity. For a class of general deterministi...
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作者：Lei, Jing; Rinaldo, Alessandro
作者单位：Carnegie Mellon University
摘要：We analyze the performance of spectral clustering for community extraction in stochastic block models. We show that, under mild conditions, spectral clustering applied to the adjacency matrix of the network can consistently recover hidden communities even when the order of the maximum expected degree is as small as log n, with n the number of nodes. This result applies to some popular polynomial time spectral clustering algorithms and is further extended to degree corrected stochastic block mo...
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作者：Chatterjee, Sourav
作者单位：Stanford University
摘要：Consider the problem of estimating the entries of a large matrix, when the observed entries are noisy versions of a small random fraction of the original entries. This problem has received widespread attention in recent times, especially after the pioneering works of Emmanuel Candes and collaborators. This paper introduces a simple estimation procedure, called Universal Singular Value Thresholding (USVT), that works for any matrix that has a little bit of structure. Surprisingly, this simple e...
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作者：Jin, Jiashun
作者单位：Carnegie Mellon University
摘要：Consider a network where the nodes split into K different communities. The community labels for the nodes are unknown and it is of major interest to estimate them (i.e., community detection). Degree Corrected Block Model (DCBM) is a popular network model. How to detect communities with the DCBM is an interesting problem, where the main challenge lies in the degree heterogeneity. We propose a new approach to community detection which we call the Spectral Clustering On Ratios-of-Eigenvectors (SC...
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作者：McGoff, Kevin; Mukherjee, Sayan; Nobel, Andrew; Pillai, Natesh
作者单位：Duke University; Duke University; Duke University; University of North Carolina; University of North Carolina Chapel Hill; Harvard University
摘要：We consider the asymptotic consistency of maximum likelihood parameter estimation for dynamical systems observed with noise. Under suitable conditions on the dynamical systems and the observations, we show that maximum likelihood parameter estimation is consistent. Our proof involves ideas from both information theory and dynamical systems. Furthermore, we show how some well-studied properties of dynamical systems imply the general statistical properties related to maximum likelihood estimatio...
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作者：Ferreira, Ana; de Haan, Laurens
作者单位：Universidade de Lisboa; Universidade de Lisboa; Erasmus University Rotterdam; Erasmus University Rotterdam - Excl Erasmus MC
摘要：In extreme value theory, there are two fundamental approaches, both widely used: the block maxima (BM) method and the peaks-over-threshold (POT) method. Whereas much theoretical research has gone into the POT method, the BM method has not been studied thoroughly. The present paper aims at providing conditions under which the BM method can be justified. We also provide a theoretical comparative study of the methods, which is in general consistent with the vast literature on comparing the method...
