相关论文: When is Nontrivial Estimation Possible for Graphon…

As relational datasets modeled as graphs keep increasing in size and their data-acquisition is permeated by uncertainty, graph-based analysis techniques can become computationally and conceptually challenging. In particular, node centrality…

With the advent of structured data in the form of social networks, genetic circuits and protein interaction networks, statistical analysis of networks has gained popularity over recent years. Stochastic block model constitutes a classical…

Stochastic blockmodels are generative network models where the vertices are separated into discrete groups, and the probability of an edge existing between two vertices is determined solely by their group membership. In this paper, we…

The advent of large-scale inference has spurred reexamination of conventional statistical thinking. In a Gaussian model for $n$ many $z$-scores with at most $k < \frac{n}{2}$ nonnulls, Efron suggests estimating the location and scale…

We study the distributed optimization problem over a graphon with a continuum of nodes, which is regarded as the limit of the distributed networked optimization as the number of nodes goes to infinity. Each node has a private local cost…

Recently network analysis has gained more and more attentions in statistics, as well as in computer science, probability, and applied mathematics. Community detection for the stochastic block model (SBM) is probably the most studied topic…

The stochastic block model (SBM) is a random graph model with different group of vertices connecting differently. It is widely employed as a canonical model to study clustering and community detection, and provides a fertile ground to study…

We study sharp detection thresholds for degree corrections in Stochastic Block Models in the context of a goodness of fit problem, and explore the effect of the unknown community assignment (a high dimensional nuisance parameter) and the…

The problem of learning graphons has attracted considerable attention across several scientific communities, with significant progress over the recent years in sparser regimes. Yet, the current techniques still require diverging degrees in…

In the high dimensional Stochastic Blockmodel for a random network, the number of clusters (or blocks) K grows with the number of nodes N. Two previous studies have examined the statistical estimation performance of spectral clustering and…

The stochastic block model is one of the oldest and most ubiquitous models for studying clustering and community detection. In an exciting sequence of developments, motivated by deep but non-rigorous ideas from statistical physics, Decelle…

Exchangeable random graphs, which include some of the most widely studied network models, have emerged as the mainstay of statistical network analysis in recent years. Graphons, which are the central objects in graph limit theory, provide a…

Statistical analysis of network is an active research area and the literature counts a lot of papers concerned with network models and statistical analysis of networks. However, very few papers deal with missing data in network analysis and…

We present asymptotic and finite-sample results on the use of stochastic blockmodels for the analysis of network data. We show that the fraction of misclassified network nodes converges in probability to zero under maximum likelihood…

In latent-position random graph models (LPMs), latent vertex positions $U_{1},\ldots,U_{n}$ are sampled from some distribution on a latent space $\Omega$, then edges of an observed graph $G = ([n],E)$ are sampled with some probability…

We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is…

We investigate possible large deviation principles (LDPs) for the $n$-vertex sampling from a given graphon with various speeds $s(n)$ and resolve all the cases except when the speed $s(n)$ is of order $n^2$. For quadratic speed…

Borgs, Chayes, Gaudio, Petti and Sen [arXiv:2007.14508] proved a large deviation principle for block model random graphs with rational block ratios. We strengthen their result by allowing any block ratios (and also establish a simpler…

We study community detection in the contextual stochastic block model arXiv:1807.09596 [cs.SI], arXiv:1607.02675 [stat.ME]. In arXiv:1807.09596 [cs.SI], the second author studied this problem in the setting of sparse graphs with…

Spectral clustering has been widely used for community detection in network sciences. While its empirical successes are well-documented, a clear theoretical understanding, particularly for sparse networks where degrees are much smaller than…