相关论文: Testing Degree Corrections in Stochastic Block Mod…

Diagnostic accuracy studies assess sensitivity and specificity of a new index test in relation to an established comparator or the reference standard. The development and selection of the index test is usually assumed to be conducted prior…

Many iterative procedures in stochastic optimization exhibit a transient phase followed by a stationary phase. During the transient phase the procedure converges towards a region of interest, and during the stationary phase the procedure…

This paper establishes the theoretical limits of graph clustering under the Popularity-Adjusted Block Model (PABM), addressing limitations of existing models. In contrast to the Stochastic Block Model (SBM), which assumes uniform vertex…

The stochastic block model is a canonical model of communities in random graphs. It was introduced in the social sciences and statistics as a model of communities, and in theoretical computer science as an average case model for graph…

The problem of community detection receives great attention in recent years. Many methods have been proposed to discover communities in networks. In this paper, we propose a Gaussian stochastic blockmodel that uses Gaussian distributions to…

We study problem-dependent rates, i.e., generalization errors that scale near-optimally with the variance, the effective loss, or the gradient norms evaluated at the "best hypothesis." We introduce a principled framework dubbed "uniform…

Consider the community detection problem in random hypergraphs under the non-uniform hypergraph stochastic block model (HSBM), where each hyperedge appears independently with some given probability depending only on the labels of its…

We consider community detection in Degree-Corrected Stochastic Block Models (DC-SBM). We propose a spectral clustering algorithm based on a suitably normalized adjacency matrix. We show that this algorithm consistently recovers the…

We investigate the unsupervised node classification problem on random hypergraphs under the non-uniform Hypergraph Stochastic Block Model (HSBM) with two equal-sized communities. In this model, edges appear independently with probabilities…

In this article, we extend a statistical test of graph clusterability, the $\delta$ test, to directed graphs with no self loops. The $\delta$ test, originally designed for undirected graphs, is based on the premise that graphs with a…

In this paper, we study the detection boundary for minimax hypothesis testing in the context of high-dimensional, sparse binary regression models. Motivated by genetic sequencing association studies for rare variant effects, we investigate…

In this survey paper it is illustrated how spectral clustering methods for unweighted graphs are adapted to the dense and sparse regimes. Whereas Laplacian and modularity based spectral clustering is apt to dense graphs, recent results show…

Measuring graph clustering quality remains an open problem. To address it, we introduce quality measures based on comparisons of intra- and inter-cluster densities, an accompanying statistical test of the significance of their differences…

We consider the problem of clustering a graph $G$ into two communities by observing a subset of the vertex correlations. Specifically, we consider the inverse problem with observed variables $Y=B_G x \oplus Z$, where $B_G$ is the incidence…

The degrees are a classical and relevant way to study the topology of a network. They can be used to assess the goodness-of-fit for a given random graph model. In this paper we introduce goodness-of-fit tests for two classes of models.…

A network may have weak signals and severe degree heterogeneity, and may be very sparse in one occurrence but very dense in another. SCORE (Jin, 2015) is a recent approach to network community detection. It accommodates severe degree…

In this paper, we analyse classical variants of the Spectral Clustering (SC) algorithm in the Dynamic Stochastic Block Model (DSBM). Existing results show that, in the relatively sparse case where the expected degree grows logarithmically…

We give nearly optimal bounds on the sample complexity of $(\widetilde{\Omega}(\epsilon),\epsilon)$-tolerant testing the $\rho$-independent set property in the dense graph setting. In particular, we give an algorithm that inspects a random…

We study the statistical performance of semidefinite programming (SDP) relaxations for clustering under random graph models. Under the $\mathbb{Z}_{2}$ Synchronization model, Censored Block Model and Stochastic Block Model, we show that SDP…

Networks are useful representations of many systems with interacting entities, such as social, biological and physical systems. Characterizing the meso-scale organization, i.e. the community structure, is an important problem in network…