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Directed graphs have asymmetric connections, yet the current graph clustering methodologies cannot identify the potentially global structure of these asymmetries. We give a spectral algorithm called di-sim that builds on a dual measure of…
In this paper we introduce an estimator for the number of communities in the Stochastic Block Model (SBM), based on the maximization of a penalized version of the so-called Krichevsky-Trofimov mixture distribution. We prove its eventual…
Discovering statistical structure from links is a fundamental problem in the analysis of social networks. Choosing a misspecified model, or equivalently, an incorrect inference algorithm will result in an invalid analysis or even falsely…
Stochastic block models (SBMs) are a very commonly studied network model for community detection algorithms. In the standard form of an SBM, the $n$ vertices (or nodes) of a graph are generally divided into multiple pre-determined…
Two-view structure from motion (SfM) is the cornerstone of 3D reconstruction and visual SLAM (vSLAM). Many existing end-to-end learning-based methods usually formulate it as a brute regression problem. However, the inadequate utilization of…
We consider the problem of estimating the distribution function, the density and the hazard rate of the (unobservable) event time in the current status model. A well studied and natural nonparametric estimator for the distribution function…
We give answer to an open problem regarding consistency of the maximum likelihood estimators (MLEs) in generalized linear mixed models (GLMMs) involving crossed random effects. The solution to the open problem introduces an interesting,…
Statistical clustering in dynamic networks aims to identify groups of nodes with similar or distinct internal connectivity patterns as the network evolves over time. While early research primarily focused on static Stochastic Block Models…
Modern network analysis often involves multi-layer network data in which the nodes are aligned, and the edges on each layer represent one of the multiple relations among the nodes. Current literature on multi-layer network data is mostly…
Estimating the number of communities is a fundamental problem in network analysis under the stochastic block model (SBM). In this paper, we study penalized estimators for this task based on normalized likelihood criteria. We show that a…
With the growth of interest in network data across fields, the Exponential Random Graph Model (ERGM) has emerged as the leading approach to the statistical analysis of network data. ERGM parameter estimation requires the approximation of an…
We propose a new hierarchy of semidefinite programming relaxations for inference problems. As test cases, we consider the problem of community detection in block models. The vertices are partitioned into $k$ communities, and a graph is…
Community detection in graphs often relies on ad hoc algorithms with no clear specification about the node partition they define as the best, which leads to uninterpretable communities. Stochastic block models (SBM) offer a framework to…
Detecting communities in high-dimensional graphs can be achieved by applying random matrix theory where the adjacency matrix of the graph is modeled by a Stochastic Block Model (SBM). However, the SBM makes an unrealistic assumption that…
Spectral clustering is a widely used method for community detection in networks. We focus on a semi-supervised community detection scenario in the Partially Labeled Stochastic Block Model (PL-SBM) with two balanced communities, where a…
Recently, the Network Representation Learning (NRL) techniques, which represent graph structure via low-dimension vectors to support social-oriented application, have attracted wide attention. Though large efforts have been made, they may…
The performance of spectral clustering can be considerably improved via regularization, as demonstrated empirically in Amini et. al (2012). Here, we provide an attempt at quantifying this improvement through theoretical analysis. Under the…
In urban spatial networks, there is an interdependency between neighborhood roles and the transportation methods between neighborhoods. In this paper, we classify docking stations in bicycle-sharing networks to gain insight into the human…
This work studies the properties of the maximum likelihood estimator (MLE) of a non-linear model with Gaussian errors and multidimensional parameter. The observations are collected in a two-stage experimental design and are dependent since…
The stochastic block model is a canonical random graph model for clustering and community detection on network-structured data. Decades of extensive study on the problem have established many profound results, among which the phase…