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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…
Networks or graphs can easily represent a diverse set of data sources that are characterized by interacting units or actors. Social networks, representing people who communicate with each other, are one example. Communities or clusters of…
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…
This paper establishes asymptotic results for the maximum likelihood and restricted maximum likelihood (REML) estimators of the parameters in the nested error regression model for clustered data when both of the number of independent…
We propose to estimate the number of communities in degree-corrected stochastic block models based on a pseudo likelihood ratio statistic. To this end, we introduce a method that combines spectral clustering with binary segmentation. This…
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…
The stochastic block model is able to generate different network partitions, ranging from traditional assortative communities to disassortative structures. Since the degree-corrected stochastic block model does not specify which mixing…
Graph clustering is a fundamental task in unsupervised learning with broad real-world applications. While spectral clustering methods for undirected graphs are well-established and guided by a minimum cut optimization consensus, their…
In Stochastic blockmodels, which are among the most prominent statistical models for cluster analysis of complex networks, clusters are defined as groups of nodes with statistically similar link probabilities within and between groups. A…
We consider the problem of community detection in the Stochastic Block Model with a finite number $K$ of communities of sizes linearly growing with the network size $n$. This model consists in a random graph such that each pair of vertices…
We propose a new class of models for variable clustering called Asymptotic Independent block (AI-block) models, which defines population-level clusters based on the independence of the maxima of a multivariate stationary mixing random…
Spectral clustering is a fast and popular algorithm for finding clusters in networks. Recently, Chaudhuri et al. (2012) and Amini et al.(2012) proposed inspired variations on the algorithm that artificially inflate the node degrees for…
The stochastic block model (SBM) is a probabilistic model de- signed to describe heterogeneous directed and undirected graphs. In this paper, we address the asymptotic inference on SBM by use of maximum- likelihood and variational…
We tackle the problem of high-dimensional nonparametric density estimation by taking the class of log-concave densities on $\mathbb{R}^p$ and incorporating within it symmetry assumptions, which facilitate scalable estimation algorithms and…
Variational methods for parameter estimation are an active research area, potentially offering computationally tractable heuristics with theoretical performance bounds. We build on recent work that applies such methods to network data, and…
Dynamical systems comprising of multiple components that can be partitioned into distinct blocks originate in many scientific areas. A pertinent example is the interactions between financial assets and selected macroeconomic indicators,…
Logistic regression is commonly used for modeling dichotomous outcomes. In the classical setting, where the number of observations is much larger than the number of parameters, properties of the maximum likelihood estimator in logistic…
The Stochastic Block Model (Holland et al., 1983) is a mixture model for heterogeneous network data. Unlike the usual statistical framework, new nodes give additional information about the previous ones in this model. Thereby the…
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…
Spectral clustering has been one of the widely used methods for community detection in networks. However, large-scale networks bring computational challenges to the eigenvalue decomposition therein. In this paper, we study the spectral…