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The stochastic block model is a popular tool for studying community structures in network data. We develop a goodness-of-fit test for the stochastic block model. The test statistic is based on the largest singular value of a residual matrix…
The stochastic block model (SBM) has been widely used to analyze network data. Various goodness-of-fit tests have been proposed to assess the adequacy of model structures. To the best of our knowledge, however, none of the existing…
The stochastic block model is a popular tool for detecting community structures in network data. Detecting the difference between two community structures is an important issue for stochastic block models. However, the two-sample test has…
Community detection is a fundamental problem in complex network data analysis. Though many methods have been proposed, most existing methods require the number of communities to be the known parameter, which is not in practice. In this…
Community detection in multi-layer networks is a fundamental task in complex network analysis across various areas like social, biological, and computer sciences. However, most existing algorithms assume that the number of communities is…
The stochastic block model is widely used for detecting community structures in network data. However, the research interest of much literature focuses on the study of one sample of stochastic block models. How to detect the difference of…
Latent block models are used for probabilistic biclustering, which is shown to be an effective method for analyzing various relational data sets. However, there has been no statistical test method for determining the row and column cluster…
We construct Bayesian and frequentist finite-sample goodness-of-fit tests for three different variants of the stochastic blockmodel for network data. Since all of the stochastic blockmodel variants are log-linear in form when block…
A valued stochastic blockmodel (SBM) is a general way to view networked data in which nodes are grouped into blocks and links between them are measured by counts or labels. This family allows for varying dyad sampling schemes, thereby…
Networks describe the, often complex, relationships between individual actors. In this work, we address the question of how to determine whether a parametric model, such as a stochastic block model or latent space model, fits a dataset well…
We present the first method for assessing the relevance of a model-based clustering result in a general framework. Standard validation criteria, like the adjusted Rand index, rely on external labels to assess partition accuracy;…
We present the first finite-sample goodness-of-fit test for the mixed membership stochastic block model (MMSBM). Using algebraic statistics theory, we derive a Markov basis that lets a Metropolis-Hastings sampler explore exactly the set of…
The objective of goodness-of-fit testing is to assess whether a dataset of observations is likely to have been drawn from a candidate probability distribution. This paper presents a rank-based family of goodness-of-fit tests that is…
We introduce a general framework for testing goodness-of-fit for Gaussian graphical models in both the low- and high-dimensional settings. This framework is based on a novel algorithm for generating exchangeable copies by conditioning on…
The Gaussian graphical model is routinely employed to model the joint distribution of multiple random variables. The graph it induces is not only useful for describing the relationship between random variables but also critical for…
We propose a goodness-of-fit test for degree-corrected stochastic block models (DCSBM). The test is based on an adjusted chi-square statistic for measuring equality of means among groups of $n$ multinomial distributions with $d_1,\dots,d_n$…
Community detection in directed networks is a central task in network analysis. Unlike undirected networks, directed networks encode inherently asymmetric relationships, giving rise to sender and receiver roles that may each follow distinct…
Methods of performing anomaly detection on high-dimensional data sets are needed, since algorithms which are trained on data are only expected to perform well on data that is similar to the training data. There are theoretical results on…
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…
We propose a nonparametric statistical test for goodness-of-fit: given a set of samples, the test determines how likely it is that these were generated from a target density function. The measure of goodness-of-fit is a divergence…