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Graph neural networks (GNNs) are learning architectures that rely on knowledge of the graph structure to generate meaningful representations of large-scale network data. GNN stability is thus important as in real-world scenarios there are…

Machine Learning · Computer Science 2021-04-27 Luana Ruiz , Zhiyang Wang , Alejandro Ribeiro

We consider the challenging problem of statistical inference for exponential-family random graph models based on a single observation of a random graph with complex dependence. To facilitate statistical inference, we consider random graphs…

Statistics Theory · Mathematics 2020-03-13 Michael Schweinberger

We consider a system of $N$ particles whose interactions are characterized by a (weighted) graph $G^N$. Each particle is a node of the graph with an internal state. The state changes according to Markovian dynamics that depend on the states…

Probability · Mathematics 2024-05-15 Sebastian Allmeier , Nicolas Gast

We propose an efficient $\epsilon$-differentially private algorithm, that given a simple {\em weighted} $n$-vertex, $m$-edge graph $G$ with a \emph{maximum unweighted} degree $\Delta(G) \leq n-1$, outputs a synthetic graph which…

Data Structures and Algorithms · Computer Science 2023-10-02 Jingcheng Liu , Jalaj Upadhyay , Zongrui Zou

Maximal clique enumeration is a fundamental graph mining task, but its utility is often limited by computational intractability and highly redundant output. To address these challenges, we introduce \emph{$\rho$-dense aggregators}, a novel…

Data Structures and Algorithms · Computer Science 2025-12-04 Noga Alon , Sabyasachi Basu , Shweta Jain , Haim Kaplan , Jakub Łącki , Blair D. Sullivan

In this work, we study the problem of community detection in the stochastic block model with adversarial node corruptions. Our main result is an efficient algorithm that can tolerate an $\epsilon$-fraction of corruptions and achieves error…

Data Structures and Algorithms · Computer Science 2022-07-26 Allen Liu , Ankur Moitra

Our main result is designing an algorithm that returns a vertex cover of $\mathcal{G}^\star$ with size at most $(3/2+\epsilon)$ times the expected size of the minimum vertex cover, using only $O(n/\epsilon p)$ non-adaptive queries. This…

Data Structures and Algorithms · Computer Science 2023-02-07 Mahsa Derakhshan , Naveen Durvasula , Nika Haghtalab

We study the frequentist properties of Bayesian statistical inference for the stochastic block model, with an unknown number of classes of varying sizes. We equip the space of vertex labellings with a prior on the number of classes and,…

Statistics Theory · Mathematics 2020-05-05 J. van Waaij , B. J. K. Kleijn

Associated to each graph G is a Gaussian graphical model. Such models are often used in high-dimensional settings, i.e. where there are relatively few data points compared to the number of variables. The maximum likelihood threshold of a…

Statistics Theory · Mathematics 2023-12-07 Daniel Irving Bernstein , Hayden Outlaw

We lower bound the complexity of finding $\epsilon$-stationary points (with gradient norm at most $\epsilon$) using stochastic first-order methods. In a well-studied model where algorithms access smooth, potentially non-convex functions…

Optimization and Control · Mathematics 2022-03-01 Yossi Arjevani , Yair Carmon , John C. Duchi , Dylan J. Foster , Nathan Srebro , Blake Woodworth

The hardcore model on a graph $G$ with parameter $\lambda>0$ is a probability measure on the collection of all independent sets of $G$, that assigns to each independent set $I$ a probability proportional to $\lambda^{|I|}$. In this paper we…

Probability · Mathematics 2021-06-25 Bhaswar B. Bhattacharya , Kavita Ramanan

We study the inference of communities in stochastic block models with a growing number of communities. For block models with $n$ vertices and a fixed number of communities $q$, it was predicted in Decelle et al. (2011) that there are…

Probability · Mathematics 2025-06-12 Byron Chin , Elchanan Mossel , Youngtak Sohn , Alexander S. Wein

We generalize the stochastic block model to the important case in which edges are annotated with weights drawn from an exponential family distribution. This generalization introduces several technical difficulties for model estimation,…

Machine Learning · Statistics 2013-05-27 Christopher Aicher , Abigail Z. Jacobs , Aaron Clauset

We consider the regression model with (known) random design. We investigate the minimax performances of an adaptive wavelet block thresholding estimator under the $\mathbb{L}^p$ risk with $p\ge 2$ over Besov balls. We prove that it is near…

Statistics Theory · Mathematics 2011-11-10 Christophe Chesneau

Significant progress has been made recently on theoretical analysis of estimators for the stochastic block model (SBM). In this paper, we consider the multi-graph SBM, which serves as a foundation for many application settings including…

Methodology · Statistics 2016-07-11 Qiuyi Han , Kevin S. Xu , Edoardo M. Airoldi

We study the problem of community recovery and detection in multi-layer stochastic block models, focusing on the critical network density threshold for consistent community structure inference. Using a prototypical two-block model, we…

Statistics Theory · Mathematics 2023-11-15 Jing Lei , Anru R. Zhang , Zihan Zhu

Bayesian network models (Erdos Renyi, stochastic block models, random dot product graphs, graphons) are widely used in neuroscience, epidemiology, and the social sciences, yet real networks are sparse, heterogeneous, and exhibit…

Statistics Theory · Mathematics 2026-01-07 Marios Papamichalis , Regina Ruane , Simon Lunagomez , Swati Chandna

We extend the latent position random graph model to the line graph of a random graph, which is formed by creating a vertex for each edge in the original random graph, and connecting each pair of edges incident to a common vertex in the…

Social and Information Networks · Computer Science 2024-02-27 Zachary Lubberts , Avanti Athreya , Youngser Park , Carey E. Priebe

Spectral graph theory has been widely applied in unsupervised and semi-supervised learning. In this paper, we find for the first time, to our knowledge, that it also plays a concrete role in supervised classification. It turns out that two…

Machine Learning · Computer Science 2017-06-14 Zhenfang Hu , Gang Pan , Zhaohui Wu

Stochastic blockmodels (SBM) and their variants, $e.g.$, mixed-membership and overlapping stochastic blockmodels, are latent variable based generative models for graphs. They have proven to be successful for various tasks, such as…

Machine Learning · Computer Science 2019-05-15 Nikhil Mehta , Lawrence Carin , Piyush Rai