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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 prove lower bounds on the error incurred when approximating any oscillating function using piecewise polynomial spaces. The estimates are explicit in the polynomial degree and have optimal dependence on the meshwidth and frequency when…

Numerical Analysis · Mathematics 2024-12-05 Jeffrey Galkowski

Consider the twin problems of estimating the connection probability matrix of an inhomogeneous random graph and the graphon of a W-random graph. We establish the minimax estimation rates with respect to the cut metric for classes of block…

Statistics Theory · Mathematics 2018-10-17 Olga Klopp , Nicolas Verzelen

The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-04-01 Fabian Kuhn , Thomas Moscibroda , Roger Wattenhofer

We consider a class of popular distributed non-convex optimization problems, in which agents connected by a network $\mathcal{G}$ collectively optimize a sum of smooth (possibly non-convex) local objective functions. We address the…

Optimization and Control · Mathematics 2020-01-08 Haoran Sun , Mingyi Hong

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

Networks are a widely-used tool to investigate the large-scale connectivity structure in complex systems and graphons have been proposed as an infinite size limit of dense networks. The detection of communities or other meso-scale…

Computation · Statistics 2021-01-05 Florian Klimm , Nick S. Jones , Michael T. Schaub

Many inference problems, notably the stochastic block model (SBM) that generates a random graph with a hidden community structure, undergo phase transitions as a function of the signal-to-noise ratio, and can exhibit hard phases in which…

Disordered Systems and Neural Networks · Physics 2019-04-09 Federico Ricci-Tersenghi , Guilhem Semerjian , Lenka Zdeborova

The study of Markov processes and broadcasting on trees has deep connections to a variety of areas including statistical physics, graphical models, phylogenetic reconstruction, Markov Chain Monte Carlo, and community detection in random…

Probability · Mathematics 2022-10-26 Frederic Koehler , Elchanan Mossel

Community detection is a central problem of network data analysis. Given a network, the goal of community detection is to partition the network nodes into a small number of clusters, which could often help reveal interesting structures. The…

Statistics Theory · Mathematics 2016-07-26 Chao Gao , Zongming Ma , Anderson Y. Zhang , Harrison H. Zhou

Neighborhood smoothing methods achieve minimax-optimal rates for estimating edge probabilities under graphon models, but their use for statistical inference has remained limited. The main obstacle is that classical neighborhood smoothers…

Methodology · Statistics 2026-03-17 Behzad Aalipur , Rachel Kilby

Inhomogeneous random graph models encompass many network models such as stochastic block models and latent position models. We consider the problem of statistical estimation of the matrix of connection probabilities based on the…

Statistics Theory · Mathematics 2017-09-14 Olga Klopp , Alexandre B. Tsybakov , Nicolas Verzelen

Bayesian predictive synthesis provides a coherent Bayesian framework for combining multiple predictive distributions, or agents, into a single updated prediction, extending Bayesian model averaging to allow general pooling of full…

Statistics Theory · Mathematics 2025-12-23 Marios Papamichalis , Regina Ruane

Sensitivity measures how much the output of an algorithm changes, in terms of Hamming distance, when part of the input is modified. While approximation algorithms with low sensitivity have been developed for many problems, no sensitivity…

Data Structures and Algorithms · Computer Science 2025-10-17 Noah Fleming , Yuichi Yoshida

The contextual stochastic block model (cSBM) was proposed for unsupervised community detection on attributed graphs where both the graph and the high-dimensional node information correlate with node labels. In the context of machine…

Social and Information Networks · Computer Science 2024-07-22 O. Duranthon , L. Zdeborová

Broadcasting on trees is a fundamental model from statistical physics that plays an important role in information theory, noisy computation and phylogenetic reconstruction within computational biology and linguistics. While this model…

Probability · Mathematics 2025-11-18 Han Huang , Elchanan Mossel

While graph convolutional networks show great practical promises, the theoretical understanding of their generalization properties as a function of the number of samples is still in its infancy compared to the more broadly studied case of…

Machine Learning · Computer Science 2024-11-22 O. Duranthon , L. Zdeborová

Large language model (LLM) training is often bottlenecked by memory constraints and stochastic gradient noise in extremely high-dimensional parameter spaces. Motivated by empirical evidence that many LLM gradient matrices are effectively…

Machine Learning · Computer Science 2026-03-24 Zehao Li , Tao Ren , Zishi Zhang , Xi Chen , Yijie Peng

Graphons offer a powerful framework for modeling large-scale networks, yet estimation remains challenging. We propose a novel approach that leverages a low-rank additive representation, yielding both a low-rank connection probability matrix…

Methodology · Statistics 2026-04-14 Xinyuan Fan , Feiyan Ma , Chenlei Leng , Weichi Wu

Robust statistical inference often faces a severe computational-statistical gap when dealing with complex parameter spaces. We investigate minimax signal detection in the Gaussian sequence model under strong $\epsilon$-contamination, where…

Statistics Theory · Mathematics 2026-05-13 Yikun Li , Matey Neykov