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Mutual information is widely used in artificial intelligence, in a descriptive way, to measure the stochastic dependence of discrete random variables. In order to address questions such as the reliability of the empirical value, one must…

Artificial Intelligence · Computer Science 2014-08-08 Marco Zaffalon , Marcus Hutter

Motivated by multi-subject experiments in neuroimaging studies, we develop a modeling framework for joint community detection in a group of related networks, which can be considered as a sample from a population of networks. The proposed…

Applications · Statistics 2020-03-24 Subhadeep Paul , Yuguo Chen

We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections. A few examples where this problem is relevant are compressed sensing, sparse superposition codes, and code division multiple access.…

Information Theory · Computer Science 2020-08-31 Jean Barbier , Nicolas Macris , Mohamad Dia , Florent Krzakala

Random factor graphs provide a powerful framework for the study of inference problems such as decoding problems or the stochastic block model. Information-theoretically the key quantity of interest is the mutual information between the…

Discrete Mathematics · Computer Science 2021-04-27 Amin Coja-Oghlan , Max Hahn-Klimroth , Philipp Loick , Noela Müller , Konstantinos Panagiotou , Matija Pasch

Stochastic blockmodels and variants thereof are among the most widely used approaches to community detection for social networks and relational data. A stochastic blockmodel partitions the nodes of a network into disjoint sets, called…

Methodology · Statistics 2015-09-16 Diego Franco Saldana , Yi Yu , Yang Feng

While Shannon's mutual information has widespread applications in many disciplines, for practical applications it is often difficult to calculate its value accurately for high-dimensional variables because of the curse of dimensionality.…

Information Theory · Computer Science 2018-04-02 Wentao Huang , Kechen Zhang

The quest for a quantitative characterization of community and modular structure of complex networks produced a variety of methods and algorithms to classify different networks. However, it is not clear if such methods provide consistent,…

Physics and Society · Physics 2016-01-08 Juan Ignacio Perotti , Claudio Juan Tessone , Guido Caldarelli

We studied the mutual information between a stimulus and a large system consisting of stochastic, statistically independent elements that respond to a stimulus. The Mutual Information (MI) of the system saturates exponentially with system…

Statistical Mechanics · Physics 2009-11-07 Kukjin Kang , Haim Sompolinsky

We consider a generalization of an important class of high-dimensional inference problems, namely spiked symmetric matrix models, often used as probabilistic models for principal component analysis. Such paradigmatic models have recently…

Information Theory · Computer Science 2020-05-19 Jean Barbier , Galen Reeves

The stochastic block model (SBM) is a random graph model with different group of vertices connecting differently. It is widely employed as a canonical model to study clustering and community detection, and provides a fertile ground to study…

Probability · Mathematics 2023-10-26 Emmanuel Abbe

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…

Statistics Theory · Mathematics 2013-10-30 Peter Bickel , David Choi , Xiangyu Chang , Hai Zhang

We consider the community detection problem in sparse random hypergraphs. Angelini et al. (2015) conjectured the existence of a sharp threshold on model parameters for community detection in sparse hypergraphs generated by a hypergraph…

Probability · Mathematics 2021-08-05 Soumik Pal , Yizhe Zhu

Mutual information is fundamentally important for measuring statistical dependence between variables and for quantifying information transfer by signaling and communication mechanisms. It can, however, be challenging to evaluate for…

Information Theory · Computer Science 2014-07-29 Clive G. Bowsher , Margaritis Voliotis

In this paper we propose a method of proving impossibility results based on applying strong data-processing inequalities to estimate mutual information between sets of variables forming certain Markov random fields. The end result is that…

Information Theory · Computer Science 2020-05-22 Yury Polyanskiy , Yihong Wu

The stochastic block model is one of the most studied network models for community detection. It is well-known that most algorithms proposed for fitting the stochastic block model likelihood function cannot scale to large-scale networks.…

Methodology · Statistics 2021-08-31 Jiangzhou Wang , Jingfei Zhang , Binghui Liu , Ji Zhu , Jianhua Guo

In the present paper we study a sparse stochastic network enabled with a block structure. The popular Stochastic Block Model (SBM) and the Degree Corrected Block Model (DCBM) address sparsity by placing an upper bound on the maximum…

Machine Learning · Statistics 2021-10-08 Majid Noroozi , Marianna Pensky , Ramchandra Rimal

Vindicating a sophisticated but non-rigorous physics approach called the cavity method, we establish a formula for the mutual information in statistical inference problems induced by random graphs and we show that the mutual information…

Discrete Mathematics · Computer Science 2018-06-28 Amin Coja-Oghlan , Florent Krzakala , Will Perkins , Lenka Zdeborova

We take an information theoretic perspective on a classical sparse-sampling noisy linear model and present an analytical expression for the mutual information, which plays central role in a variety of communications/processing problems.…

Information Theory · Computer Science 2014-03-25 Wasim Huleihel , Neri Merhav , Shlomo Shamai

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

In statistical physics entropy is usually introduced as a global quantity which expresses the amount of information that would be needed to specify the microscopic configuration of a system. However, for lattice models with infinitely many…

Statistical Mechanics · Physics 2015-06-12 Ulrich Müller , Haye Hinrichsen