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Compressive sensing over graphs

Weiyu Xu, Enrique Mallada, Ao Tang
2011 2011 Proceedings IEEE INFOCOM  
In this paper, motivated by network inference and tomography applications, we study the problem of compressive sensing for sparse signal vectors over graphs.  ...  In particular, we are interested in recovering sparse vectors representing the properties of the edges from a graph.  ...  Note for edge e, the number of visiting random walks is equal to the degree of edge e's corresponding "edge" node in the bipartite graph. Theorem 8 bounds d max and d min . Theorem 8.  ... 
doi:10.1109/infcom.2011.5935018 dblp:conf/infocom/XuMT11 fatcat:odbgjrc7uzd7hpaarwf5xtdfiu

Compressive Sensing over Graphs [article]

Weiyu Xu, Enrique Mallada, Ao Tang
2010 arXiv   pre-print
In this paper, motivated by network inference and tomography applications, we study the problem of compressive sensing for sparse signal vectors over graphs.  ...  In particular, we are interested in recovering sparse vectors representing the properties of the edges from a graph.  ...  Note for edge e, the number of visiting random walks is equal to the degree of edge e's corresponding "edge" node in the bipartite graph. Theorem 8 bounds d max and d min . Theorem 8.  ... 
arXiv:1008.0919v1 fatcat:ilz4ognowzb7neabiduqwzox3a

Inferring Graphs from Cascades: A Sparse Recovery Framework [article]

Jean Pouget-Abadie, Thibaut Horel
2015 arXiv   pre-print
In the Network Inference problem, one seeks to recover the edges of an unknown graph from the observations of cascades propagating over this graph.  ...  In this paper, we approach this problem from the sparse recovery perspective.  ...  We are also grateful to the anonymous reviewers for their insightful feedback and suggestions.  ... 
arXiv:1505.05663v1 fatcat:ncd56t4a6vaybgaszaha4ypleu

Topology discovery of sparse random graphs with few participants

Animashree Anandkumar, Avinatan Hassidim, Jonathan Kelner
2012 Random structures & algorithms (Print)  
We also demonstrate that while consistent discovery is tractable for sparse random graphs using a small number of participants, in general, there are graphs which cannot be discovered by any algorithm  ...  We finally obtain a lower bound on the number of participants required by any algorithm to reconstruct the original random graph up to a given edit distance.  ...  be inferred using the knowledge of the bounds on delay variance in (2) .  ... 
doi:10.1002/rsa.20420 fatcat:5xhvb4pbavezvnbyxootfvyury

Topology discovery of sparse random graphs with few participants

Animashree Anandkumar, Avinatan Hassidim, Jonathan Kelner
2011 Proceedings of the ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems - SIGMETRICS '11  
We also demonstrate that while consistent discovery is tractable for sparse random graphs using a small number of participants, in general, there are graphs which cannot be discovered by any algorithm  ...  We finally obtain a lower bound on the number of participants required by any algorithm to reconstruct the original random graph up to a given edit distance.  ...  be inferred using the knowledge of the bounds on delay variance in (2) .  ... 
doi:10.1145/1993744.1993774 dblp:conf/sigmetrics/AnandkumarHK11 fatcat:lxr2oi3aprhmfdwrknq6mujsga

Topology discovery of sparse random graphs with few participants

Animashree Anandkumar, Avinatan Hassidim, Jonathan Kelner
2011 Performance Evaluation Review  
We also demonstrate that while consistent discovery is tractable for sparse random graphs using a small number of participants, in general, there are graphs which cannot be discovered by any algorithm  ...  We finally obtain a lower bound on the number of participants required by any algorithm to reconstruct the original random graph up to a given edit distance.  ...  be inferred using the knowledge of the bounds on delay variance in (2) .  ... 
doi:10.1145/2007116.2007146 fatcat:iqrbchm2p5gmxp44fhxd2v3avq

Concentration of random graphs and application to community detection [article]

Can M. Le, Elizaveta Levina, Roman Vershynin
2018 arXiv   pre-print
Applications of concentration results to the problem of community detection in networks are discussed in detail.  ...  We also review relevant network models that may be of interest to probabilists considering directions for new random matrix theory developments, and random matrix theory tools that may be of interest to  ...  For all nodes with degrees larger than 2a, reduce the weights of the edges incident to them in an arbitrary way, but so that all degrees of the new (weighted) network become bounded by 2a, resulting in  ... 
arXiv:1801.08724v1 fatcat:hokwnjsykrgexgp7256hatau4q

Information-theoretic limits of Bayesian network structure learning [article]

Asish Ghoshal, Jean Honorio
2017 arXiv   pre-print
In this paper, we study the information-theoretic limits of learning the structure of Bayesian networks (BNs), on discrete as well as continuous random variables, from a finite number of samples.  ...  En route to obtaining our main results, we obtain tight bounds on the number of sparse and non-sparse essential-DAGs.  ...  This gives a lower bound on the number of ways to add a terminal vertex to G 0 as: = for the sparse case, the number of possible choices for parents of a node in layer i is |G|, for some ensemble of  ... 
arXiv:1601.07460v4 fatcat:szgf6pzzwzg4dceqnoilfcwisi

Joint Inference of Multiple Graphs from Matrix Polynomials [article]

Madeline Navarro, Yuhao Wang, Antonio G. Marques, Caroline Uhler, Santiago Segarra
2020 arXiv   pre-print
A prominent example is that of Markov random fields, where the inverse of the covariance yields the sparse matrix of interest.  ...  Particularly important from an empirical viewpoint, we provide high-probability bounds on the recovery error as a function of the number of signals observed and other key problem parameters.  ...  Lemma 2 bounds in probability the sum of the norm of bounded random vectors whereas Lemma 3 is a standard result about tail bounds of chi-squared random variables.  ... 
arXiv:2010.08120v1 fatcat:vd4ms4jr5rfmrhopq2yp2hhhr4

Inferring Graphs from Cascades

Jean Pouget-Abadie, Thibaut Horel
2015 Proceedings of the 24th International Conference on World Wide Web - WWW '15 Companion  
In the Network Inference problem, one seeks to recover the edges of an unknown graph from the observations of cascades propagating over this graph.  ...  In this paper, we approach this problem from the sparse recovery perspective.  ...  We are also grateful to the anonymous reviewers for their insightful feedback and suggestions.  ... 
doi:10.1145/2740908.2744107 dblp:conf/www/Pouget-AbadieH15 fatcat:2b2h23h6zjaizghllstuw5eu4u

Topology Discovery of Sparse Random Graphs With Few Participants [article]

Animashree Anandkumar, Avinatan Hassidim, Jonathan Kelner
2012 arXiv   pre-print
We also demonstrate that while consistent discovery is tractable for sparse random graphs using a small number of participants, in general, there are graphs which cannot be discovered by any algorithm  ...  We finally obtain a lower bound on the number of participants required by any algorithm to reconstruct the original random graph up to a given edit distance.  ...  The first author is supported in part by the setup funds at UCI and the AFOSR Award FA9550-10-1-0310.  ... 
arXiv:1102.5063v3 fatcat:g45iw6rj6vh7fcnfnbbtoi2efe

Lower Bounds on Information Requirements for Causal Network Inference [article]

Xiaohan Kang, Bruce Hajek
2021 arXiv   pre-print
Comparison of the bounds and the performance achieved by two representative recovery algorithms are given for sparse random networks based on the Erdős-Rényi model.  ...  As a step to address this problem, this paper gives lower bounds on the error probability for causal network support recovery in a linear Gaussian setting.  ...  INTRODUCTION Causal networks refer to the directed graphs representing the causal relationships among a number of entities, and the inference of sparse large-scale causal networks is of great importance  ... 
arXiv:2102.00055v2 fatcat:vy6ddeik5nelngshemhpfiq7qq

Mouse obesity network reconstruction with a variational Bayes algorithm to employ aggressive false positive control

Benjamin A Logsdon, Gabriel E Hoffman, Jason G Mezey
2012 BMC Bioinformatics  
, in an experiment previously used for discovery and validation of network connections: an F2 intercross between the C57BL/6 J and C3H/HeJ mouse strains, where apolipoprotein E is null on the background  ...  that use the lasso and have bounds on type I error control.  ...  We would also like to thank two anonymous reviewers for suggestions which significantly improved the quality of this manuscript.  ... 
doi:10.1186/1471-2105-13-53 pmid:22471599 pmcid:PMC3338387 fatcat:4ebwp2drtrgczgqovh6qrwjdei

Peer-to-Peer Compressive Sensing for Network Monitoring

Ali Fattaholmanan, Hamid R. Rabiee, Payam Siyari, Ali Soltani-Farani, Ali Khodadadi
2015 IEEE Communications Letters  
Using this model, for the first time, an upper bound is derived for the number of measurements that each node must generate, such that the expected number of measurements observed by each node is sufficient  ...  In applications such as network routing, where all nodes need to monitor the status of the entire network, the situation is even worse.  ...  In addition, we theoretically derive an upper bound for the number of measurements that each node must generate.  ... 
doi:10.1109/lcomm.2014.2360386 fatcat:abmkeamyvrehzkecxpw7yt7x74

Inferring Broad Regulatory Biology from Time Course Data: Have We Reached an Upper Bound under Constraints Typical of In Vivo Studies?

Saurabh Vashishtha, Gordon Broderick, Travis J. A. Craddock, Mary Ann Fletcher, Nancy G. Klimas, Attila Csikász-Nagy
2015 PLoS ONE  
There is a growing appreciation for the network biology that regulates the coordinated expression of molecular and cellular markers however questions persist regarding the identifiability of these networks  ...  NetSim simulations of sparsely connected biological networks were used to evaluate two simple feature selection techniques used in the construction of linear Ordinary Differential Equation (ODE) models  ...  Acknowledgments This research was conducted in collaboration with and using the resources of the University of Miami Center for Computational Science (CCS), and the WestGrid platform supported by Compute  ... 
doi:10.1371/journal.pone.0127364 pmid:25984725 pmcid:PMC4435750 fatcat:lihyg4s5evhcvpb2vg4lcycha4
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