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Compressive sensing over graphs

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. ...

##
###
Compressive Sensing over Graphs
[article]

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. ...

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

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. ...

##
###
Topology discovery of sparse random graphs with few participants

2012
*
Random structures & algorithms (Print)
*

We also demonstrate that while consistent discovery is tractable

doi:10.1002/rsa.20420
fatcat:5xhvb4pbavezvnbyxootfvyury
*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) . ...##
###
Topology discovery of sparse random graphs with few participants

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

doi:10.1145/1993744.1993774
dblp:conf/sigmetrics/AnandkumarHK11
fatcat:lxr2oi3aprhmfdwrknq6mujsga
*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) . ...##
###
Topology discovery of sparse random graphs with few participants

2011
*
Performance Evaluation Review
*

We also demonstrate that while consistent discovery is tractable

doi:10.1145/2007116.2007146
fatcat:iqrbchm2p5gmxp44fhxd2v3avq
*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) . ...##
###
Concentration of random graphs and application to community detection
[article]

2018
*
arXiv
*
pre-print

Applications

arXiv:1801.08724v1
fatcat:hokwnjsykrgexgp7256hatau4q
*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*...##
###
Information-theoretic limits of Bayesian network structure learning
[article]

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*...

##
###
Joint Inference of Multiple Graphs from Matrix Polynomials
[article]

2020
*
arXiv
*
pre-print

A prominent example is that

arXiv:2010.08120v1
fatcat:vd4ms4jr5rfmrhopq2yp2hhhr4
*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. ...##
###
Inferring Graphs from Cascades

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. ...

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

2012
*
arXiv
*
pre-print

We also demonstrate that while consistent discovery is tractable

arXiv:1102.5063v3
fatcat:g45iw6rj6vh7fcnfnbbtoi2efe
*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. ...##
###
Lower Bounds on Information Requirements for Causal Network Inference
[article]

2021
*
arXiv
*
pre-print

Comparison

arXiv:2102.00055v2
fatcat:vy6ddeik5nelngshemhpfiq7qq
*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 ...##
###
Mouse obesity network reconstruction with a variational Bayes algorithm to employ aggressive false positive control

2012
*
BMC Bioinformatics
*

,

doi:10.1186/1471-2105-13-53
pmid:22471599
pmcid:PMC3338387
fatcat:4ebwp2drtrgczgqovh6qrwjdei
*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. ...##
###
Peer-to-Peer Compressive Sensing for Network Monitoring

2015
*
IEEE Communications Letters
*

Using this model,

doi:10.1109/lcomm.2014.2360386
fatcat:abmkeamyvrehzkecxpw7yt7x74
*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. ...##
###
Inferring Broad Regulatory Biology from Time Course Data: Have We Reached an Upper Bound under Constraints Typical of In Vivo Studies?

2015
*
PLoS ONE
*

There is a growing appreciation

doi:10.1371/journal.pone.0127364
pmid:25984725
pmcid:PMC4435750
fatcat:lihyg4s5evhcvpb2vg4lcycha4
*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 ...
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