Compressed Network Tomography for Probabilistic Tree Mixture Models
We consider the problem of network tomography in probabilistic tree mixture models. We invoke the theory of compressed sensing and prove that the distribution of a random communication network model with n nodes represented by a probabilistic mixture of k trees can be identified using low order rout...
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| creator | Khajehnejad, M. A. Khojastepour, A. Hassibi, B. |
| description | We consider the problem of network tomography in probabilistic tree mixture models. We invoke the theory of compressed sensing and prove that the distribution of a random communication network model with n nodes represented by a probabilistic mixture of k trees can be identified using low order routing summaries pertinent to groups of small sizes d |
| doi_str_mv | 10.1109/GLOCOM.2011.6133853 |
| format | Conference Proceeding |
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A. ; Khojastepour, A. ; Hassibi, B.</creator><creatorcontrib>Khajehnejad, M. A. ; Khojastepour, A. ; Hassibi, B.</creatorcontrib><description>We consider the problem of network tomography in probabilistic tree mixture models. We invoke the theory of compressed sensing and prove that the distribution of a random communication network model with n nodes represented by a probabilistic mixture of k trees can be identified using low order routing summaries pertinent to groups of small sizes d <;<; n in the network. We prove that, if the number of collected statistics m is at least O(n log k ), then certain classes of inference algorithms can successfully determine the unknown model, i.e. the topologies of mixing trees and their corresponding probabilities. We show that a variation of ℓ 1 minimization over the space of all possible trees of n nodes can be used for this purpose. In addition, we propose a novel inference algorithm with a complexity polynomial in n log k , with the same provable guarantee. The proposed model is applicable to practical situations such as ad-hoc and Peer-to-Peer(P2P) networks, and the presented inference method can lead to distributed protocols for network monitoring and tomography. 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A.</creatorcontrib><creatorcontrib>Khojastepour, A.</creatorcontrib><creatorcontrib>Hassibi, B.</creatorcontrib><title>Compressed Network Tomography for Probabilistic Tree Mixture Models</title><title>2011 IEEE Global Telecommunications Conference - GLOBECOM 2011</title><addtitle>GLOCOM</addtitle><description>We consider the problem of network tomography in probabilistic tree mixture models. We invoke the theory of compressed sensing and prove that the distribution of a random communication network model with n nodes represented by a probabilistic mixture of k trees can be identified using low order routing summaries pertinent to groups of small sizes d <;<; n in the network. We prove that, if the number of collected statistics m is at least O(n log k ), then certain classes of inference algorithms can successfully determine the unknown model, i.e. the topologies of mixing trees and their corresponding probabilities. We show that a variation of ℓ 1 minimization over the space of all possible trees of n nodes can be used for this purpose. In addition, we propose a novel inference algorithm with a complexity polynomial in n log k , with the same provable guarantee. The proposed model is applicable to practical situations such as ad-hoc and Peer-to-Peer(P2P) networks, and the presented inference method can lead to distributed protocols for network monitoring and tomography. In particular, we provide preliminary insight and numerical results on how the ideas are amenable to wireless sensor networks.</description><subject>Ad hoc networks</subject><subject>Inference algorithms</subject><subject>Mathematical model</subject><subject>Peer to peer computing</subject><subject>Probabilistic logic</subject><subject>Routing</subject><subject>Tomography</subject><issn>1930-529X</issn><issn>2576-764X</issn><isbn>9781424492664</isbn><isbn>1424492661</isbn><isbn>9781424492688</isbn><isbn>9781424492671</isbn><isbn>1424492688</isbn><isbn>142449267X</isbn><fulltext>true</fulltext><rsrctype>conference_proceeding</rsrctype><creationdate>2011</creationdate><recordtype>conference_proceeding</recordtype><sourceid>6IE</sourceid><sourceid>RIE</sourceid><recordid>eNpVkLtOwzAYRs1NopQ-QZe8QILvjkcUQUFKKUOQulWx8xsMiRzZQbRvTyW6MJ3hk470HYSWBBeEYH23qjfVZl1QTEghCWOlYGdooVVJOOVcU1mW52hGhZK5knx78W-T_BLNiGY4F1Rvr9FNSp8YC14KMkNVFYYxQkrQZS8w_YT4lTVhCO-xHT8OmQsxe43BtMb3Pk3eZk0EyNZ-P33HI0MHfbpFV67tEyxOnKO3x4emesrrzeq5uq9zT5SYcsqtNVIaZ4m0zDrTua7FlGsthFUGlNDAACt1fGeNkNwYwkA6YS0F5zCbo-Wf1wPAbox-aONhd-rBfgGzMlGg</recordid><startdate>201112</startdate><enddate>201112</enddate><creator>Khajehnejad, M. A.</creator><creator>Khojastepour, A.</creator><creator>Hassibi, B.</creator><general>IEEE</general><scope>6IE</scope><scope>6IH</scope><scope>CBEJK</scope><scope>RIE</scope><scope>RIO</scope></search><sort><creationdate>201112</creationdate><title>Compressed Network Tomography for Probabilistic Tree Mixture Models</title><author>Khajehnejad, M. A. ; Khojastepour, A. ; Hassibi, B.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-i175t-24ccb66bfc16c3cfbdfda0249955c7be759e3e077853cb564bb13e6f5cc2eff03</frbrgroupid><rsrctype>conference_proceedings</rsrctype><prefilter>conference_proceedings</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Ad hoc networks</topic><topic>Inference algorithms</topic><topic>Mathematical model</topic><topic>Peer to peer computing</topic><topic>Probabilistic logic</topic><topic>Routing</topic><topic>Tomography</topic><toplevel>online_resources</toplevel><creatorcontrib>Khajehnejad, M. A.</creatorcontrib><creatorcontrib>Khojastepour, A.</creatorcontrib><creatorcontrib>Hassibi, B.</creatorcontrib><collection>IEEE Electronic Library (IEL) Conference Proceedings</collection><collection>IEEE Proceedings Order Plan (POP) 1998-present by volume</collection><collection>IEEE Xplore All Conference Proceedings</collection><collection>IEEE Electronic Library (IEL)</collection><collection>IEEE Proceedings Order Plans (POP) 1998-present</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Khajehnejad, M. A.</au><au>Khojastepour, A.</au><au>Hassibi, B.</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>Compressed Network Tomography for Probabilistic Tree Mixture Models</atitle><btitle>2011 IEEE Global Telecommunications Conference - GLOBECOM 2011</btitle><stitle>GLOCOM</stitle><date>2011-12</date><risdate>2011</risdate><spage>1</spage><epage>6</epage><pages>1-6</pages><issn>1930-529X</issn><eissn>2576-764X</eissn><isbn>9781424492664</isbn><isbn>1424492661</isbn><eisbn>9781424492688</eisbn><eisbn>9781424492671</eisbn><eisbn>1424492688</eisbn><eisbn>142449267X</eisbn><abstract>We consider the problem of network tomography in probabilistic tree mixture models. We invoke the theory of compressed sensing and prove that the distribution of a random communication network model with n nodes represented by a probabilistic mixture of k trees can be identified using low order routing summaries pertinent to groups of small sizes d <;<; n in the network. We prove that, if the number of collected statistics m is at least O(n log k ), then certain classes of inference algorithms can successfully determine the unknown model, i.e. the topologies of mixing trees and their corresponding probabilities. We show that a variation of ℓ 1 minimization over the space of all possible trees of n nodes can be used for this purpose. In addition, we propose a novel inference algorithm with a complexity polynomial in n log k , with the same provable guarantee. The proposed model is applicable to practical situations such as ad-hoc and Peer-to-Peer(P2P) networks, and the presented inference method can lead to distributed protocols for network monitoring and tomography. In particular, we provide preliminary insight and numerical results on how the ideas are amenable to wireless sensor networks.</abstract><pub>IEEE</pub><doi>10.1109/GLOCOM.2011.6133853</doi><tpages>6</tpages></addata></record> |
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| ispartof | 2011 IEEE Global Telecommunications Conference - GLOBECOM 2011, 2011, p.1-6 |
| issn | 1930-529X 2576-764X |
| language | eng |
| recordid | cdi_ieee_primary_6133853 |
| source | IEEE Electronic Library (IEL) Conference Proceedings |
| subjects | Ad hoc networks Inference algorithms Mathematical model Peer to peer computing Probabilistic logic Routing Tomography |
| title | Compressed Network Tomography for Probabilistic Tree Mixture Models |
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