NDLI: Learning the graph of epidemic cascades

Content Provider	ACM Digital Library
Author	Sanghavi, Sujay Netrapalli, Praneeth
Abstract	We consider the problem of finding the graph on which an epidemic spreads, given only the times when each node gets infected. While this is a problem of central importance in several contexts -- offline and online social networks, e-commerce, epidemiology -- there has been very little work, analytical or empirical, on finding the graph. Clearly, it is impossible to do so from just one epidemic; our interest is in learning the graph from a small number of independent epidemics. For the classic and popular "independent cascade" epidemics, we analytically establish sufficient conditions on the number of epidemics for both the global maximum-likelihood (ML) estimator, and a natural greedy algorithm to succeed with high probability. Both results are based on a key observation: the global graph learning problem decouples into n local problems -- one for each node. For a node of degree d, we show that its neighborhood can be reliably found once it has been infected $O(d^{2}$ log n) times (for ML on general graphs) or O(d log n) times (for greedy on trees). We also provide a corresponding information-theoretic lower bound of Ω(d log n); thus our bounds are essentially tight. Furthermore, if we are given side-information in the form of a super-graph of the actual graph (as is often the case), then the number of epidemic samples required -- in all cases -- becomes independent of the network size n.
Starting Page	211
Ending Page	222
Page Count	12
File Format	PDF
ISSN	01635999
DOI	10.1145/2318857.2254783
Journal	ACM SIGMETRICS Performance Evaluation Review (PERV)
Volume Number	40
Issue Number	1
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2014-01-10
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Epidemics Graph structure learning Cascades
Content Type	Text
Resource Type	Article
Subject	Computer Networks and Communications Hardware and Architecture Software

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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