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Inference_for_Graphs_and_Networks.pdf

Classical inferential frameworks are precisely what

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Classical inferential frameworks are precisely what is most needed in practice, and yet as we have seen, their exact implementation can prove remarkably difficult in the setting of modern high-dimensional, non- Euclidean network data. To this end, we hope that this chapter has suc- ceeded in helping to chart a path toward the ultimate goal of a unified and coherent framework for the statistical analysis of large-scale network data sets. Acknowledgments Research supported in part by the National Science Foundation under Grants DMS-0631636 and CBET-0730389; by the Defense Advanced Research Projects Agency under Grant No. HR0011-07-1-0007; by the US Army Research Office under PECASE Award W911NF-09-1-0555 and MURI Award 58153-MA-MUR; by the UK EPSRC under Mathematical Sciences Established Career Fellowship EP/K005413/1 and Institutional Sponsorship Award EP/K503459/1; by the UK Royal Society under a Wolfson Research Merit Award; and by Marie Curie FP7 Integration Grant PCIG12-GA-2012-334622 within the 7th European Union Frame- work Program. Copyright © 2014. Imperial College Press. All rights reserved. May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law. EBSCO Publishing : eBook Collection (EBSCOhost) - printed on 2/16/2016 3:37 AM via CGC-GROUP OF COLLEGES (GHARUAN) AN: 779681 ; Heard, Nicholas, Adams, Niall M..; Data Analysis for Network Cyber-security Account: ns224671
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22 B. P. Olding and P. J. Wolfe Appendix: A Review of Approaches to Network Analysis Three canonical problems in network data analysis have consistently drawn attention across different contexts: network model elicitation, network model inference, and methods of approximate inference. A.1. Model Elicitation With new network data sets being generated or discovered at rapid rates in a wide variety of fields, model elicitation – independent even of model selection – remains an important topic of investigation. Although graph theory provides a natural starting point for identifying possible models for graph-valued data, practitioners have consistently found that models such as Erd¨ os–R´ enyi lack sufficient explanatory power for complex data sets. Its inability to model all but the simplest of degree distributions has forced researchers to seek out more complicated models. Barab´asi (2002) and Palla et al. (2005) survey a wide variety of network data sets and conclude that commonly encountered degree sequences follow a power law or similarly heavy-tailed distribution; the Erd¨ os–R´ enyi model, with its marginally binomial degree distribution, is obviously insufficient to describe such data sets. Barab´asi and Albert (1999) introduced an alterna- tive by way of a generative network modeling scheme termed “preferential attachment” to explicitly describe power-law degree sequences. Under this scheme, nodes are added sequentially to the graph, being preferentially linked to existing nodes based on the current degree sequence. A moment’s reflection will convince the reader that this model is in fact an example of a Dirichlet process (Pemantle, 2007).
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  • Spring '12
  • Kushal Kanwar
  • Graph Theory, Statistical hypothesis testing, Imperial College Press, applicable copyright law

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