Entries in relational data sets are often better

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entries in relational data sets are often better thought of as unobserved (Clauset et al. , 2008; Marchette and Priebe, 2008). The implications of this fact for subsequent analysis procedures – as well as on approximate likelihood maximization procedures and spectral methods in particular – remain unclear. The second assumption, that all nodes of interest have in fact been recorded, also appears rarely justified in practice. Indeed, it seems an arti- fact of this assumption that most commonly studied data sets consist of nodes which form a connected network. While in some cases the actual net- work may in fact consist of a single connected component, researchers may have unwittingly selected their data conditioned upon its appearance in the largest connected component of a much larger network. How this selection in turn may bias the subsequent fitting of models has only recently begun to be investigated (Handcock and Gile, 2010). A better understanding of missingness may also lend insight into opti- mal sampling procedures. Although researchers themselves may lack influ- ence over data gathering mechanisms, the potential of such methods for data reduction is clear. One particularly appealing approach is to first 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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Inference for Graphs and Networks 21 sample very large network data sets in a controlled manner, and then apply exact analysis techniques. In some cases the resultant approximation error can be bounded (Belabbas and Wolfe, 2009), implying that the effects on inferential procedures in question can be quantified. Other data reduction techniques may also help to meet the computa- tional challenges of network analysis; for example, Krishnamurthy et al. (2007) examined contractions of nodes into groups as a means of lessen- ing data volume. Such strategies of reducing network size while preserving relevant information provide an alternative to approximate likelihood max- imization that is deserving of further study. 1.6. Conclusion In many respects, the questions being asked of network data sets are not at all new to statisticians. However, the increasing prevalence of large net- works in contemporary application areas gives rise to both challenges and opportunities for statistical science. Tests for detecting network structure in turn form a key first step toward more sophisticated inferential procedures, and moreover provide practitioners with much-needed means of formal data analysis.
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