The stepped appearance of the curve is an artifact of

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nate hypotheses. (The stepped appearance of the curve is an artifact of the importance sampling weights.) Also shown is an ROC upper bound, obtained using knowledge of the true group membership for each node. sup under two-group stochastic block likelihood for the exact sup operation. The substantial power of this test for the data of Section 1.4.1 is visible in Figure 1.6 ; the estimated p-value of this data set remains below 10 3 . Note that specification of parameters p 00 , p 01 , and p 11 was required to generate Figure 1.6 via simulation; here, we manually fit these three parameters to the data, starting with their estimates under the two-group stochastic block model, until the likelihood of the observed data approached the median likelihood under our parameterization. A more formal fitting procedure could, of course, be adopted in practice. 1.5. Open Problems in Network Inference The examples of Sections 1.3 and 1.4 were designed to be illustrative, and yet they also serve to illuminate broader questions that arise as we seek to extend classical notions of statistics to network data. As we have seen in Section 1.3, for instance, the inclusion of latent k -ary categorical covari- ates immediately necessitates a variety of combinatorial calculations. The increasing prevalence of large, complex network data sets presents an even more significant computational challenge for statistical inference. Indeed, longstanding inferential frameworks – as exemplified by the hypothesis tests of Section 1.4, for instance – are crucial to the analysis of networks 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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18 B. P. Olding and P. J. Wolfe and relational data, and yet their implementations can prove remarkably difficult even for small data sets. To address these broader questions and impact the future of network inference, we believe that statisticians should focus on the following three main categories of open problems, whose descriptions comprise the remain- der of this section: (1) We must work to specify models that can more realistically describe observed network data. For instance, the fixed-degree models intro- duced earlier account explicitly for heterogeneous degree sequences; in the case of large-scale network data sets, even more flexible models are needed. (2) We must build approximations to these models for which likelihood maximization can be readily achieved, along with tools to evaluate the quality of these approximations. The spectral partitioning approach featured in our examples of Section 1.4 serves as a prime example; however, validation of approximate inference procedures remains an important open question.
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  • Spring '12
  • Kushal Kanwar
  • Graph Theory, Statistical hypothesis testing, Imperial College Press, applicable copyright law

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