3 we must seek to understand precisely how network

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(3) We must seek to understand precisely how network sampling influences our statistical analyses. In addition to better accounting for data gath- ering mechanisms, sampling can serve as a method of data reduction. This in turn will enable the application of a variety of methods to data sets much larger than those exhibited here. 1.5.1. Model elicitation and selection More realistic network models can only serve to benefit statistical inference, regardless of their computational or mathematical convenience (Banks and Constantine, 1998). Models tailored to different fields, and based on the- ory fundamental to specific application areas, are of course the long-term goal – with the exponential random graph models reviewed by Anderson et al. (1999) and Snijders et al. (2006) among the most successful and widely known to date. However, additional work to determine more general models for network structure will also serve to benefit researchers and practitioners alike. As detailed in the Appendix, there are presently several competing models of this type, each with its own merits: stochastic block models (Wang and Wong, 1987), block models with mixed membership (Airoldi et al. , 2007), and structural models that explicitly incorporate information regarding the degree sequence in addition to group membership (Chung et al. , 2003). 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 19 At present, researchers lack a clearly articulated strategy for selecting between these different modeling approaches – the goodness-of-fit proce- dures of Hunter et al. (2008), based on graphical comparisons of various network statistics, provide a starting point, but comparing the complexity of these different modeling strategies poses a challenge. Indeed, it is not even entirely clear how best to select the number of groups used in a single modeling strategy alone. For the data of Section 1.4.1, for example, we restricted our definition of network structure to be a binary division of the data into two groups, whereas many observed data sets may cluster into an a priori unknown number of groups. It is also worth noting that many different fields of mathematics may provide a source for network data models. While graph theory forms a natural starting point, other approaches based on a combination of random matrices, algebra, and geometry may also prove useful. For example, the many graph partitioning algorithms based on spectral methods suggest the use of corresponding generative models based on the eigenvectors and eigen- values of the graph Laplacian. The primary challenge in this case appears to be connecting such models to the observed data matrix A , which typically consists of binary entries.
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  • Spring '12
  • Kushal Kanwar
  • Graph Theory, Statistical hypothesis testing, Imperial College Press, applicable copyright law

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