3 we must seek to understand precisely how network

Info icon This preview shows pages 18–20. Sign up to view the full content.

View Full Document Right Arrow Icon
(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
Image of page 18

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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.
Image of page 19
Image of page 20
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern