152 approximate inference and validation

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1.5.2. Approximate inference and validation Computationally or mathematically convenient models will also continue to play a key role in network analysis. Even simple generic models of structure are very high-dimensional, and with network data sets commonly consisting of thousands to millions of nodes, model dimensionality spirals out of con- trol at an impossible rate. Somehow this fundamental challenge of network data – how to grapple with the sheer number of relational observations – must be turned into a strength so that further analysis may proceed. Reduc- ing the dimensionality through an approximate clustering is an excellent first step to build upon, but computationally realizable inference schemes must also follow in turn. The usefulness of such approximations will ultimately be determined by the extent to which evaluation tools can be developed for massive data sets. Whenever models are sufficiently complex to necessitate approximate inference procedures, such models must be paired with mechanisms to relate the quality of the resulting analysis back to the original problem and model specification. Indeed, assurances are needed to convince thoughtful practitioners that analyzing a different model, or maximizing a quantity other than desired likelihood, is a useful exercise. 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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20 B. P. Olding and P. J. Wolfe Other approaches to validation may focus on the outcome of the anal- ysis in some way, rather than its theoretical underpinnings. With ground truth by its very definition available only for small-scale illustrative prob- lems, or for those which are generally felt to have already been solved, prediction may provide a valuable substitute. By monitoring the results of approximation over time relative to revealed truth, confidence in the adopted inference procedure may be grown. 1.5.3. Sampling, missingness, and data reduction A final concern is to better understand how sampling mechanisms influence network inference. Consider that two critical assumptions almost always underpin the vast majority of contemporary network analyses: First, that all links within the collection of observed nodes have been accounted for; and second, that observed nodes within the network comprise the only nodes of interest. In general, neither of these assumptions may hold in practice. To better understand the pitfalls of the first assumption, consider that while observing the presence of a link between nodes is typically a feasible and well-defined task, observing the absence of a link can in many cases pose a substantial challenge. Indeed, careful reflection often reveals that zero
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  • Spring '12
  • Kushal Kanwar
  • Graph Theory, Statistical hypothesis testing, Imperial College Press, applicable copyright law

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