10000 10000 971108out exp768585 x 215632 980410out

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Unformatted text preview: 999 - 2005, explosion of observations of “power laws” in networks (also of “small-worlds”). 10000 10000 "971108.out" exp(7.68585) * x ** ( -2.15632 ) "980410.out" exp(7.89793) * x ** ( -2.16356 ) 1000 1000 100 100 10 10 1 1 10 100 1 1 10 100 • M. Mitzenmacher, “The Future of Power Law Research” Internet Mathematics, 2 (4), 2006. (Editorial piece) 10000 10000 "981205.out" exp(8.11393) * x ** ( -2.20288 ) "routes.out" exp(8.52124) * x ** ( -2.48626 ) – A call to move beyond observation and model building to validation and control. 1000 1000 – Power laws ‘the signature of human activity’ 100 100 • Clauset, Shalizi, Newman, “Power-law distributions in empirical data”, SIAM Review 51, 661-703 (2009). (http://arxiv.org/abs/0706.1062) 10 10 – Techniques to detect if actually have a power law, and if so, to extract exponents. 1 1 10 100 1 1 10 100 “Inferring network mechanisms: The Drosophila melanogaster protein interaction network” Middendorf, Ziv, and Wiggins PNAS 102, 2005 • Study the Drosophila protein interaction network • Use machine learning techniques (discriminative classification) to compare with seven proposed models to determine which model best describes data. • Classification rather than statistical tests on specific attributes. Data: Giot et al, Science 302, 1727 (2003) • Accept any edge with p > 0.65, 3,359 vertices and 2,795 edges. 7 candidate models • DMC – duplication-complementation-mutation (Vasquez et al) • DMR – duplication-mutation with random mutations • RDS – random static (Erdos-Renyi) • RDG – random growing graph (Callaway et al.) • LPA – Linear pref attachment (Barabasi-Albert) • AGV – Aging vertices • SMW – Small world (Watts-Strogatz) The procedure • Generate 1000 random instances of a network with N=3359 and E=2795 for each of the seven models (7000 random instances in total). (Training data) Fig. 2. ADT: The first few nodes of one of the trained ADTs are shown. At each boosting iteration one new decision node (recta...
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This document was uploaded on 03/12/2014 for the course CSCI 289 at UC Davis.

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