Copyright 2014 imperial college press all rights

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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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Statistical Detection of Intruders Within Computer Networks 87 Equation (3.7) becomes ˆ α ( z t +1 ) = Pr( X t = x t | Z t = z t , φ ) z t ˆ α ( z t ) Pr( Z t +1 = z t +1 | Z t = z t ) c t , where c t = 1 k =0 Pr( X t = x t | Z t = k, φ ) k ˆ α ( z t 1 ,k ) Pr( Z t = k | Z t 1 = k ) is the constant required to normalize ˆ α ( z t ). Equations (3.8), (3.9), and (3.10) become ˆ β ( z t ) = P z t +1 ˆ β ( z t +1 ) Pr( X t +1 = x t +1 | Z t +1 = z t +1 , φ ) Pr( Z t +1 = z t +1 | Z t = z t ) c t +1 ξ ( z t 1 , z t ) = c t ˆ α ( z t 1 ) Pr( X t = x t | Z t = z t , φ ) × Pr( Z t = z t | Z t 1 = z t 1 ) ˆ β ( z t ) γ ( z t ) = ˆ α ( z t ) ˆ β ( z t ) . 3.4.3. New edges The approach described above discusses the stochastic modeling of existing edges, and seeks paths upon which the data have deviated from baseline models. Through examination of historic attacks, however, it is clear that new edges can be indicative of attacks. The subject of new edges is related to link prediction in the social network literature (Liben-Nowell and Kleinberg, 2007), where suggesting “friends” is an important topic. In this chapter, however, we ask about the tail of the probability distribution. Instead of finding most probable new “friends,” we seek the most unlikely new edges between pairs of computers, in order to identify anomalies. For existing edges, one can associate a model with the observed behav- ior, and then estimate the parameters of the model given observed behavior. A more complicated problem is to estimate the probability of observing a new edge, since we have no existing behavior upon which to base our esti- mation. Instead, we borrow information from the frequency at which the source and destination nodes make and receive new edges from other nodes in the network. Specifically, suppose that we observe source node x initiating a new edge to destination node y . To establish a probability of observing this 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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88 J. Neil, C. Storlie, C. Hash and A. Brugh edge, we propose a logistic model: logit ( P xy ) = α + β x + γ y , where P xy is the probability of the new edge initiated by x , bound for y ; α is an effect for the overall rate at which new edges are produced in the network; β x is an effect for how often x initiates new edges; and γ y is an effect for how often y receives new edges.
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