Hub Node Detection in Directed Acyclic Graphs 2008
Hub Node Detection in Directed Acyclic Graphs 2008. 3. 11. Kim, Byoung-Hee
Directions of Future Work on HBN l Algorithm ¨ Extension from binary-tree type structure to n-ary tree ¨ Fast and effective learning by hub node detection ¨ Incorporate features of latent variable models l Theoretical Analysis ¨ Information compression – efficiency, measurement l Application & Empirical Analysis ¨ Biological networks – gene regulatory networks, metabolic networks ¨ Text ¨ Social networks
Preliminary Experiment for Detecting Hub Nodes s 1 sampling s 2 … s 5000 X 1 X 2 … X 100 Estimation Structure Hub nodes Mutual information / Conditional MI • 100 node scale-free/modular BN • all nodes have binary states l Conjectures ¨ D-separation vs conditionam mutual information ¨ d(x, y) > d(x, z) then I(x; y) < I(x; z) asymptotically (mutual information) ¨ the difference between I(X; Y) and I(X; Y|Z) increases as the degree of Z increases
¨ Shortest path vs normalized mutual information < Data: 5, 000 samples out of 100 node networks (1 scale free and 1 modular) ¨ d(x, y) > d(x, z) then I(x; y) < I(x; z) asymptotically ? ?
Example 1: some short paths btw X 65 and X 86 86 72 65 0. 000905 49 0. 05604 84 7 0. 08434 2 0. 0693 0. 0759 31 28 0. 0859 1 0. 0821 0. 07947 26 0. 0829 I(X 65; X 86) = 0. 082375 17 0. 083 I(X 65; X 86 | Z) =?
Example 2: some short paths btw X 7 and X 31 0. 023 86 72 65 0. 0177 0. 0183 49 0. 0224 84 7 0. 0545 2 I(X 7; X 31) = 0. 0194 0. 00453 31 28 1 0. 00703 26 0. 00754 17 0. 0122 0. 00895 I(X 7; X 31 | Z) = ?
Experimetns to Verify Conjectures l d(x, y) > d(x, z) then I(x, y) < I(x, z) asymptotically ¨ Shortest path vs normalized mutual information < Data: 5, 000 samples out of 100 node networks (1 scale free and 1 modular)
Mutual Information l In probability theory and information theory, the mutual information, or transinformation, of two random variables is a quantity that measures the mutual dependency of the two variables
Updates Code for the conditional MI has a bug l Couldn’t find any function for calculating MI/c. MI in Matlab and R l ‘empirical’ MI/c. MI calculation: biased. . Need to reduce bias l
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