1. Hub Node Detection in Directed Acyclic Graphs
Kim, Byoung-Hee
I will talk about evolving DNA-encoded genetic programs in a test tube. We evaluate the potentials of this approach by solving a medical diagnosis problem on a simulated DNA computer. The individual genetic program represents a decision list of variable length and the whole population takes part in making probabilistic decisions.

2. Directions of Future Work on HBN
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
Theoretical Analysis
Information compression – efficiency, measurement
Application & Empirical Analysis
Biological networks – gene regulatory networks, metabolic networks
Text
Social networks

3. Preliminary Experiment for Detecting Hub Nodes…
s5000 X1 X2
X100
sampling
Estimation
Structure
Hub nodes
Mutual information /
Conditional MI
100 node scale-free/modular BN
all nodes have binary states
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

4. 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 ????

5. Example 1: some short paths btw X65 and X8672 49 84 7 2
0.0693
0.0759
I(X65; X86) = 31 28 1
I(X65; X86 | Z) =?
0.0859
0.0821 26 17
0.0829
0.083

6. Example 2: some short paths btw X7 and X3165 86 72
0.0177
0.023
0.0183 49
0.0224 84 7
0.0545 2
I(X7; X31) =
I(X7; X31 | Z) = ? 31 28 1 26 17
0.0122

7. Experimetns to Verify Conjectures
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)

8. Mutual Information
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

9. Updates Code for the conditional MI has a bug
Couldn’t find any function for calculating MI/cMI in Matlab and R
‘empirical’ MI/cMI calculation: biased.. Need to reduce bias