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Subnetwork State Functions Define Dysregulated Subnetworks in Cancer. Salim A. Chowdhury, Rod K. Nibbe, Mark R.Chance, Mehmet Koyuturk. JCB 2011. Previous Work. Mutual Information. Entropy H(X) Mutual Information I(Y;X) = H(X)-H(X|Y). high entropy. low entropy. low mutual information.
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Subnetwork State Functions Define Dysregulated Subnetworks in Cancer Salim A. Chowdhury, Rod K. Nibbe, Mark R.Chance, Mehmet Koyuturk JCB 2011
Mutual Information • Entropy H(X) • Mutual Information I(Y;X) = H(X)-H(X|Y) high entropy low entropy low mutual information high mutual information
0 0 1 1 0 0 1 1 0 0 0 1 1 1 0 1 1 0 1 0 0 1 0 1 Mutual Information – Dysregulation Measure C
Combinatorial Coordinate Dysregulation State function is considered informative if: • There is no redundancy in the state function • for every
Pruning the search space Where • Notice that Jbound() is not J() • This result will help us decide if we would like to extend subnetwork S. If we will not extend S.
0 0 1 1 1 0 KRANE Algorithm • S is extensible if • From the possible extension we choose to further check only b extensions with the top J() value. • Stop extending S if |S|>d.
Complexity • Complexity is exponential in d. • To make sure we don’t miss subnetworks we should use • Using Jbound()we could prune the search space thus reducing running time without loosing results.
Neural Network Classification • Rank the subnetwork according to I(FS;C)and take the top K ranked subnetworks that are not overlapping. • Use these Network as input for NN that predicts metastasis.
Conclusion Advantages: • Combinatorial dysregulation. • More sophisticated heuristics base on theoretical bound (“almost” exhaustive search). Shortcomings: • Runtime is exponential in d so we could check only relatively small networks. • Even for small values of d we have dimensionality problems. • No post-processing that tries to merge subnetworks. • Dismissing of overlapping subnetworks.