Probabilistic methods in the analysis of protein interaction networks

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Random matrix analysis for gene interaction networks in cancer cells

Investigations of topological uniqueness of gene interaction networks in cancer cells are essential for understanding this disease. Based on the random matrix theory, we study the distribution of the nearest neighbor level spacings $P(s)$ of interaction matrices for gene networks in human cancer cells. The interaction matrices are computed using the Cancer Network Galaxy (TCNG) database, which is a repository of gene interactions inferred by a Bayesian network model. 256 NCBI GEO entries regarding gene expressions in human cancer cells have been selected for the Bayesian network calculations in TCNG. We observe the Wigner distribution of $P(s)$ when the gene networks are dense networks that have more than $\sim 38,000$ edges. In the opposite case, when the networks have smaller numbers of edges, the distribution $P(s)$ becomes the Poisson distribution. We investigate relevance of $P(s)$ both to the size of the networks and to edge frequencies that manifest reliance of the inferred gene interactions.Comment: 22 pages, 7 figure

Structural Drift: The Population Dynamics of Sequential Learning

We introduce a theory of sequential causal inference in which learners in a chain estimate a structural model from their upstream teacher and then pass samples from the model to their downstream student. It extends the population dynamics of genetic drift, recasting Kimura's selectively neutral theory as a special case of a generalized drift process using structured populations with memory. We examine the diffusion and fixation properties of several drift processes and propose applications to learning, inference, and evolution. We also demonstrate how the organization of drift process space controls fidelity, facilitates innovations, and leads to information loss in sequential learning with and without memory.Comment: 15 pages, 9 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/sdrift.ht