Methods for the estimation and application of biological networks

Thesis (Ph.D.)--University of Washington, 2013The advent of high-dimensional biological data from technologies like microarrays and mass spectrometers has transformed both biology and statistical theory; however, the tremendous potential of these datasets to explore the interactive behavior of genes or proteins has been largely unexplored. This dissertation describes two advances in the study of biological networks in these datasets, introducing improved methods for estimating network structure and for describing changes in pathway behavior in disease. The first method, the "Joint Graphical Lasso," is an extension of existing network estimation methods to datasets with multiple classes of observations, for example cancer and healthy cells. We describe a convex penalized likelihood equation whose solution has desirable properties for joint network estimation, and we detail an algorithm for its solution. The second method is a test for biologically meaningful changes in the pattern of co-regulation in biological pathways. Analysis of biological pathways has been almost entirely restricted to investigation of marginal effects; our method instead focuses on the joint behavior of features, examining important and previously unexplored aspects of pathway behavior