Recovery and Analysis of Regulatory Networks from Expression Data Using Sums of Separable Functions
Ryan T. Botts · OhioLink ETD Center (Ohio Library and Information Network) · 2010
Many regulation networks and control systems may be modeled using systems of ordinary differential equations, e.g.gene regulatory networks.These equations are functions of many variables and are usually unknown.It is possible to collect time course network expression data using equipment such as microarrays.The large number of components in these networks coupled with relatively small sets of data yields an ugly showing of the curse of dimensionality.Here we develop an alternating least squares regression algorithm using sums of separable functions and total derivatives to approximate the system of regulation functions from the set of expression data.Considering these as tensor product approximation routines, we develop many new results regarding the best rank-1 tensor approximations.These results help us understand the performance of these regression algorithms.We then consider the analysis of these models to understand the network dynamics and connectivity.