Matrix-Based Analytical Methods for Recasting Jacobian Models to Power-Law Models

Abstract

New methods for inferring data-consistent, self-reconfigurable power-law models from time series data are required and developed. These novel methods may be categorised into two broad groups, namely: straightforward (or direct) inference methods based on power-law models; and a jacobian based indirect inference method. The direct method involves applying direct means to infer a power-law model from time series data. The indirect method, however, uses a new system identification method to first infer a jacobian model as instant and temporal solution to the inverse problem before recasting the inferred jacobian model to corresponding power-law model using our newly developed recast technique. The recast method, in addition to normal behaviour, also provides a novel analytical technique for integrating power-law and jacobian models together. The modelling approach we have developed extends previous work on matrix-based network inference to model interoperability and multiple model transformation in terms of finding two distinct models (solutions) to an inverse problem.