Graphical Model Driven Methods in Adaptive System Identification
Atulya Yellepeddi, Ph.D., 2016
James Preisig, Advisor
Identifying and tracking an unknown linear system from observations of its inputs and outputs is a problem at the heart of many different applications. Due to the complexity and rapid variability of modern systems, there is extensive interest in solving the problem with as little data and computation as possible.
This thesis introduces the novel approach of reducing problem dimension by exploiting statistical structure on the input. By modeling the input to the system of interest as a graph-structured random process, it is shown that a large parameter identification problem can be reduced into several smaller pieces, making the overall problem considerably simpler.
Several algorithms that can leverage this property in order to either improve the performance or reduce the computational complexity of the estimation problem are developed. The performance of the algorithms developed in the thesis in applications including adaptive equalization demonstrate that the gains admitted by the graph framework are realizable in practice.
The contributions of the thesis illustrate the power of graphical model structure in simplifying difficult learning problems, even when the target system is not directly structured.