Markov Approximations: The Characterization of Undermodeling Errors

<p>This thesis is concerned with characterizing the quality of Hidden Markov modeling when learning from limited data. It introduces a new perspective on different sources of errors to describe the impact of undermodeling. Our view is that modeling errors can be decomposed into two primary sources of errors: the approximation error and the estimation error. This thesis takes a first step towards exploring the approximation error of low order HMMs that best approximate the true system of a HMM. We introduce the notion minimality and show that best approximations of the true system with complexity greater or equal to the order of a minimal system are actually equivalent realizations. Understanding this further allows us to explore integer lumping and to present a new way named weighted lumping to find realizations. We also show that best approximations of order strictly less than that of a minimal realization are truly approximations; they are incapable of mimicking the true system exactly. Our work then proves that the resulting approximation error is non-decreasing as the model order decreases, verifying the intuitive idea that increasingly simplified models are less and less descriptive of the true system.</p>

Name thesis:degree_name

MS

Grantor dc:publisher

Brigham Young University - Provo

Author dc:creator

• Lei, Lei

• Hidden Markov model
• dynamic system
• aggregation
• lumping
• realization
• approximation
• minimal system
• Computer Sciences

Language dc:language

English

Repository record dc:identifier

https://scholarsarchive.byu.edu/etd/517

OAI identifier oai:identifier

oai:scholarsarchive.byu.edu:etd-1516