Title page for ETD etd-04042012-171726

Type of Document Dissertation
Author Ali Akbar Soltan, Reza
Author's Email Address soltan@vt.edu
URN etd-04042012-171726
Title Enhancements in Markovian Dynamics
Degree PhD
Department Mechanical Engineering
Advisory Committee
Advisor Name Title
Ahmadian, Medhi Committee Chair
Asl, Farshid M. Committee Member
Ball, Joseph A. Committee Member
Hall, T. Simin Committee Member
Southward, Steve C. Committee Member
Taheri, Saied Committee Member
  • Duration Dependent Hidden Markov
  • Expectation Maximization
  • Nonlinear Stochastic Model
  • Hidden Markov Model
  • Maximum Likelihood Estimation
Date of Defense 2012-03-27
Availability unrestricted
Many common statistical techniques for modeling multidimensional dynamic data sets can be seen as variants of one (or multiple) underlying linear/nonlinear model(s). These statistical techniques fall into two broad categories of supervised and unsupervised learning. The emphasis of this dissertation is on unsupervised learning under multiple generative models. For linear models, this has been achieved by collective observations and derivations made by previous authors during the last few decades. Factor analysis, polynomial chaos expansion, principal component analysis, gaussian mixture clustering, vector quantization, and Kalman filter models can all be unified as some variations of unsupervised learning under a single basic linear generative model. Hidden Markov modeling (HMM), however, is categorized as an unsupervised learning under multiple linear/nonlinear generative models. This dissertation is primarily focused on hidden Markov models (HMMs).

On the first half of this dissertation we study enhancements on the theory of hidden Markov modeling. These include three branches: 1) a robust as well as a closed-form parameter estimation solution to the expectation maximization (EM) process of HMMs for the case of elliptically symmetrical densities; 2) a two-step HMM, with a combined state sequence via an extended Viterbi algorithm for smoother state estimation; and 3) a duration-dependent HMM, for

estimating the expected residency frequency on each state. Then, the second half of the dissertation studies three novel applications of these methods: 1) the applications of Markov switching models on the Bifurcation Theory in nonlinear dynamics; 2) a Game Theory application of HMM, based on fundamental theory of card counting and an example on the game of Baccarat; and 3) Trust modeling and the estimation of trustworthiness metrics in cyber security systems via Markov switching models.

As a result of the duration dependent HMM, we achieved a better estimation for the expected duration of stay on each regime. Then by robust and closed form solution to the EM algorithm we achieved robustness against outliers in the training data set as well as higher computational efficiency in the maximization step of the EM algorithm. By means of the two- step HMM we achieved smoother probability estimation with higher likelihood than the standard HMM.

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