Unit:
Κατεύθυνση Στατιστική και Επιχειρησιακή ΈρευναLibrary of the School of Science
Author:
Christakis Christos
Supervisors info:
Χελιώτης Δημήτριος, Αναπληρωτής Καθηγητής, Τμήμα Μαθηματικών, Σχολή Θετικών Επιστημών
Παπαδάτος Νικόλαος, Καθηγητής, Τμήμα Μαθηματικών, Σχολή Θετικών Επιστημών
Τρέβεζας Σάμης, Λέκτορας, Τμήμα Μαθηματικών, Σχολή Θετικών Επιστημών
Original Title:
Κρυμμένα Μαρκοβιανά Μοντέλα και Γραμμικά Δυναμικά Συστήματα μέσω Θεωρίας Γράφων
Translated title:
Hidden Markov Models and Linear Dynamical Systems via Graph Theory
Summary:
In order to extenuate the Markov assumption for a set of data points, we can consider a hidden Markov model, in which we consider each observation as a result of a stochastic process under one of several unobserved states. In this thesis we will consider the Baum-Welch algorithm and the Viterbi algorithm of the hidden Markov models not the algebraic way, but we will ascertain that these can be viewed as special cases of the sum-product algorithm and the max-sum algorithm of the graphical models. For this purpose, we will make an extended reference to the graph theory, included the two algorithms referred above, as well as the very helpful d-seperation property. Afterwards, we will deal with the EM algorithm. In the main part, we will see the basic results of the theory of the classic HMM, as well as some extensions of it. Moreover, since we make worthy of our knowledge about the HMMs in combination with some results of the normal distribution, we will obtain the basic results of the theory of the Linear Dynamical Systems.
Main subject category:
Science
Keywords:
Hidden Markov Models, Linear Dynamical Systems, Graphical Models, Baum-Welch algorithm, Viterbi algorithm
