The topics will be further introduced and the students can choose between topics in an introductory seminar on Tuesday, Oct 1 at 14.15 in room 405.
It turns out that main segmentation algorithms (Viterbi, PMAP) can be applied for PMM’s, because they solely relay on Markov property of (X,Y). Therefore, from a segmentation point of view, there is no restriction to use PMM’s instead of HMM’s.
• Gets familiar with HMM and PMM models
• Gives the classification of PMM models and the sufficient conditions fo Y being Markov chain.
• Studies Viterbi, PMAP and hybrid algorithms for HMM’s and generalizes them for PMM’s.
• Implements these algorithms for linear Markov switching models.
• Investigates the effect of PMM (correlated noise) in segmentation. Does the increase of dependence between the observations decrease the difference between PMAP and Viterbi paths.
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2. S. Derrode, W. Piecynski, Signal and image segmentation using pairwise Markov chains, IEEE Trans. Signal Process. 52 (9) (2004) 2477–2489.
3. W. Pieczynski, Pairwise Markov chains, IEEE Trans. Pattern Anal. Mach. Intell. 25 (5) (2003) 634–639.
4. I. Gorynin, H. Gangloff, E. Monfrini, W. Pieczynski, Assessing the segmentation performance of pairwise and triplet Markov models, Signal Process. 145 (2018) 183–192.
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7. J. Hamilton, Regime switching models, in: Macroeconometrics and Time Series Analysis, Springer, (2010), 202–209.
8. J. Lember, J.Sova, Existence of infinite Viterbi path for pairwise Markov model, Stochastic Processes and their Applications (to appear)
9. J. Lember, Introduction to statistical learning theory (lecture notes), 2012
10. A. Koloydenko, K. Kuljus, J. Lember, Theory of segmentation, In: Hidden Markov Models, INTECH (2011)
11. L. Rabiner, A tutorial on Hidden Markov Models and selected applications in speech recognition, Proc. IEEE (1989), 1-58
Requirements for graduation thesis and procedure for defence in the Faculty of Science and Technology
About presentation (defense): The presentation materials must be checked and uploaded to the computer in defense room before the start of the defense. Also, the students whose defense is after the break, can use the break time for these preparations.
The time limit for the defense talk is 15 minutes.