Jüri Lember (University of Tartu)

Abstract Pairwise Markov model (PMM) is a two dimentsional Markov chain (X,Y). Typically one of the marginal processes (X) is observed and the other (Y) is hidden (latent variable). It turns out that such a simple definition describes a large class of models, including many well-known models like hidden Markov models as a subclass. We shall give an overview of PMM and their applications in segmentation. In particular the following issues are addressed:

1. Pairwise Markov models: definition, classification, main properties. Sufficient conditions for a marginal process being Markov. Triplet Markov model.
2. Examples of different kind of PMM’s.
3. Segmentation problem from statistical learning viewpoint.
4. Standard PMM-tools — forward-backward algorithms, Viterbi algorithm, EM-algorithm, Viterbi training.
5. Hybrid classifiers, their properties. Local Viterbi property.
6. Asymptotics of segmentation. Regenerative processes. The existence of Viterbi process.
7. Asymptotics of smoothing probabilities, exponential forgetting.
8. Segmentation with triplet Markov models.