=== Schedule ===

Lectures are given every week on Monday 14:30-16:00 in KN:E-127.

=== Syllabus ===

^ Lect. ^ Topic ^
| 01 | Markov chains, equivalent representations, ergodicity, convergence theorem for homogeneous Markov chains |
| 02 | Hidden Markov Models on chains for speech recognition: pre-processing, dynamic time warping, HMM-s |
| 03 | Recognising the generating model -- calculating the emission probability for a measured signal sequence. |
| 04 | Recognising the most probable sequence of hidden states and the sequence of most probable states. |
| 05 | Possible formulations for supervised and unsupervised learning tasks (parameter estimation). |
| 06 | Supervised and unsupervised learning according to the Maximum-Likelihood principle, the Expectation Maximisation algorithm. |
| 07 | Hidden Markov models on acyclic graphs (trees). Estimating the graph structure. |
| 08 | Hidden Markov models with continuous state spaces. Kalman filter and particle filters. |
| 09 | Markov Random Fields - Markov models on general graphs. Equivalence to Gibbs models, Examples from Computer Vision. |
| 10 | Relations to Constraint Satisfaction Problems and Energy Minimisation tasks, unified formulation, semi-rings. |
| 11 | Searching the most probable state configuration: transforming the task into a MinCut-problem for the submodular case. |
| 12 | Searching the most probable state configuration: approximative algorithms for the general case. |
| 13 | The partition function and marginal probabilities: Approximative algorithms for their estimation. |
| 14 | Duality between marginal probabilities and Gibbs potentials. The Expectation Maximisation algorithm for parameter learning. |