The course addresses mathematical methods of information processing based on the exploitation of intrinsic correlations between hidden variables in data. These methods are widely used in different domains including image and video processing, speech recognition, social network analysis, machine learning, etc. We describe Bayesian and Markov networks, hidden Markov models, approximate and exact inference methods, structural learning algorithms. The lectures are accompanied with practical sessions. The course is read in HSE and MSU
- Introduction to the course. Examples of structural data. Matrix calculations.
- Graphical models: Bayesian and Markov networks.
- Exact inference in acyclic graphical models. Belief Propagation algorithm.
- Hidden Markov Models. Viterbi algorithm for signal segmentation.
- Learning in Hidden Markov Models. Baum-Welsh algorithm. EM-algorithm. HMM extensions.
- Linear Dynamical Systems. Kalman filter. Extended Kalman filter.
- Approximate inference in graphical models. Tree-ReWeighted Message Passing.
- Graph cuts.
- Structural Support Vector Machine.
- Approximate Bayesian inference: Markov Chain Monte Carlo. Particle filters.
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