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Introduction (2 lectures)
- multivariate distributions, sample space and random variables
- operations: inference, sampling, maximum liklihood config, ..
- examples and applications
- curse of dimensionality
- graphical representations of conditional independence
- extended example: hidden Markov models
- Basics (~6 lectures)
- directed and undirected graphical models
- Markov properties
- expression of joint distribution
- factor graphs
- log-linear models
- conditional independence; d-maps and i-maps
- explaining away; correlation and causation
- latent vs. observed variables
- entropy and mutual information as measures of edge strength
- inference as summation over configurations
- using graph structure to simplify calculations
- variable elimination
- moral, chordal, and decomposable graphs; triangulation
- the junction-tree algorithm
- computational complexity, including tree width, cut-sets and
phase transitions
- Approximate inference (3 lectures)
- forward sampling and importance sampling
- Gibbs sampling, the Swenden-Wang algorithm
- belief propagation
- local density approximation methods
- Learning (5 lectures)
- methods for estimating from sparse data
- iterative proportional fitting
- EM for latent variables
- induction of tree graphs
- structural priors
- discriminitive training for classification
- conditional Markov random fields
- Beyond discrete expectation (3 lectures)
- continuous distributions
- Kalman filter; Gaussian models
- decision theory, decomposable utility fns, optimization problems
- constraint networks and logic gates
- algebra of commutative semirings
- optimization: finding the maximal configuration
- linear programming bounds and branch-and-bound
- annealing
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