Syllabus

Introduction: what is statistical learning (1 lecture)
 supervised and unsupervised learning
 a little history
 the curse of dimensionality
 Basics: statistical inference and probabilistic independence (2 lectures)
 multivariate distributions, sample space and random variables
 operations: inference, sampling, maximum liklihood config, ..
 examples and applications
 Graphical Models (4 lectures)
 graphical representations of conditional independence
 directed and undirected graphical models
 Markov properties
 expression of joint distribution
 factor graphs
 loglinear models
 conditional independence; dmaps and imaps
 explaining away; correlation and causation
 latent vs. observed variables
 entropy and mutual information as measures of edge strength
 Inference in graphical models (4 lectures)
 inference as summation over configurations
 using graph structure to simplify calculations
 variable elimination
 moral, chordal, and decomposable graphs; triangulation
 the junctiontree algorithm
 computational complexity, including tree width, cutsets and
phase transitions
 Approximate inference and sampling (~3 lectures)
 belief propagation and message passing algorithms
 forward sampling and importance sampling
 Gibbs sampling, the SwendsenWang algorithm
 Model estimation (4 lectures)
 Parameter estimation: mutinomial distribtions, iterative proportional fitting
 Priors for parameters
 induction of tree graphs
 structure estimation
 Clustering (4 lectures)
 Model based clustering and the EM algorithm
 Clustering as optimization
 Clustering on graphs
 Cluster validation and finding the number of clusters
 Guest Lectures  if time permits
