Syllabus
Introduction to graphical models (Polito)
Basics on graphical models and statistics
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Basics of graph teory. Families
of probability distributions associated to direcetd and undirected graphs.
Markov properties and conditional independence.
·
Statistical concepts as
building blocks for graphical models. MAP and ML estimation.
Density estimation, classification and regression.
Learning from data
·
Model structure and
parameters estimation.
·
Complete observations
and latent variables.
·
The EM algorithm.
·
Model selection.
Exact inference
·
The junction tree and
related algorithms. Belief propagation and belief revision.
·
The generalized
distributive law.
·
Hidden Markov Models and
Kalmann Filtering with graphical models.
Approximate inference
·
Variational methods.
·
Monte Carlo Methods.
·
Loopy junction graphs
and loopy belief propagation.
·
Performance of loopy
belief propagation.
·
Kullback-Leibler
divergence and entropy. Bethe approximation of free energy and belief
propagation.
Applications to Vision (Perona)
·
Bayesian Networks
applied to a speech and visual recognition system.
·
Low level vision:
inferring scene for image. Application to super-resolution, shading/reflectance
variations, motion estimation.
·
Application to human
motion detection. Labelling problem.
Applications to Coding Theory (McEliece)
Belief Propagation and Spin Glasses