Bayesian Theory and Graphical Models - Sec. 1.2-1.4 (21 min)
Channel: Prof. Laurenz Wiskott
Date: 26/01/2017

Bayesian Theory and Graphical Models - Sec. 1.2-1.4 (21 min)


LECTURE 1 VIDEO 2 of the

Lecture Notes on Bayesian Theory and Graphical Models

Prof. Laurenz Wiskott
Institut für Neuroinformatik
Ruhr-Universität Bochum, Germany, EU

Bayesian theory is about probabilities and how to infer something about one random
variable if one knows something about some other random variables.  It provides a
principled way to deal with uncertainty.  The first lecture covers the basics.  If many
variables are involved, graphical models, such as Bayesian or Gibbsian networks, offer
methods to handle the computational complexity of the inference process.  The last
lecture presents methods to learn probabilities from data in a Bayes-optimal way.


==================================================================== LECTURE 1 [57 min]
---------------------------------------------------------------------- VIDEO 1 (27 min, on Youtube)
1 Bayesian inference
1.1 Discrete random variables and basic Bayesian formalism
---------------------------------------------------------------------- VIDEO 2 (21 min, on Youtube)
1.2 Partial evidence
1.3 Expectation values
1.4 Continuous random variables
---------------------------------------------------------------------- VIDEO 3 (9 min, on Youtube)
1.5 A joint as a product of conditionals
1.6 Marginalization
------------------------------------------------------------------------------ (not done yet)
1.7 Application: Visual attention +
----------------------------------------------------------------------
==================================================================== LECTURE 2 [23 min]
---------------------------------------------------------------------- VIDEO 1 (23 min, on Youtube)
2 Inference in Bayesian networks
2.1 Graphical representation
2.2 Conditional (in)dependence
2.3 Inverting edges
2.4 d-Separation in Bayesian networks
------------------------------------------------------------------------------ (not done yet)
2.5 Calculating marginals and message passing in Bayesian networks
2.6 Message passing with evidence
------------------------------------------------------------------------------ (not done yet)
2.7 Application: Image super-resolution
----------------------------------------------------------------------
==================================================================== LECTURE 3 [14 min]
------------------------------------------------------------------------------ (not done yet)
3 Inference in Gibbsian networks +
3.1 Introduction
3.2 Moral graph
3.3 Junction tree and message passing in a Gibbsian network
3.4 Most probable explanation
3.5 Triangulated graphs
---------------------------------------------------------------------- VIDEO 1 (14 min, on Youtube)
4 Approximate inference
4.1 Introduction
4.2 Gibbs sampling
----------------------------------------------------------------------
==================================================================== LECTURE 4 [42 min]
---------------------------------------------------------------------- VIDEO 1 (33 min, on Youtube)
5 Bayesian learning for binary variables
5.1 Levels of Bayesian learning
5.2 A simple example
5.3 The Beta distribution
---------------------------------------------------------------------- VIDEO 2 (9 min, on Youtube)
6 Learning in Bayesian networks
6.1 Breaking down the learning problem
6.2 Learning with complete data
6.3 Learning with incomplete data
----------------------------------------------------------------------
====================================================================

More material is available at
https://www.ini.rub.de/PEOPLE/wiskott/Teaching/Material/index.html