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19-475-0301 PROBABILISTIC GRAPHICAL MODELS
Core/Elective: Core Semester: 3 Credits: 4
Course Description

Probabilistic graphical models (PGM) is one of the most advanced techniques in machine learning to represent data and models in the real world with probabilities. PGM present a general framework for constructing and using probabilistic models of complex systems that would enable a computer to use available information for making decisions. This course is for anyone who has to deal with lots of data and draw conclusions from it, especially when the data is noisy or uncertain. Data scientists, machine learning enthusiasts, engineers, and those who curious about the latest advances in machine learning will find PGM interesting

Course Objectives

Understand the concepts of PGM and which type of PGM to use for which problem
To understand techniques for representation, inference and learning from graph based models
To apply Bayesian networks and Markov networks to many real world problems

Course Content

Module I
Probabilistic reasoning: Representing uncertainty with probabilities – Random variables and joint distributions – Independence – Querying a distribution - Graphs

Module II
Representation: Bayesian Network (BN) representation – Independencies in BN – Factorizing a distribution – D-separation- Algorithm for D-separation – From distributions to Graphs

Module III
Undirected Graphical Models: Factor products – Gibbs distribution and Markov networks – Markov network independencies – Factor graphs – Learning parameters – Conditional Random Fields

Module IV
Gaussian Network Models: Multivariate Gaussians – Gaussian Bayesian networks – Gaussian Markov Random Fields – Exact Inference: variable elimination- Sum-product and belief updates – The Junction tree algorithm

Module V
Learning: Learning Graphical Models – Learning as optimization – Learning tasks – Parameter estimation – Structure learning in BN – Learning undirected models – Actions and decisions

REFERNCES

1. Daphne Koller, Nir Friedman, Probabilistic Graphical Models- Principles and Techniques, 1e, MIT Press, 2009
2. Christian Borgelt, Rudolf Kruse and Matthias Steinbrecher, Graphical Models- Methods for data analysis and Mining, 2e, Wiley, 2009
3. David Bellot, Learning Probabilistic Graphical Models in R, Packt Publishing, 1e, 2016
4. Luis Enrique Sucar, Probabilistic Graphical Models, 1e, Springer Nature, 2015


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