Course

Introduction: Probability distributions, random variables, joint distributions, random process, graphs, undirected and Directed Graphical Models. Representation: Bayesian Networks – Independence in graphs – d-separation, I-equivalence, minimal I-maps. Undirected Graphical models: Gibbs distribution and Markov Networks, Markov models and Hidden Markov Models. From Bayesian to Markov and Markov to Bayesian networks, Triangulation and Chordal Graphs. Directed Gaussian graphical models. Exponential Family Models. Factor Graph Representation. Conditional Random Fields. Other special Cases: Chains, Trees.

Inference: Variable Elimination (Sum Product and Max-Product). Junction Tree Algorithm. Forward Backward Algorithm (for HMMs). Loopy Belief Propagation. Markov Chain Monte Carlo Metropolis Hastings. Importance Sampling. Gibbs Sampling. Variational Inference.

Learning Graphical models: Discriminative vs. Generative Learning., Density estimation, learning as optimization, maximum likelihood estimation for Bayesian networks, structure learning in Bayesian networks, Parameter Estimation in Markov Networks. Structure Learning. Learning undirected models- EM: Handling Missing Data. Applications in Vision, Web/IR, NLP and Biology. Advanced Topics: Statistical Relational Learning, Markov Logic Networks

CO-PO Mapping

CO-PO Mapping

Preamble

Probabilistic graphical models use a graph-based representation for encoding complex distributions over a high-dimensional space. This course deals with representation, inference, and learning of probabilistic graphical models. Students will gain an in-depth understanding of several types of graphical models; basic ideas underlying exact inference in probabilistic graphical models and learning probabilistic models from data.

Course Objectives

• To enable students to model problems using graphical models
• To design inference algorithms
• To learn the structure of the graphical model from the data set

Course Outcomes

Prerequisites

• Probability and Statistics
• Programming Languages
• Algorithm Design

Evaluation Pattern – 70:30

• Midterm Exam – 30%
• Continuous Evaluation – 20%
• End Semester Exam – 50%

Text Book / References

1. Daphne Koller and Nir Friedman, ”Probabilistic Graphical Models: Principles and Techniques”, First Edition, MIT Press, 2009.
2. Michael Jordan, ”Learning in Graphical Models”. MIT Press, 1998. Collection of Papers.
3. Judea Pearl, Morgan Kaufmann, ”Probabilistic Reasoning in Intelligent Systems”, 1988.
4. Kevin P. Murphy, “Machine Learning, a probabilistic perspective”, The MIT Press Cambridge, Massachusetts, 2012.
5. Darwiche Adnan, ”Modeling and reasoning with Bayesian networks”, Cambridge university press, 2009.