COL 776: Learning Probabilistic Graphical Models

General Information

Instructor: Parag Singla (email: parags AT

Class Timings/Venue:
  • Slot H. Time: Mon,Wed: 11:00 am - 11:50 am. Thu: 12:00 noon - 12:50 pm.
  • Venue: LH 416.

Office Hours:
  • Time:
  • Venue: SIT 404

Teaching Assistants:
Ankit Anand (csz138105 AT cse),Dhruvin Patel (cs5120293 AT cse)
Happy Mittal (csz138233 AT cse), Prachi Jain (csz148211 AT cse)
Shubhankar Singh (csz168113 AT cse)

TA Assignment


  • [November 12, 2016] Check out the updated Assignment 3 below. As was already announced, due date is Tuesday Nov 15, 11:50 pm.
  • [October 27, 2016] Assignment 3 is out on the web! Due Date: Sunday November 13, 11:50 pm.
  • [September 30, 2016] Assignment 2 is out on the web! Due Date: Thursday October 20, 11:50 pm.
  • [August 18, 2016] Assignment 1 is out on the web! Due Date: Tuesday September 13, 11:50 pm.

Course Objective and Content

Obective: This course is meant to be the first graduate level course in the area of Probabilistic Graphical Models (PGM). PGMs have emerged as a very important research field during last decade or so with wide range of applications including Computer Vision, Information Retrieval, Natural Language Processing, Biology and Robotics. This course aims to provide students with a comprehensive overview of PGMs. The course content will include introduction to Probabilistic Graphical Models, directed and undirected representations, inference and learning algorithms and practical applications. This course is also meant to provide the required background for pursuing research in this area.

Content: Basics: Introduction. Undirected and Directed Graphical Models. Bayesian Networks. Markov Networks. Exponential Family Models. Factor Graph Representation. Hidden Markov Models. Conditional Random Fields. Triangulation and Chordal Graphs. Other pecial 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: Discriminative Vs. Generative Learning. Parameter Estimation in Bayesian and Markov Networks. Structure Learning. EM: Handling Missing Data. Applications in Vision, Web/IR, NLP and Biology. Advanced Topics: Statistical Relational Learning, Markov Logic Networks.

Note: All the topics above may not be covered in the course.

Week-Wise Schedule

Note: KF below stands for Koller and Friedman Book (2009 ed.) on Probabilistic Graphical Models.
WeekTopic Book ChaptersClass Notes/
Supplementary Material
1 Introduction, Basics KF Chapter 1, 2 Introduction
2 Bayesian Networks KF Chapter 3 Bayes Net-1
Bayes Net-2
3 Markov Networks KF Chapter 4 Markov Network-1
Markov Network-2
4,5 Factor Graph Representation, HMMs, CRFs,
Expoential Family
KF Chapter 4,8 Factor Graphs
Log Linear Models

Hidden Markov Models
Condiation Random Fields
6,7 Exact Inference: Variable Elimination KF Chapter 9 Variable Elimination-1
Variable Elimination-2
8,9,10 Exact Inference: Junction Tree Algorithm.
Belief Propagation (Loopy or not)
KF Chapter 10,11 Clique Tree Message Passing-1
Clique Tree Message Passing-2
Cique Tree Message Passing-3
Loopy Belief Propagation
Max-Product Belief Propagation
11,12 Sampling Based Approximate Inference:
MCMC, Metropolis Hastings, Gibbs Sampling,
Importance Sampling
KF Chapter 12 Sampling Based Inference - Basics
Forward Sampling, Likelihood Weighting, Importance Sampling
Importance Sampling
Markov Chain Monte Carlo
Markov Chain Monte Carlo-1
Gibbs Sampling, Metropolis Hastings
Gibbs Sampling - Additional Notes
13 Learning: Overview, Learning in Bayesian
Networks, Learning in Markov Networks
KF Chapter 16,17,19 Parameter Estimation, Expectation Maximization
14 Markov Logic, Contextual Symmetries. Revision Markov Logic Presentation, Contextual Symmetries
* Additional Notes Learning Parmaters
Expectation Maximiation

Additional Reading

Review Material

Topic Notes
Probability prob.pdf
Borrowed from Andrew Ng's
Machine Learning Course at Stanford


  1. Probabilistic Graphical Models: Principles and Techniques. Daphne Koller and Nir Friedman. First Edition, MIT Press, 2009.
  2. Learning in Graphical Models. Michael Jordan (ed.). MIT Press, 1998. Collection of Papers.
  3. Probabilistic Reasoning in Intelligent Systems. Judea Pearl. Morgan Kaufmann, 1988.

Other Places where a Similar Course is Offered

Assignment Submission Instructions

  1. You are free to discuss the problems with other students in the class. You should include the names of the people you had a significant discussion with in your submission.
  2. All your solutions should be produced independently without referring to any discussion notes or the code someone else would have written.
  3. All the non-programming solutions should be submitted using a hard copy. If you are writing by hand, write legibly.
  4. Required code should be submitted using Moodle Page.
  5. You should archive all your submission (code, plots etc.) in one single zip file. This zip file should be named as "". For example, if your entry number is "2008anz7535" and your name is "Nilesh Pathak", your submission should be named as " Inside your zip folder, you should create a separate sub-directory for each question in the assignment which should be named as "qk", k being the question number. All the code (and plots etc.) for a question should be placed in the corresponding sub-directory.
  6. Honor Code: Any cases of copying will be awarded a zero on the assignment. An additional penalty of 5 points will also be imposed (on the total course points out of 100). More severe penalties may follow.
  7. Late policy: You are allowed a total of 5 late days acorss all the assignments. You are free to decide how you would like to use them. You will get a zero on an assignment once you exceed the (total) allowed exemption of 5 days.

Practice Questions


  • Assignment 3. [Weight : 10% (tentative)]. Due: Sunday November 13, 2016. 11:50 pm.
    Version Updated on: Nov 12, 2016.

  • Assignment 2. [Weight : 10%]. Due: Thursday October 20, 2016. 11:50 pm.
  • Assignment 1. [Weight : 8%]. Due: Tuesday September 13, 2016. 11:50 pm.
    • Question 1 Dataset:
    • Question 2 Dataset: (link accessible only from the IIT Delhi network)

Grading Secheme (Tentative)

Assignment 1 8%
Assignment 2 10%
Assignment 3 10% (tentative)
Quiz 1 2%
Quiz 2 (Tentative) TBD
Minor 1 15%
Minor 2 15%
Major 36-40%