How can we get global insight from local observations?

Many real world problems in AI, computer vision, robotics, computer systems, computational neuroscience, computational biology and natural language processing require to reason about highly uncertain, structured data, and draw global insight from local observations. Probabilistic graphical models allow addressing these challenges in a unified framework. These models generalize approaches such as hidden Markov models and Kalman filters, factor analysis and Markov random fields.

In this course, we will study the problem of learning such models from data, performing inference (both exact and approximate) and using these models for making decisions. The techniques draw from statistics, algorithms and discrete and convex optimization. The course will be heavily research oriented, covering current developments such as probabilistic relational models, models for naturally combining logical and probabilistic inference and nonparametric Bayesian methods. The course is designed for graduatestudents and advanced undergraduate students.


  • Poster session Thursday Dec 3, 4-6pm, Annenberg 2nd floor atrium
  • New location:  Starting Monday Oct 5 we'll meet in Steele 102.
  • Questionnaire about background ([doc] [pdf]). Please return to Sheri Garcia by Oct 1 4pm.
  • I'm looking into finding a bigger room.  We might have to reschedule the class.  Please enter your availabilities in the survey.


  • Instructor: Andreas Krause (krausea [at] caltech.edu)
  • Teaching Assistants:
    • Pete Trautman (trautman [at] cds.caltech.edu)
    • Hongchao Zhou (hzhou [at] caltech.edu)
  • Time and Location: Fall ’09/’10, Mon & Wed 2:30pm-4pm in 102 Steele
  • Prerequisites: Learning Systems (CS/CNS/EE 156a) or permission by instructor
  • Textbooks and References:
    • Probabilistic Graphical Models by Daphne Koller & Nir Friedman (required)
    • Pattern Recognition and Machine Learning by Chris Bishop (optional)
    • Modeling and Reasoning with Bayesian Networks by Adnan Darwiche (optional)
  • 9 Units (3-0-6): Grading based on
    • Homework assignments (50 %)
    • Class project (50 %)
  • Office hours:
    • Andreas Krause: Monday 4pm-5:30pm in 300 Annenberg
    • Pete Trautman / Hongchao Zhou: Tuesday 4pm-5:30pm in 243 Annenberg
  • Collaboration policy:
    • Homeworks: Discussion of the problems is allowed, however, everybody must turn in their own solutions.
    • Project: Groups of 2-3 students (exceptions possible with instructor's permission)
  • Late day policy: Everybody has 3 late days that can be used for any homework assignment (e.g., you can be later for HW2 for 2 days and HW1 for 1 day). No credits when turning in after the late days have been used. Late days can not be used for the project proposal and reports. Start early!



  • Possible project ideas
  • Proposals (1-2 pages)  due Monday Oct 19. Please clearly specify
    • What is the idea of this project?
    • Who will you be collaborating with?
    • What data will you use?  Will you need time "cleaning up" the data?
    • What code will you need to write?  What existing code are you planning to use?
    • What references are relevant?  Mention 1-3 related papers.
    • What are you planning to accomplish by the Nov 9 milestone?
  • Project milestone due Monday Nov 9 
  • Poster session Dec 3, 4pm-6pm 2nd floor Annenberg
    • Poster boards, easels and cookies provided
  • Final project writeup due Wednesday Dec 9

Lecture notes

  • Sep 30 - Introduction [pdf]
  • Oct 5 - Bayesian Networks Semantics [pdf]
  • Oct 7 - Bayesian Networks Semantics 2 [pdf]
  • Oct 12 - Learning Bayesian Networks (MLE) [pdf]
  • Oct 14 - Bayesian Parameter and Structure Learning [pdf]
  • Oct 19 - Structure learning and variable elimination [pdf]
  • Oct 21 - Variable elimination continued [pdf]
  • Oct 26 - Junction trees [pdf]
  • Oct 28 - Undirected models [pdf]
  • Nov 2 - Learning Markov Networks [pdf]
  • Nov 4 - CRFs, exponential family [pdf]
  • Nov 9 - Hidden Markov Models and Kalman Filters [pdf]
  • Nov 11 - DBNs; Approximate inference [pdf]
  • Nov 16 - Guest Lecture by Baback Moghaddam on Variational Inference [pdf]
  • Nov 18 - Variational inference, Assumed Density Filtering [pdf]
  • Nov 23 - Sampling, Gibbs Sampling [pdf]
  • Nov 25 - Missing data, EM [pdf]
  • Nov 30
  • Dec 2 - NO LECTURE (instead, poster session on Dec 3)