Course Information

Probabilistic Reasoning (Topics in Control and Automation) - Fall 2009
Course Number: 4541.729 003
Time: Tu/Th 9:00-10:15AM
Location: Building 301 Room 104
Instructor: Prof. Songhwai Oh (오성회)
Email: songhwai(at)
Office: Building 301 Room 702
Phone: 880-1511

Poster Session

Course Description

Uncertainty in engneering systems can be introduced by intrinsic randomness in the physical world, measurement errors, and modeling errors. At a coarser level (traditional systems), the performance of a system is usually unaffected by uncertainty. But at a finer level (modern systems), uncertainty is unavoidable and must be treated properly. In modern engineering systems, the proper treatment of uncertainty in a system is of paramount importance for the success of the system. While many tools have been proposed to address uncertainty, probability is the only known mathematical tool that can treat uncertainty with mathematical consistency. Probability has been widely applied to many science and engineering problems where it is used to model, design, and analyze uncertain or complex systems.

This course is designed to introduce the foundation of probability theory to first or second year graduate students and describe how probability can be applied to model and analyze complex physical or engineering systems. The course is suitable for science or engineering students who do not have a background in measure theory. The first part of the course will describe fundamental results in probability including Markov chains, conditional expectation, martingales, and laws of large numbers. The second part of the course is dedicated to applications of probability theory for probabilistic reasoning or statistical inference. Students will learn how to build a probability model of a complex system and how to perform probabilistic reasoning.


  • [Required] Pattern Recognition and Machine Learning, Christopher M. Bishop, Publisher: Springer; 1 edition (October 1, 2007), ISBN-13: 978-0387310732
  • [Recommended] Essentials of Stochastic Processes, Rick Durrett, Publisher: Springer; Corr. 2nd printing edition (March 30, 2001), ISBN-13: 978-0387988368


Students must have background in undergraduate-level probability, linear algebra, and algorithms.

Topics (* if time permits)

  • Probability space, Conditional probability and independence
  • Random variables and distributions, Expected value and moments
  • Markov chains
  • Conditional expectation and martingales(*)
  • Limiting behavior of sequences of random variables
  • * Detection and estimation
  • Basic concepts of Bayesian networks
  • Linear regression
  • Linear classification
  • * Exponential family and generalized linear models
  • Mixture models and EM algorithm
  • Hidden Markov models, Kalman filtering
  • Junction tree algorithm, Belief propagation
  • Approximate inference, Sampling (Gibbs, MCMC, particle filtering)
  • * Advanced topics: Nonparametric estimation (Gaussian processes, Support vector machines)
  • * Model selection (AIC, BIC, MDL)