Course Information
Course Number: 4541.729 003 Time: Tu/Th 9:0010:15AM Location: Building 301 Room 104 
Instructor: Prof. Songhwai Oh (오성회) Email: songhwai(at)snu.ac.kr Office: Building 301 Room 702 Phone: 8801511 
Poster Session
 Time: 3:005:00PM, Friday (2009/12/11)
 Location: 1st Floor East Lobby, Building 301
 Posters and photos from the 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.
Textbooks

[Required] Pattern Recognition and Machine Learning, Christopher M. Bishop, Publisher: Springer; 1 edition (October 1, 2007), ISBN13: 9780387310732
 [Recommended] Essentials of Stochastic Processes, Rick Durrett, Publisher: Springer; Corr. 2nd printing edition (March 30, 2001), ISBN13: 9780387988368
Prerequisites
Students must have background in undergraduatelevel 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)