Introduction to Probabilistic Graphical Models
Course Objectives:
Probabilistic Graphical Models (PGMs) are an indispensable tool to machine learning, with
applications in many different fields.
As a marriage between
probability theory and graph theory, PGMs provide
a tool for dealing with two problems that occur throughout applied mathematics
and engineering – uncertainty and
complexity. Under probabilistic
models, data are modeled as a collection of random variables with a particular
pattern of possible dependencies between them.
Using the model, we can then discover knowledge, predict future events,
and infer hidden causes.
This
3-credit graduate-level course will introduce theories and applications for
various PGMs including Bayesian Networks, Markov
Random Fields, Conditional Random Fields, and Hidden Markov Models. Theoretically, we will study various model learning
and inference methods. Application-wise, we will demonstrate the use of
graphical models for different applications including computer vision, human
computer interaction, natural language processing, data mining, and
bioinformatics. Through
this course, students will understand the basic theories underlying different
application models. In addition, it will
provide students with a strong foundation for both applying graphical models to
complex problems in their own research areas and for addressing core research
topics in graphical models.
Optional Textbook: Bayesian
network and decision graphs by Finn V. Jensen
Course Coordinator: Qiang Ji, Associate Professor, Electrical,
Computer, and Systems Engineering
Prerequisites by Topic: Students entering the class should have a pre-existing
working knowledge of probability, statistics, and algorithms, though the class
has been designed to allow students with a strong numerate background to catch
up and fully participate.
Topics: Probability
Calculus, Bayesian Networks, Learning and Inference in BN, Dynamic Bayesian
Networks, Influence Diagram for Decision Making, Hidden Markov Model, Markov
Network, Conditional Random Fields, and various application examples of
different graphical models.
Course Evaluation:
The
evaluation of this course will be based on homework assignments and projects.