Probabilistic Graphical Models --- theory, algorithm, and application

                              Eric Xing
                       Carnegie Mellon University


 
The past decade has seen a growing trend of applying probability theory to machine 
intelligence systems that deal with complex real-world data with rich semantic structure 
and temporal and/or spatial dynamics. Probabilistic graphical model is a formalism that 
exploits the conjoined talents of graph theory and probability theory to build complex 
models out of simpler pieces, which offers a powerful language to elegantly define expressive 
distributions under complex scenarios, and provide a systematic computational framework 
for probabilistic inference. I discuss the mathematical underpinnings for recent developments 
in graphical models---including hierarchical and nonparametric Bayesian modeling, approximate 
inference, and relationships to other machine learning methods such as kernel machines and 
maximum margin learning---which lie in the theory of Bayesian statistics and convex analysis. 
I also discuss a number of applications: (1) Modeling topic evolution in document collections, 
(2) Unraveling actor functions in social networks, (3) Finding regulatory elements in DNA 
sequences, and (4) Reconstructing evolutionary history of human populations.