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Second
Meeting:
WORKSHOP ON GRAPHICAL MODELS
Thursday, 19 February
2004
Abstracts
2:30 PM - 3:30 PM
"An Introduction to Probabilistic Graphical Models and Their
Lyapunov Functions and Algorithms for Inference and Learning"
Brendan J. Frey
Probabilistic and Statistical Inference Group
Electrical and Computer Engineering
University of Toronto
ABSTRACT: Many problems in science and engineering
require that we take into account uncertainties in the observed
data and uncertainties in the model that is used to analyze the
data. Probability theory (in particular, Bayes rule) provides a
way to account for uncertainty, by combining the evidence provided
by the data with prior knowledge about the problem. Recently, we
have seen an increasing abundance of data and computational power,
and this has motivated researchers to develop techniques for solving
large-scale problems that require complex chains of reasoning applied
to large datasets. For example, a typical problem that my group
works on will have 100,000 to 1,000,000 or more unobserved random
variables. In such large-scale systems, the structure of the probability
model plays a crucial role and this structure can be easily represented
using a graph. In this talk, I will review the definitions and properties
of the main types of graphical model, and the Lyapunov functions
and optimization algorithms that can be used to perform inference
and learning in these models. Throughout the talk, I will use a
simple example taken from the application area of computer vision,
to demonstrate the concepts.
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3:45 PM - 4:45 PM
"Modeling and Inference of Dynamic Visual Processes"
Ralf Koetter
Assistant Professor
Coordinated Science Laboratory and Department of Electrical Engineering
University of Illinois, Urbana-Champaign
ABSTRACT: The use of graphical models of sytems is a well established
technique to characterize a represented behavior. While these models
are often given by nature in some cases it is possible to choose
the underlying graphical framework. If in addition the represented
behavior satisfies certain linearity requirements, surprising structural
properties of the underlying graphical models can be derived. We
give an overview over a developing structure theory for linear systems
in graphical models and point out numerous directions for further
research. Examples of applications of this theory are given that
cover areas as different as coding, state space models and network
information theory.
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5:00 PM - 6:00 PM
"Computational Anatomy and Models for Image Analysis"
Michael I. Jordan
Professor
Department of Computer Science
University of California Berkeley
ABSTRACT: The formalism of probabilistic graphical
models provides a unifying framework for the development of large-scale
multivariate statistical models. Graphical models have become a
focus of research in many applied statistical and computational
fields, including bioinformatics, information theory, signal and
image processing, information retrieval and machine learning. Many
problems that arise in specific instances---including the key problems
of computing marginals and modes of probability distributions---are
best studied in the general setting. Exploiting the conjugate duality
between the cumulant generating funciton and the entropy for exponential
families, we develop general variational representations of the
problems of computing marginals and modes. We describe how a wide
variety of known computational algorithms---including mean field,
sum-product and cluster variational techniques---can be understand
in terms of these variational representations. We also present novel
convex relaxations based on the variational framework. We present
applications to problems in bioinformatics and information retrieval.
[Joint work with Martin Wainwright]
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