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Foundations of Robotics
Seminar, November 27, 2007
Time
and Place | Seminar Abstract
Algebraic
Structure in Probabilistic Inference
Jonathan
Huang
(Joint
work with Carlos Guestrin and Leonidas Guibas)
Smith hall 100
Talk 4:00 pm
I'll start off by describing a compact way of
summarizing a probability distribution over the group of permutations (the
Symmetric Group) using marginal probabilities.
Compact summary statistics are necessary since representing
probabilities over the Symmetric group exactly would otherwise require O(n!)
storage. As I'll show, our summary
statistics have Fourier theoretic interpretations, which will allow us to
formulate basic inference operations, such as marginalization and conditioning,
which are defined directly in the Fourier domain. Our Fourier domain algorithms will have the
nice property that you can choose to trade off between speed and accuracy by
"bandlimiting". In the last part, I'll talk about generalizing the
above ideas to other groups and provide, in particular, a brief introduction to
Fourier analysis on SO(3).
The Robotics Institute is part of the School of Computer Science, Carnegie Mellon University.