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ANC/DTC Seminar: Martin Wainwright, UC Berkeley

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Belief Propagation for continuous State Spaces: Stochastic Message-Passing with Quantitative Guarantees

What
  • ANC/DTC Seminar
When Feb 19, 2013
from 02:10 PM to 03:00 PM
Where AT Lecture Theatre 3
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Graphical models and associated message-passing algorithms are used in many application domains of machine learning.  The belief propagation (BP) algorithm is used for computing approximate marginal distributions.
Although easy to implement for discrete random variables, it is challenging for continuous (non-Gaussian) variables, since the messages are density functions.  We introduce a new technique, called stochastic orthogonal series message-passing (SOSMP), for computing the BP fixed point in models with continuous random variables.  It is based on a deterministic approximation of the messages via orthogonal series expansion, and a stochastic approximation via Monte Carlo estimates of the integral updates of the basis coefficients.  Under mild conditions, we show that the algorithm's iterates converge to a delta-neighbourhood of the BP fixed point, and demonstrate how to choose the number of basis coefficients as a function of the desired approximation accuracy.  We illustrate our theory with both simulated examples and in application to optical flow estimation.

Based on joint work with Nima Noorshams http://arxiv.org/abs/1212.3850