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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Tuesday, January 25, 2000}
\centerline{Sequoia Hall Rm. 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl Daphne Koller}
\centerline{\sl Dept. of Computer Science}
\centerline{\sl Stanford University}
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\centerline{\bf Inference and learning in models of complex stochastic systems}
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Consider a real-world dynamic system such as a freeway with multiple
vehicles, a large industrial plan whose state evolves over time, or even
the behavior of the stock market.  Systems such as these are
complex, involving many relevant variables, exhibit unpredictable dynamics,
and involve variables that we can never observe. Our goal is to construct
models of such a system that will allow us to better understand its
behavior, track the system trajectory over time, and predict its future
behavior.  We use Dynamic Bayesian networks, a general framework that
includes hidden Markov models and Kalman filters, to represent these
systems.  I will discuss our work on inference in these models and on
learning them from data.  The main technical difficulty is that most
algorithms involve the use of a belief state -- a probability distribution
over the state of the process at a given point in time.  Unfortunately,
most real-world systems are too complex to allow a belief state to be
represented exactly.  In the talk, I will discuss an approximate inference
algorithm that exploits the hierarchical structure of real-world domains to
allow efficient inference even for large complex systems. I will present a
theoretical analysis that allows us to bound the error resulting from our
approximation.  I will also present empirical results that show that our
algorithm achieves orders of magnitude faster inference with only a tiny
degradation in accuracy.  The algorithm can also be used as the key
subroutine within algorithms that learn models from data.  I will present
preliminary results
showing how this technique can be extended to deal with hybrid systems --
ones involving both discrete and continuous variables.

Joint work with Xavier Boyen, Uri Lerner, and Ron Parr.

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