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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, March 9, 2004}
\centerline{Sequoia Hall Room 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl Alexander G. Gray}
\centerline{\sl Carnegie Mellon}
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\centerline{\bf Generalized N-Body Problems: A Story of Statistics, Computation, and Science}
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Abstract:

In this talk I'll review the fundamental connections between
statistics, computation, and science, and the modern trends which have
amplified their importance.  I'll illustrate these connections and
trends through several projects I've been working on, in which
progress toward answering fundamental questions in cosmology has been
held back by the inability to apply well-motivated multivariate
statistics/machine learning methods to very large modern datasets.  I
will present a collection of simple yet powerful ideas which
constitute a theory and toolkit for efficient solutions to a large
class of algorithmic problems I call 'generalized N-body problems'.
The results so far include, among others, the fastest practical
multivariate algorithms to date for kernel density estimation, the
all-nearest-neighbors problem, smoothed particle hydrodynamics, and
the n-point correlation functions.  In only the last year, the early
scientific consequences of these developments so far include an
explosion in the size of the best available quasar catalog by one
order of magnitude, the largest-scale effort to statistically validate
the Standard Model by over 3 orders of magnitude, and the strongest
experimental evidence to date of the existence of dark energy, the
2003 Science Magazine \#1 Breakthrough of the Year.  Looking ahead,
I'll touch on further outstanding fundamental problems in statistics
(e.g. high-dimensional estimation), computation (e.g. high-dimensional
integration), and science (e.g. some problems in proteomics), and some
perspectives I believe may lead to new results on these problems in
the next few years.  


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