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Department of Statistics, The Ohio State University
Statistics and Biostatistics Colloquium Series
Handling Sparsity via the Horseshoe
Carlos Carvalho
University of Chicago Booth School of Business
3:30PM - Thursday, April 30, 2009
Room 170, Eighteenth Avenue Bldg. (EA 170)
ABSTRACT
In this talk, I will present a new approach to sparse-signal detection
called the horseshoe estimator. A theoretical framework is proposed for
understanding why the horseshoe is a better default sparsity estimator
than those that arise from powered-exponential priors. Comprehensive
numerical evidence is presented to show that the difference in
performance can often be large. Most importantly, I will show that the
horseshoe estimator corresponds quite closely to the answers one would
get if one pursued a full Bayesian model-averaging approach using a
point mass at zero for noise, and a continuous density for signals.
Surprisingly, this correspondence holds both for the estimator itself
and for the classification rule induced by a simple threshold applied to
the estimator. For most of this talk I will study sparsity in the
simplified context of estimating a vector of normal means. It is here
that the lessons drawn from a comparison of different approaches for
modeling sparsity are most readily understood, but these lessons
generalize straightforwardly to more difficult problems--regression,
covariance regularization, function estimation--where many of the
challenges of modern statistics lie. This is joint work with Nicholas
Polson and James Scott.
And a link to a quick read on the topic...
Meet the speaker in Room 212 Cockins Hall at 4:30
p.m. Refreshments will be served.
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