Statistics Seminar

  • Assistant Research Professor
  • Toyota Technological Institute at Chicago

Self-Tuning in Nonparametric Regression

Contemporary statistical procedures are making inroads into a diverse
range of applications in the natural sciences and engineering.  However
it is difficult to use those procedures ``off-the-shelf'' because they
have to be properly tuned to the particular application.

In this talk, we present some ``adaptive'' regression procedures,
i.e. procedures which self-tune, optimally, to the unknown 
parameters of the problem at hand.

We consider regression on a general metric space of X of unknown
dimension, where the output Y is given as f(x) + noise.  We are 
interested in adaptivity at any input point x in X: the algorithm
must self-tune to the unknown ``local'' parameters of the problem at
x.  The most important such parameters, are (1) the unknown smoothness
of f, and (2) the unknown intrinsic dimension, both defined over a
neighborhood of x.  Existing results on adaptivity have typically
treated these two problem parameters separately, resulting in methods
that solve only part of the self-tuning problem.

Using various regressors as an example, we first develop insight
into tuning to unknown dimension.  We then present an approach
for kernel regression which allows simultaneous adaption to
smoothness and dimension locally at a point x.  This latest
approach combines intuition for tuning to dimension, and
intuition from so-called Lepski's methods for tuning to
smoothness.  The overall approach is likey to generalize to
other nonparametric methods.
Refreshents will be served in the Department of Statistics Lounge,
Baker Hall 132Q, at 3:30 p.m. preceding the seminar.

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