The 18th Statistical Machine Learning Seminar (2014.7.7)

The 18th Statistical Machine Learning Seminar
Date/time: July 7 (Mon) 16:00-
Place: Seminar Room 5 (3F, D313),
Institute of Statistical Mathematics (Tachikawa, Tokyo)

Title: Self-tuning in nonparametric regression.

Speaker: Samory Kpotufe, Toyota Technological Institute Chicago

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 \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 adaptivity 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 likely to generalize to other
nonparametric methods.