## 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)

Access: http://www.ism.ac.jp/access/index_e.html

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Title: Self-tuning in nonparametric regression.

Speaker: Samory Kpotufe, Toyota Technological Institute Chicago

Abstract:

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.