Three-Toed Sloth

"Dependence Estimation in High-Dimensional Euclidean Spaces" (Next Week at the Statistics Seminar)

For the first seminar of the new academic year, we are very pleased to welcome —

Barnabas Pcozos, "Dependence Estimation in High-Dimensional Euclidean Spaces"

Abstract: In this presentation we review some recent results on dependence estimation in high-dimensional Euclidean spaces. We survey several different dependence measures with their estimators and discuss the main difficulties and open problems with a special emphasis on how to avoid the curse of dimensionality. We will also propose a new dependence measure which extends the maximum mean discrepancy to the copula of the joint distribution. We prove that this approach has several advantageous properties. Similarly to Shannon's mutual information, the proposed dependence measure is invariant to any strictly increasing transformation of the marginal variables. This is important in many appications, for example, in feature selection. The estimator is consistent, robust to outliers, and does not suffer from the curse of dimensionality. We derive upper bounds on the convergence rate and propose independence tests too. We illustrate the theoretical contributions through a series of numerical experiments.

Time and place: 4--5 pm on Monday, 10 September 2012, in the Adamson Wing (136) of Baker Hall

As always, the seminar is free and open to the public.

Enigmas of Chance