High Dimensional Probability (11w5122)
Richard M. Dudley (Massachusetts Institute of Technology)
Christian Houdré (Georgia Institute of Technology)
David M. Mason (University of Delaware)
Jan Rosinski (University of Tennessee)
Jon Wellner (University of Washington)
(1) To bring together experts in high dimensional probability and those
in a number of the "areas of strong interaction" to discuss some of the
major problems in this area and report on progress towards their solution.
(2) To facilitate interactions and communications between the experts actively involved in the development of new theory in high dimensional probability, and leading researchers in statistics, machine learning, and computer science. Our intention is to deepen contacts between several different communities with common research interests focusing
on probability inequalities, empirical processes, strong approximations, Gaussian and related chaos processes of higher order, Markov processes, and applications of these methods to a wide range of problems in other areas of mathematics or to applications in statistics, optimization theory, and machine learning.
(3) To foster and develop interest in this area of research by new researchers and recent Ph.D.'s in mathematics, statistics, and computer science. There are many interesting and exciting problems, which can be formulated in a way that can be understood by graduate students, postdoctoral students, and new researchers. We plan to capitalize on this by including a number of promising young people in the program for this workshop.
Particular areas of focus and interest for the 2011 meeting include:
A. Applications of concentration of measure results and methods to random matrices.
B. Concentration of measure inequalities for U-processes
C. Interactions between small ball probabilities, approximation theory, prior distributions for nonparametric Bayes procedures, entropy bounds for high-dimensional function classes.
D. Applications of modern empirical process and strong approximation methods to treat problems in machine learning, nonparametric estimation and inference, with a particular focus on high- and infinite-dimensional statistical models. As noted in the program description for the meeting on Semiparametric and Nonparametric Methods in Econometrics to be held at BIRS in April 2009,``Empirical process theory is an essential tool for the understanding of uniform performance and of convergence rates of nonparametric estimates and for efficiency considerations in semiparametric models.''
E. Identification of major problems and areas of potentially high impact for applications and use in other areas of mathematics, statistics, and computer science.