High-Dimensional Adaptive Basis Density Estimation

• Activity Number: 244
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Susan Buchman*+ and Ann Lee and Chad Schafer
• Companies: Carnegie Mellon University and Carnegie Mellon University and Carnegie Mellon University
• Keywords: dimensionality reduction ; tropical cyclones ; high-dimensional data ; density estimation ; diffusion maps

Abstract

We present a method for high-dimensional density estimation that assumes the ability to cheaply sample from an instrumental distribution that captures the low-dimensional structure in the data distribution. This assumption is satisfied in the application area of interest: the distribution of tropical cyclone tracks in the Atlantic Ocean. Physical models are capable of generating realistic tracks, but not in the correct distribution; our method allows for their use in determining the location of the central mass of the distribution in the vast high-dimensional space. Using orthogonal series density estimation with a basis that is adapted to the instrumental distribution, one can produce a density for the data distribution with respect not to the Lebesgue measure, but with respect to the instrumental distribution, which could improve rates of convergence.