High-Dimensional Adaptive Basis Density Estimation ...

• Main Author: Buchman, Susan
• Format: Text
• Language: unknown
• Published: Carnegie Mellon University 2011
• Subjects: Probability; Statistics; FOS Mathematics; North Atlantic
• Online Access: https://dx.doi.org/10.1184/r1/6719834.v1; https://kilthub.cmu.edu/articles/High-Dimensional_Adaptive_Basis_Density_Estimation/6719834/1

In the realm of high-dimensional statistics, regression and classification have received much attention, while density estimation has lagged behind. Yet there are compelling scientific questions which can only be addressed via density estimation using high-dimensional data, such as the paths of North Atlantic tropical cyclones. If we cast each track as a single high-dimensional data point, density estimation allows us to answer such questions via integration or Monte Carlo methods. In this dissertation, I present three new methods for estimating densities and intensities for high-dimensional data, all of which rely on a technique called diffusion maps. This technique constructs a mapping for high-dimensional, complex data into a low-dimensional space, providing a new basis that can be used in conjunction with traditional density estimation methods. Furthermore, I propose a reordering of importance sampling in the high-dimensional setting. Traditional importance sampling estimates high-dimensional integrals ...