A Family of Nonparametric Density Estimation Algorithms
Article first published online: 20 SEP 2012
Copyright © 2012 Wiley Periodicals, Inc.
Communications on Pure and Applied Mathematics
Volume 66, Issue 2, pages 145–164, February 2013
How to Cite
Tabak, E. G. and Turner, C. V. (2013), A Family of Nonparametric Density Estimation Algorithms. Comm. Pure Appl. Math., 66: 145–164. doi: 10.1002/cpa.21423
- Issue published online: 28 NOV 2012
- Article first published online: 20 SEP 2012
- Manuscript Revised: JUN 2011
- Manuscript Received: MAR 2011
A new methodology for density estimation is proposed. The methodology, which builds on the one developed by Tabak and Vanden-Eijnden, normalizes the data points through the composition of simple maps. The parameters of each map are determined through the maximization of a local quadratic approximation to the log-likelihood. Various candidates for the elementary maps of each step are proposed; criteria for choosing one includes robustness, computational simplicity, and good behavior in high-dimensional settings. A good choice is that of localized radial expansions, which depend on a single parameter: all the complexity of arbitrary, possibly convoluted probability densities can be built through the composition of such simple maps. © 2012 Wiley Periodicals, Inc.