A family of nonparametric density estimation algorithms

E. G. Tabak, Cristina V. Turner

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)145-164
Number of pages20
JournalCommunications on Pure and Applied Mathematics
Issue number2
StatePublished - Feb 2013

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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