Abstract

Estimating density functionals of analog sources is an important problem in statistical signal processing and information theory. Traditionally, estimating these quantities requires either making parametric assumptions about the underlying distributions or using non-parametric density estimation followed by integration. In this paper we introduce a direct nonparametric approach which bypasses the need for density estimation by using the error rates of k-NN classifiers as 'data-driven' basis functions that can be combined to estimate a range of density functionals. However, this method is subject to a non-trivial bias that dramatically slows the rate of convergence in higher dimensions. To overcome this limitation, we develop an ensemble method for estimating the value of the basis function which, under some minor constraints on the smoothness of the underlying distributions, achieves the parametric rate of convergence regardless of data dimension.

Original languageEnglish (US)
Title of host publication2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2866-2870
Number of pages5
Volume2018-April
ISBN (Print)9781538646588
DOIs
StatePublished - Sep 10 2018
Event2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018 - Calgary, Canada
Duration: Apr 15 2018Apr 20 2018

Other

Other2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018
CountryCanada
CityCalgary
Period4/15/184/20/18

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Keywords

  • Divergence estimation
  • Ensemble estimation
  • K-nearest neighbor classifier
  • Non-parametric

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

Cite this

Wisler, A., Moon, K., & Berisha, V. (2018). Direct Ensemble Estimation of Density Functionals. In 2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018 - Proceedings (Vol. 2018-April, pp. 2866-2870). [8462308] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP.2018.8462308