Probability density estimation from optimally condensed data samples

Girolami, M. and Chao, H. (2003) Probability density estimation from optimally condensed data samples. IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(10), pp. 1253-1264. (doi: 10.1109/TPAMI.2003.1233899)

[img]
Preview
Text
probability_density_estimation.pdf

2MB

Publisher's URL: http://dx.doi.org/10.1109/TPAMI.2003.1233899

Abstract

The requirement to reduce the computational cost of evaluating a point probability density estimate when employing a Parzen window estimator is a well-known problem. This paper presents the Reduced Set Density Estimator that provides a kernel-based density estimator which employs a small percentage of the available data sample and is optimal in the L/sub 2/ sense. While only requiring /spl Oscr/(N/sup 2/) optimization routines to estimate the required kernel weighting coefficients, the proposed method provides similar levels of performance accuracy and sparseness of representation as Support Vector Machine density estimation, which requires /spl Oscr/(N/sup 3/) optimization routines, and which has previously been shown to consistently outperform Gaussian Mixture Models. It is also demonstrated that the proposed density estimator consistently provides superior density estimates for similar levels of data reduction to that provided by the recently proposed Density-Based Multiscale Data Condensation algorithm and, in addition, has comparable computational scaling. The additional advantage of the proposed method is that no extra free parameters are introduced such as regularization, bin width, or condensation ratios, making this method a very simple and straightforward approach to providing a reduced set density estimator with comparable accuracy to that of the full sample Parzen density estimator.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Girolami, Prof Mark
Authors: Girolami, M., and Chao, H.
Subjects:Q Science > QA Mathematics > QA75 Electronic computers. Computer science
College/School:College of Science and Engineering > School of Computing Science
Journal Name:IEEE Transactions on Pattern Analysis and Machine Intelligence
Publisher:Institute of Electrical and Electronics Engineers
ISSN:0162-8828
Copyright Holders:Copyright © 2003 Institute of Electrical and Electronics Engineers
First Published:First published in IEEE Transactions on Pattern Analysis and Machine Intelligence 25(10):1253-1264
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

University Staff: Request a correction | Enlighten Editors: Update this record