Memory-Effcient Orthogonal Least Squares Kernel Density Estimation using Enhanced Empirical Cumulative Distribution Functions

Martin Schaffoner, Edin Andelic, Marcel Katz, Sven E. Krüger, Andreas Wendemuth
Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, PMLR 2:428-435, 2007.

Abstract

A novel training algorithm for sparse kernel density estimates by regression of the empirical cumulative density function (ECDF) is presented. It is shown how an overdetermined linear least-squares problem may be solved by a greedy forward selection procedure using updates of the orthogonal decomposition in an order-recursive manner. We also present a method for improving the accuracy of the estimated models which uses output-sensitive computation of the ECDF. Experiments show the superior performance of our proposed method compared to stateof-the-art density estimation methods such as Parzen windows, Gaussian Mixture Models, and ε-Support Vector Density models [1].

Cite this Paper

BibTeX
@InProceedings{pmlr-v2-schaffoner07a, title = {Memory-Effcient Orthogonal Least Squares Kernel Density Estimation using Enhanced Empirical Cumulative Distribution Functions}, author = {Schaffoner, Martin and Andelic, Edin and Katz, Marcel and Krüger, Sven E. and Wendemuth, Andreas}, booktitle = {Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics}, pages = {428--435}, year = {2007}, editor = {Meila, Marina and Shen, Xiaotong}, volume = {2}, series = {Proceedings of Machine Learning Research}, address = {San Juan, Puerto Rico}, month = {21--24 Mar}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v2/schaffoner07a/schaffoner07a.pdf}, url = {https://proceedings.mlr.press/v2/schaffoner07a.html}, abstract = {A novel training algorithm for sparse kernel density estimates by regression of the empirical cumulative density function (ECDF) is presented. It is shown how an overdetermined linear least-squares problem may be solved by a greedy forward selection procedure using updates of the orthogonal decomposition in an order-recursive manner. We also present a method for improving the accuracy of the estimated models which uses output-sensitive computation of the ECDF. Experiments show the superior performance of our proposed method compared to stateof-the-art density estimation methods such as Parzen windows, Gaussian Mixture Models, and ε-Support Vector Density models [1].} }
Endnote
%0 Conference Paper %T Memory-Effcient Orthogonal Least Squares Kernel Density Estimation using Enhanced Empirical Cumulative Distribution Functions %A Martin Schaffoner %A Edin Andelic %A Marcel Katz %A Sven E. Krüger %A Andreas Wendemuth %B Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2007 %E Marina Meila %E Xiaotong Shen %F pmlr-v2-schaffoner07a %I PMLR %P 428--435 %U https://proceedings.mlr.press/v2/schaffoner07a.html %V 2 %X A novel training algorithm for sparse kernel density estimates by regression of the empirical cumulative density function (ECDF) is presented. It is shown how an overdetermined linear least-squares problem may be solved by a greedy forward selection procedure using updates of the orthogonal decomposition in an order-recursive manner. We also present a method for improving the accuracy of the estimated models which uses output-sensitive computation of the ECDF. Experiments show the superior performance of our proposed method compared to stateof-the-art density estimation methods such as Parzen windows, Gaussian Mixture Models, and ε-Support Vector Density models [1].
RIS
TY - CPAPER TI - Memory-Effcient Orthogonal Least Squares Kernel Density Estimation using Enhanced Empirical Cumulative Distribution Functions AU - Martin Schaffoner AU - Edin Andelic AU - Marcel Katz AU - Sven E. Krüger AU - Andreas Wendemuth BT - Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics DA - 2007/03/11 ED - Marina Meila ED - Xiaotong Shen ID - pmlr-v2-schaffoner07a PB - PMLR DP - Proceedings of Machine Learning Research VL - 2 SP - 428 EP - 435 L1 - http://proceedings.mlr.press/v2/schaffoner07a/schaffoner07a.pdf UR - https://proceedings.mlr.press/v2/schaffoner07a.html AB - A novel training algorithm for sparse kernel density estimates by regression of the empirical cumulative density function (ECDF) is presented. It is shown how an overdetermined linear least-squares problem may be solved by a greedy forward selection procedure using updates of the orthogonal decomposition in an order-recursive manner. We also present a method for improving the accuracy of the estimated models which uses output-sensitive computation of the ECDF. Experiments show the superior performance of our proposed method compared to stateof-the-art density estimation methods such as Parzen windows, Gaussian Mixture Models, and ε-Support Vector Density models [1]. ER -
APA
Schaffoner, M., Andelic, E., Katz, M., Krüger, S.E. & Wendemuth, A.. (2007). Memory-Effcient Orthogonal Least Squares Kernel Density Estimation using Enhanced Empirical Cumulative Distribution Functions. Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 2:428-435 Available from https://proceedings.mlr.press/v2/schaffoner07a.html.

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