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Sparse probability density function estimation using the minimum integrated square error

Sparse probability density function estimation using the minimum integrated square error
Sparse probability density function estimation using the minimum integrated square error
We develop a new sparse kernel density estimator using a forward constrained regression framework, within which the nonnegative and summing-to-unity constraints of the mixing weights can easily be satisfied. Our main contribution is to derive a recursive algorithm to select significant kernels one at time based on the minimum integrated square error (MISE) criterion for both the selection of kernels and the estimation of mixing weights. The proposed approach is simple to implement and the associated computational cost is very low. Specifically, the complexity of our algorithm is in the order of the number of training data N, which is much lower than the order of N2 offered by the best existing sparse kernel density estimators. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with comparable accuracy to those of the classical Parzen window estimate and other existing sparse kernel density estimators.
0925-2312
122-129
Hong, Xia
e6551bb3-fbc0-4990-935e-43b706d8c679
Chen, Sheng
9310a111-f79a-48b8-98c7-383ca93cbb80
Qatawneh, Abdulrohman
b8c9c465-e9c6-43dc-b022-d291584f020d
Daqrouq, Khaled
1ba1973a-eec2-4290-9745-a3e61dc299d5
Sheikh, Muntasir
d336fc10-a1a6-4a86-ad81-75f07663c7c9
Morfeq, Ali
e70b81b2-1d0e-4de9-adae-0ee1098cc76e
Hong, Xia
e6551bb3-fbc0-4990-935e-43b706d8c679
Chen, Sheng
9310a111-f79a-48b8-98c7-383ca93cbb80
Qatawneh, Abdulrohman
b8c9c465-e9c6-43dc-b022-d291584f020d
Daqrouq, Khaled
1ba1973a-eec2-4290-9745-a3e61dc299d5
Sheikh, Muntasir
d336fc10-a1a6-4a86-ad81-75f07663c7c9
Morfeq, Ali
e70b81b2-1d0e-4de9-adae-0ee1098cc76e

Hong, Xia, Chen, Sheng, Qatawneh, Abdulrohman, Daqrouq, Khaled, Sheikh, Muntasir and Morfeq, Ali (2013) Sparse probability density function estimation using the minimum integrated square error. Neurocomputing, 115, 122-129. (doi:10.1016/j.neucom.2013.02.003).

Record type: Article

Abstract

We develop a new sparse kernel density estimator using a forward constrained regression framework, within which the nonnegative and summing-to-unity constraints of the mixing weights can easily be satisfied. Our main contribution is to derive a recursive algorithm to select significant kernels one at time based on the minimum integrated square error (MISE) criterion for both the selection of kernels and the estimation of mixing weights. The proposed approach is simple to implement and the associated computational cost is very low. Specifically, the complexity of our algorithm is in the order of the number of training data N, which is much lower than the order of N2 offered by the best existing sparse kernel density estimators. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with comparable accuracy to those of the classical Parzen window estimate and other existing sparse kernel density estimators.

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Published date: 4 September 2013
Organisations: Southampton Wireless Group

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Local EPrints ID: 352865
URI: http://eprints.soton.ac.uk/id/eprint/352865
ISSN: 0925-2312
PURE UUID: 72246ac4-3cc0-456a-b981-b9f66f14fe07

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Date deposited: 20 May 2013 09:21
Last modified: 19 Jul 2019 21:35

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