Sparse probability density function estimation using the minimum integrated square error

Xia Hong

doi:10.1016/j.neucom.2013.02.003

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Sparse probability density function estimation using the minimum integrated square error

2013-09-01

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DOI：10.1016/j.neucom.2013.02.003

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Abstract

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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 N-2 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. (C) 2013 Elsevier B.V. All rights reserved.

Keywords:

Probability density function

Sparse modelling

Minimum integrated square error

Forward constrained regression

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