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Regression based D-optimality experimental design for sparse kernel density estimation

Chen, S., Hong, X. and Harris, C. J. (2010) Regression based D-optimality experimental design for sparse kernel density estimation. Neurocomputing, 73 (4-6). pp. 727-739. ISSN 0925-2312

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To link to this item DOI: 10.1016/j.neucom.2009.11.002


This paper derives an efficient algorithm for constructing sparse kernel density (SKD) estimates. The algorithm first selects a very small subset of significant kernels using an orthogonal forward regression (OFR) procedure based on the D-optimality experimental design criterion. The weights of the resulting sparse kernel model are then calculated using a modified multiplicative nonnegative quadratic programming algorithm. Unlike most of the SKD estimators, the proposed D-optimality regression approach is an unsupervised construction algorithm and it does not require an empirical desired response for the kernel selection task. The strength of the D-optimality OFR is owing to the fact that the algorithm automatically selects a small subset of the most significant kernels related to the largest eigenvalues of the kernel design matrix, which counts for the most energy of the kernel training data, and this also guarantees the most accurate kernel weight estimate. The proposed method is also computationally attractive, in comparison with many existing SKD construction algorithms. Extensive numerical investigation demonstrates the ability of this regression-based approach to efficiently construct a very sparse kernel density estimate with excellent test accuracy, and our results show that the proposed method compares favourably with other existing sparse methods, in terms of test accuracy, model sparsity and complexity, for constructing kernel density estimates.

Item Type:Article
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Computer Science
ID Code:16727
Uncontrolled Keywords:Probability density function; Parzen window estimate; Sparse kernel modelling; Orthogonal forward regression; Optimal experimental design; D-optimality

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