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On Entropy Approximation for Gaussian Mixture Random Vectors

Huber, Marco F.; Bailey, Tim; Durrant-Whyte, Hugh; Hanebeck, Uwe D.


For many practical probability density representations such as for the widely used Gaussian mixture densities, an analytic evaluation of the differential entropy is not possible and thus, approximate calculations are inevitable. For this purpose, the first contribution of this paper deals with a novel entropy approximation method for Gaussian mixture random vectors, which is based on a component-wise Taylor-series expansion of the logarithm of a Gaussian mixture and on a splitting method of Gaussian mixture components. The employed order of the Taylor-series expansion and the number of components used for splitting allows balancing between accuracy and computational demand. The second contribution is the determination of meaningful and efficiently to calculate lower and upper bounds of the entropy, which can be also used for approximation purposes. In addition, a refinement method for the more important upper bound is proposed in order to approach the true entropy value.

Volltext §
DOI: 10.5445/IR/1000034848
DOI: 10.1109/MFI.2008.4648062
Zitationen: 162
Cover der Publikation
Zugehörige Institution(en) am KIT Fakultät für Informatik – Institut für Anthropomatik (IFA)
Publikationstyp Proceedingsbeitrag
Publikationsjahr 2008
Sprache Englisch
Identifikator ISBN: 978-1-4244-2143-5
KITopen-ID: 1000034848
Erschienen in Proceedings of the 2008 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2008), Seoul, Republic of Korea, August, 2008
Verlag Institute of Electrical and Electronics Engineers (IEEE)
Seiten 181-188
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