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Published in:
2003 | OriginalPaper | Chapter
Geometric Ideas in Minimum Cross-Entropy
Author : L. Lore Campbell
Published in: Entropy Measures, Maximum Entropy Principle and Emerging Applications
Publisher: Springer Berlin Heidelberg
Included in: Professional Book Archive
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This article reviews three geometric approaches to the understanding of the minimum cross-entropy method for estimating a probability distribution. The first approach is to regard the method as a projection based on an analogue of Pythagoras’ Theorem. The second is to regard the set of probability distributions as a differentiable manifold and to introduce a Riemannian geometry on this manifold. The third uses the idea of Hausdorff dimension to support the use of the method.