NDLI: A globally convergent algorithm for MAP estimation in the linear model with non-Gaussian priors

Content Provider	IEEE Xplore Digital Library
Author	Palmer, J.A. Kreutz-Delgado, K.
Copyright Year	2002
Description	Author affiliation: Dept. of Electr. & Comput. Eng., Univ. of California, La Jolla, CA, USA (Palmer, J.A.; Kreutz-Delgado, K.)
Abstract	We develop a framework for analyzing non-Gaussian densities in terms of the curvature of the density function itself rather than moments of the random variable. The framework suggests a new criterion for sub- and super-gaussianity of densities that is seen to be of a wider range of application than the commonly used kurtosis criterion. We show that the notion of relative curvature introduced can be seen as a generalization of the notion of convexity, where classical convexity of a function is seen as a relationship between the function and a linear model. We use the curvature framework to derive an inequality that holds for all functions that are super-Gaussian in the sense of the proposed criterion. This inequality allows proof of global convergence of a certain re-weighted minimum norm algorithm by providing a weighting matrix that yields descent without line search. The algorithm is equivalent to the FOCUSS algorithm (Rao, B.D. and Gorodnitsky, I.F., IEEE Trans. Sig. Processing, vol.45, p.600-6, 1997; Rao and Kreutz-Delgado, K., IEEE Trans. Sig. Processing, vol.47, p.187-200, 1999) in the case of independent generalized Gaussian densities in the linear model.
Starting Page	1772
Ending Page	1776
File Size	333764
Page Count	5
File Format	PDF
ISBN	0780375769
ISSN	10586393
DOI	10.1109/ACSSC.2002.1197079
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2002-11-03
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Random variables Vectors Algorithm design and analysis Gaussian processes Linear matrix inequalities Shape Inverse problems Bayesian methods Sparse matrices Neurons
Content Type	Text
Resource Type	Article
Subject	Signal Processing Computer Networks and Communications

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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