Strong sub-and super-gaussianity

Authors:
Jason A. Palmer;Ken Kreutz-Delgado;Scott Makeig
Affiliations:
Swartz Center for Computational Neuroscience, University of California San Diego, La Jolla, CA;Department of Electrical and Computer Engineering, University of California San Diego, La Jolla, CA;Swartz Center for Computational Neuroscience, University of California San Diego, La Jolla, CA
Venue:
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
Year:
2010

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Abstract

We introduce the terms strong sub- and super-Gaussianity to refer to the previously introduced class of densities log-concave is x2 and log-convex in x2 respectively. We derive relationships among the various definitions of suband super-Gaussianity, and show that strong sub- and super-Gaussianity are related to the score function being star-shaped upward or downward with respect to the origin. We illustrate the definitions and results by extending a theorem of Benveniste, Goursat, and Ruget on uniqueness of separating local optima in ICA.