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A Tight Version of the Gaussian min-max theorem in the Presence of Convexity

Thrampoulidis, Christos and Oymak, Samet and Hassibi, Babak (2014) A Tight Version of the Gaussian min-max theorem in the Presence of Convexity. . (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20150120-073025721

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Abstract

Gaussian comparison theorems are useful tools in probability theory; they are essential ingredients in the classical proofs of many results in empirical processes and extreme value theory. More recently, they have been used extensively in the analysis of underdetermined linear inverse problems. A prominent role in the study of those problems is played by Gordon's Gaussian min-max theorem. It has been observed that the use of the Gaussian min-max theorem produces results that are often tight. Motivated by recent work due to M. Stojnic, we argue explicitly that the theorem is tight under additional convexity assumptions. To illustrate the usefulness of the result we provide an application example from the field of noisy linear inverse problems.


Item Type:Report or Paper (Working Paper)
Related URLs:
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http://arxiv.org/abs/1408.4837arXivUNSPECIFIED
Record Number:CaltechAUTHORS:20150120-073025721
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20150120-073025721
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:53852
Collection:CaltechAUTHORS
Deposited By: Shirley Slattery
Deposited On:20 Jan 2015 18:10
Last Modified:20 Jan 2015 18:10

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