Timeline for "Entropy" proof of Brunn-Minkowski Inequality?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Mar 4, 2017 at 15:16 | comment | added | Mokshay Madiman | For more general alphabets, there is a beautiful geometric approach of Csiszár that builds on his theory of information projections, provided one is interested in the probability that an empirical measure based on an i.i.d. sequence lies in a convex set of probability measures. See his 1984 paper "Sanov property, generalized I-projection, and a conditional limit theorem". | |
| Mar 4, 2017 at 15:11 | comment | added | Mokshay Madiman | There is indeed a geometric way of understanding large deviation results using information theory. For finite alphabets, the classical "method of types" can be used to prove Sanov's theorem (the prototypical result of large deviation theory); this can be found either in the textbook "Elements of Information Theory" by Cover and Thomas, or in the 1998 survey article "The Method of Types" by Csiszár, or in this blog post by Ramon van Handel: blogs.princeton.edu/sas/2013/10/10/lecture-3-sanovs-theorem | |
| Mar 4, 2017 at 15:04 | history | edited | Mokshay Madiman | CC BY-SA 3.0 |
Fixed a typo in definition of Rényi entropy.
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| Mar 4, 2017 at 3:17 | comment | added | john mangual | I found functional analysis unwieldy and unmotivated. Unfortunately certain limit theorems from combinatorics and random matrix theory do have a large deviations step, so I tried to learn them in some kind of way. Information theory could offer a geometric way of viewing these inequalities. Or I had hoped. I know even less than when I started. | |
| Mar 4, 2017 at 0:25 | review | Late answers | |||
| Mar 4, 2017 at 0:28 | |||||
| Mar 4, 2017 at 0:06 | history | answered | Mokshay Madiman | CC BY-SA 3.0 |