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Maximum Entropy and Sufficiency
July 08, 2016 Β· Declared Dead Β· π Entropy
"No code URL or promise found in abstract"
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Authors
Peter HarremoΓ«s
arXiv ID
1607.02259
Category
math-ph
Cross-listed
cs.IT
Citations
13
Venue
Entropy
Last Checked
3 months ago
Abstract
The notion of Bregman divergence and sufficiency will be defined on general convex state spaces. It is demonstrated that only spectral sets can have a Bregman divergence that satisfies a sufficiency condition. Positive elements with trace 1 in a Jordan algebra are examples of spectral sets, and the most important example is the set of density matrices with complex entries. It is conjectured that information theoretic considerations lead directly to the notion of Jordan algebra under some regularity conditions.
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