最大熵与充分性
Maximum Entropy and Sufficiency
摘要：
Bregman散度和充分性的概念将在一般的凸状态空间上定义。它表明，只有谱集可以有一个Bregman分歧，满足一个充分条件。若当代数中迹为1的正元素是谱集的例子，最重要的例子是具有复数元素的密度矩阵的集合。它是澄清，信息论的考虑直接导致约旦代数的概念在某些正则性条件下。
英文摘要：
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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