论文标题
信息理论原理的熵和相对熵
Entropy and relative entropy from information-theoretic principles
论文作者
论文摘要
我们为仅依赖于最小信息理论公理的熵和相对熵引入了一种公理方法，即混合和数据处理下的单调性以及产品分布的添加性。我们发现这些公理会诱导足够的结构，以在概率单纯性的内部和有意义的上限和下限内建立连续性，例如，我们发现每个相对熵都必须位于订单$ 0 $ $ 0 $和$ \ \ iftty $之间的rényi偏差之间。我们进一步显示了这种相对熵的积极确定性的简单条件，并在相对胜过的变体方面表征。我们的主要结果是熵和相对熵之间的一对一对应关系。
We introduce an axiomatic approach to entropies and relative entropies that relies only on minimal information-theoretic axioms, namely monotonicity under mixing and data-processing as well as additivity for product distributions. We find that these axioms induce sufficient structure to establish continuity in the interior of the probability simplex and meaningful upper and lower bounds, e.g., we find that every relative entropy must lie between the Rényi divergences of order $0$ and $\infty$. We further show simple conditions for positive definiteness of such relative entropies and a characterisation in term of a variant of relative trumping. Our main result is a one-to-one correspondence between entropies and relative entropies.
