论文标题
指数家族密度之间的某些常见（dis）相似性的无累积封闭式公式
Cumulant-free closed-form formulas for some common (dis)similarities between densities of an exponential family
论文作者
论文摘要
众所周知，Bhattacharyya，Hellinger，Kullback-Leibler，$α$ - divergences和Jeffreys在属于同一指数家族的密度之间的差异具有依赖于严格的convex和真实累积累积功能的通用封闭式公式。在这项工作中，我们报告了（dis）相似性公式，该公式绕过了累积函数的明确使用，并突出了准算术均值及其多元均值操作员扩展的作用。实际上，这些无累积的公式在使用旧式应用程序编程界面（API）实施这些（DIS）相似性时非常方便，因为我们的方法仅需要部分分别分别对所考虑的指数族的典型分配密度。
It is well-known that the Bhattacharyya, Hellinger, Kullback-Leibler, $α$-divergences, and Jeffreys' divergences between densities belonging to a same exponential family have generic closed-form formulas relying on the strictly convex and real-analytic cumulant function characterizing the exponential family. In this work, we report (dis)similarity formulas which bypass the explicit use of the cumulant function and highlight the role of quasi-arithmetic means and their multivariate mean operator extensions. In practice, these cumulant-free formulas are handy when implementing these (dis)similarities using legacy Application Programming Interfaces (APIs) since our method requires only to partially factorize the densities canonically of the considered exponential family.
