多对测度的混合$f$ -发散
Mixed $f$-divergence for multiple pairs of measures
摘要：
本文将经典的一对测度的$f$ -散度的概念推广到多对测度的混合$f$ -散度。混合$f$ -发散提供了一种测量多对（概率）测量之间差异的方法。建立了混合$f$ -发散的性质，如排列不变性和分布对称性。证明了混合$f$ -发散的Alexandrov-Fenchel型不等式和等周不等式.
英文摘要：
In this paper, the concept of the classical $f$-divergence for a pair of measures is extended to the mixed $f$-divergence for multiple pairs of measures. The mixed $f$-divergence provides a way to measure the difference between multiple pairs of (probability) measures. Properties for the mixed $f$-divergence are established, such as permutation invariance and symmetry in distributions. An Alexandrov-Fenchel type inequality and an isoperimetric inequality for the mixed $f$-divergence are proved.
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