论文标题
与一对严格可比的准算术相关的α-差异
The α-divergences associated with a pair of strictly comparable quasi-arithmetic means
论文作者
论文摘要
我们使用一对严格可比的加权方法概括了$α$ - 差异的家族。特别是，我们在极限情况下获得了$ 1 $ - 差异$α\ rightarrow 1 $（对kullback-leibler Divergence的概括）和$ 0 $ divergence在限制情况下$α\ rightArrow 0 $（反向kullback-lebeleibler divergence的概括）。我们陈述了一对准算术手段的条件，要严格可比，并报告了准算术$α$ -DIVERGENCES及其属于CSISár's$ f $ d $ divergences的Bipower y-Divergences的公式。最后，我们表明这些广义的准算术$ 1 $ - 差异和$ 0 $ - diverences可以分解为通用的跨凝管减去熵的总和，并使用单调嵌入式将其重写为保形的Bregman Divergences。
We generalize the family of $α$-divergences using a pair of strictly comparable weighted means. In particular, we obtain the $1$-divergence in the limit case $α\rightarrow 1$ (a generalization of the Kullback-Leibler divergence) and the $0$-divergence in the limit case $α\rightarrow 0$ (a generalization of the reverse Kullback-Leibler divergence). We state the condition for a pair of quasi-arithmetic means to be strictly comparable, and report the formula for the quasi-arithmetic $α$-divergences and its subfamily of bipower homogeneous $α$-divergences which belong to the Csisár's $f$-divergences. Finally, we show that these generalized quasi-arithmetic $1$-divergences and $0$-divergences can be decomposed as the sum of generalized cross-entropies minus entropies, and rewritten as conformal Bregman divergences using monotone embeddings.
