论文标题
二人布雷格曼（Bregman）和富伦（Fenchel-Young）的分歧
The duo Bregman and Fenchel-Young divergences
论文作者
论文摘要
通过计算属于不同指数家族的两个概率度量之间的kullback-leibler差异，我们最终获得了一个公式，该公式概括了普通的fenchel-young差异。受此公式的启发，我们定义了二人组合的差异，并在其对发电机上报告了多数化条件，以确保这种差异始终是非负的。二人组合的分歧也等同于二人组成的布雷格曼分歧。我们通过计算嵌套指数家族的密度之间的kullback-leibler差异来显示这些二人组发散的使用，并报告了截断的正常分布之间的kullback-leibler差异的公式。最后，我们证明嵌套指数家庭之间的偏斜的bhattacharyya距离等于偏斜的二人组詹森（Jensen）的差异。
By calculating the Kullback-Leibler divergence between two probability measures belonging to different exponential families, we end up with a formula that generalizes the ordinary Fenchel-Young divergence. Inspired by this formula, we define the duo Fenchel-Young divergence and report a majorization condition on its pair of generators which guarantees that this divergence is always non-negative. The duo Fenchel-Young divergence is also equivalent to a duo Bregman divergence. We show the use of these duo divergences by calculating the Kullback-Leibler divergence between densities of nested exponential families, and report a formula for the Kullback-Leibler divergence between truncated normal distributions. Finally, we prove that the skewed Bhattacharyya distance between nested exponential families amounts to an equivalent skewed duo Jensen divergence.
