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Semilocal properties of canonical divergences in dually flat spaces

机译:双平坦空间中正则散度的半局部性质

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The properties of divergences in dually flat spaces are investigated beyond the local perspective. First, an approximative representation of divergence is shown on the basis of the expansion with respect to relative coordinates. A consideration concerning triangular relation is done from similar perspective and an equation which extends classical multidimensional scaling to incorporate Riemannian metric and affine connection coefficients is obtained. Furthermore, a consideration from a viewpoint of probability distribution is done. The representation of divergence can be regarded as Kullback-Leibler divergence between normal distributions with a common covariance matrix. Especially, it is shown that the asymmetry of divergence arises from the spatial change in differential entropy in those distributions.
机译:在双重平面空间中发散的性质超出了局部视角。首先,基于相对坐标的展开,显示了发散的近似表示。从相似的角度进行了关于三角关系的考虑,并获得了一个方程,该方程扩展了经典的多维缩放比例,以合并黎曼度量和仿射连接系数。此外,从概率分布的角度进行了考虑。散度的表示可以视为具有共同协方差矩阵的正态分布之间的Kullback-Leibler散度。特别地,表明了发散的不对称性是由那些分布中的微分熵的空间变化引起的。

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