We present a method to approximate Rao's distance between multivariate normal distributions based on discretizing curves joining normal distributions and approximating Rao distances between successive nearby normals on the curve by using Jeffrey's divergence. We consider experimentally the linear interpolation curves in the ordinary, natural and expectation parameterizations of the normal distributions. We further consider a curve derived from the Calvo and Oller's isometric embedding of the Fisher-Rao $d$-variate normal manifold into the cone of $(d+1)\times (d+1)$ symmetric positive-definite matrices [Journal of multivariate analysis 35.2 (1990): 223-242]. Last, we present some information-geometric properties of the Calvo and Oller's mapping.
翻译：我们提出一种方法,通过使用Jeffrey的偏差,根据离散曲线连接正常分布和拉奥在曲线上相近正常人之间相近的距离,使拉奥在多变正常分布之间的距离接近拉奥的距离。我们从实验的角度考虑正常分布的普通、自然和预期参数中的线性内插曲线。我们进一步考虑从Calvo和Oller的Calvo和Oller的等分法中得出的一条曲线,从Fisher-Rao $d$-differate management command嵌入$(d+1)\time(d+1)$(d+1)的锥形正对正对立矩阵[多变分析杂志35.2(1990年):223-242]。最后,我们介绍了Calvo和Oller的绘图的一些信息地理特征。
相关内容
微信扫码咨询专知VIP会员