摘要 We consider three different approaches to define

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• 類型：已發表論文
• 日期：2014-06-06

摘要

We consider three different approaches to define natural Riemannian metrics on polytopes of 隨機 matrices. First, we define a natural class of 隨機 maps between these polytopes and give a metric characterization of Chentsov type in terms of invariance with respect to these maps. Second, we consider the Fisher metric defined on arbitrary polytopes through their embeddings as exponential families in the probability simplex. We show that these metrics can also be characterized by an invariance principle with respect to morphisms of exponential families. Third, we consider the Fisher metric resulting from embedding the polytope of 隨機 matrices in a simplex of joint distributions by specifying a marginal distribution. All three approaches result in slight variations of products of Fisher metrics. Th

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