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We give a simple description of the Fisher metric and the Amari–Chentsov tensor of the family of Poincaré distributions on the upper half plane by using a coordinate compatible with \(SL(2,\mathbb {R})\) -action.

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The Fisher Metric and the Amari–Chentsov Tensor of the Family of Poincaré Distributions

  • 会议论文

  • 发表日期：

    2026年

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  • Koichi Tojo,
  • Taro Yoshino

摘要

We give a simple description of the Fisher metric and the Amari–Chentsov tensor of the family of Poincaré distributions on the upper half plane by using a coordinate compatible with \(SL(2,\mathbb {R})\) -action.