Codivergences and information matrices

Alexis Derumigny*, Johannes Schmidt-Hieber

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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We propose a new concept of codivergence, which quantifies the similarity between two probability measures P1,P2 relative to a reference probability measure P0. In the neighborhood of the reference measure P0, a codivergence behaves like an inner product between the measures P1-P0 and P2-P0. Codivergences of covariance-type and correlation-type are introduced and studied with a focus on two specific correlation-type codivergences, the χ2-codivergence and the Hellinger codivergence. We derive explicit expressions for several common parametric families of probability distributions. For a codivergence, we introduce moreover the divergence matrix as an analogue of the Gram matrix. It is shown that the χ2-divergence matrix satisfies a data-processing inequality.

Original languageEnglish
Pages (from-to)253-282
Number of pages30
JournalInformation Geometry
Early online date22 May 2024
Publication statusPublished - Jun 2024


  • UT-Hybrid-D
  • Divergence
  • Gram matrix
  • Hellinger affinity
  • Chi-square divergence


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