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Bibliographic Details
Main Authors: Derumigny, Alexis, Schmidt-Hieber, Johannes
Format: Preprint
Published: 2023
Subjects:
Online Access:https://arxiv.org/abs/2303.08122
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Table of Contents:
  • We propose a new concept of codivergence, which quantifies the similarity between two probability measures $P_1, P_2$ relative to a reference probability measure $P_0$. In the neighborhood of the reference measure $P_0$, a codivergence behaves like an inner product between the measures $P_1 - P_0$ and $P_2 - P_0$. Codivergences of covariance-type and correlation-type are introduced and studied with a focus on two specific correlation-type codivergences, the $χ^2$-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 $χ^2$-divergence matrix satisfies a data-processing inequality.