mlsanityData to 7 Oct 2026

A numerical approximation method for the Fisher-Rao distance between multivariate normal distributions

arXiv 2302.08175 ↗First posted 16 Feb 2023cs.IT cs.CV cs.LGcited by 11

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Abstract (arXiv)

We present a simple method to approximate Rao's distance between multivariate normal distributions based on discretizing curves joining normal distributions and approximating Rao's distances between successive nearby normal distributions on the curves by the square root of Jeffreys divergence, the symmetrized Kullback-Leibler divergence. We consider experimentally the linear interpolation curves in the ordinary, natural and expectation parameterizations of the normal distributions, and compare these curves with 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)× (d+1) symmetric positive-definite matrices [Journal of multivariate analysis 35.2 (1990): 223-242]. We report on our experiments and assess the quality of our approximation technique by comparing the numerical approximations with both lower and upper bounds. Finally, we present several information-geometric properties of the Calvo and Oller's isometric embedding.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Builds on 13 of its 107 references that are in the map. First posted on arXiv 16 Feb 2023.

Builds on

13 of 107 references.

References · 13

  1. 2017Fisher-Rao Metric, Geometry, and Complexity of Neural Networkscited by 99
  2. 2019On a generalization of the Jensen-Shannon divergence and the JS-symmetrization of distances relying on abstract meanscited by 61
  3. 2021GeomNet: A Neural Network Based on Riemannian Geometries of SPD Matrix Space and Cholesky Space for 3D Skeleton-Based Interaction Recognitioncited by 27
  4. 2015Riemannian Dictionary Learning and Sparse Coding for Positive Definite Matricescited by 24
  5. 2021On the Variance of the Fisher Information for Deep Learningcited by 22
  6. 2021Adversarial Robustness via Fisher-Rao Regularizationcited by 19
  7. 2017Gradient Flows in Filtering and Fisher-Rao Geometrycited by 12
  8. 2020Hilbert geometry of the Siegel disk: The Siegel-Klein disk modelcited by 7
  9. 2017Clustering in Hilbert simplex geometrycited by 4
  10. 2022Riemannian optimization for non-centered mixture of scaled Gaussian distributionscited by 4
  11. 2015A New Robust Regression Method Based on Minimization of Geodesic Distances on a Probabilistic Manifold: Application to Power Lawscited by 1
  12. 2016Optimal Transport vs. Fisher-Rao distance between Copulas for Clustering Multivariate Time Seriescited by 1
1 more
  1. 2022The Fisher-Rao Loss for Learning under Label Noisecited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 2; 2025: 5; 2026: 1.

11 papers.

  1. 2023The Fisher-Rao geometry of CES distributionscited by 5
  2. 2024Approximation and bounding techniques for the Fisher-Rao distances between parametric statistical modelscited by 2
  3. 2025Geometric Moment Alignment for Domain Adaptation via Siegel Embeddingscited by 2
  4. 2023Fisher-Rao distance and pullback SPD cone distances between multivariate normal distributionscited by 1
  5. 2024Fast proxy centers for Jeffreys centroids: The Jeffreys-Fisher-Rao and the inductive Gauss-Bregman centerscited by 1
  6. 2025Federated Generalised Variational Inference: A Robust Probabilistic Federated Learning Frameworkcited by 1
  7. 2025Robust Estimation in metric spaces: Achieving Exponential Concentration with a Fr'echet Mediancited by 1
  8. 2023Non-parametric regression for robot learning on manifoldscited by 0
  9. 2025Supervised Quadratic Feature Analysis: Information Geometry Approach for Dimensionality Reductioncited by 0
  10. 2025Rao Differential Privacycited by 0
  11. 2026PRISM: A 3D Probabilistic Neural Representation for Interpretable Shape Modelingcited by 0