A numerical approximation method for the Fisher-Rao distance between multivariate normal distributions
arXiv:2302.08175 · doi:10.3390/e25040654
Abstract
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 -variate normal manifold into the cone of 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.
arXiv comment46 pages, 19 figures, 3 tables
References in corpus (10)
- On a generalization of the Jensen-Shannon divergence and the JS-symmetrization of distances relying on abstract means
- Fisher-Rao Metric, Geometry, and Complexity of Neural Networks
- Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition
- On Approximating the Riemannian 1-Center
- Adversarial Robustness via Fisher-Rao Regularization
- Optimal Transport vs. Fisher-Rao distance between Copulas for Clustering Multivariate Time Series
- A New Robust Regression Method Based on Minimization of Geodesic Distances on a Probabilistic Manifold: Application to Power Laws
- Hilbert geometry of the Siegel disk: The Siegel-Klein disk model
- The Fisher-Rao Loss for Learning under Label Noise
- Geometry of the Fisher-Rao metric on the space of smooth densities on a compact manifold