Fisher Rao Distance

The Fisher-Rao distance measures the dissimilarity between probability distributions, utilizing the Riemannian geometry induced by the Fisher information metric. Current research focuses on developing efficient approximation and bounding techniques for this distance, particularly for multivariate normal distributions, exploring alternative metrics like pullback cone distances, and applying it in various contexts such as sampling algorithms and robust loss functions for machine learning. This work is significant for its potential to improve data analysis in diverse fields, including image processing, signal processing, and statistical inference, by providing principled and computationally tractable methods for comparing and manipulating probability distributions.