# Geometric Jensen-Shannon Divergence Between Gaussian Measures On Hilbert Space

arXiv: https://arxiv.org/abs/2506.10494 · HTML: https://mlsanity.com/paper/2506.10494/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 29 references that are in the map.
- First posted on arXiv 12 Jun 2025.

## Builds on (most cited first, 4 of 4)

- [On a generalization of the Jensen-Shannon divergence and the JS-symmetrization of distances relying on abstract means](https://mlsanity.com/paper/1904.04017/) (2019)
- [Kullback-Leibler and Renyi divergences in reproducing kernel Hilbert space and Gaussian process settings](https://mlsanity.com/paper/2207.08406/) (2022)
- [Bootstrap Methods for the Empirical Study of Decision-Making and Information Flows in Social Systems](https://mlsanity.com/paper/1302.0907/) (2013)
- [Estimation of Riemannian distances between covariance operators and Gaussian processes](https://mlsanity.com/paper/2108.11683/) (2021)

## Built on by (most cited first, 1 of 1)

- [Two tales for a geometric Jensen--Shannon divergence](https://mlsanity.com/paper/2508.05066/) (2025)

## Abstract (arXiv)

This work studies the Geometric Jensen-Shannon divergence, based on the notion of geometric mean of probability measures, in the setting of Gaussian measures on an infinite-dimensional Hilbert space. On the set of all Gaussian measures equivalent to a fixed one, we present a closed form expression for this divergence that directly generalizes the finite-dimensional version. Using the notion of Log-Determinant divergences between positive definite unitized trace class operators, we then define a Regularized Geometric Jensen-Shannon divergence that is valid for any pair of Gaussian measures and that recovers the exact Geometric Jensen-Shannon divergence between two equivalent Gaussian measures when the regularization parameter tends to zero.