Geometric Jensen-Shannon Divergence Between Gaussian Measures On Hilbert Space
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909646968586240 |
|---|---|
| author | Quang, Minh Ha Nielsen, Frank |
| author_facet | Quang, Minh Ha Nielsen, Frank |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10494 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric Jensen-Shannon Divergence Between Gaussian Measures On Hilbert Space Quang, Minh Ha Nielsen, Frank Probability Information Theory Machine Learning 28C20, 60G15, 47B65 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. |
| title | Geometric Jensen-Shannon Divergence Between Gaussian Measures On Hilbert Space |
| topic | Probability Information Theory Machine Learning 28C20, 60G15, 47B65 |
| url | https://arxiv.org/abs/2506.10494 |