A note on the unique properties of the Kullback--Leibler divergence for sampling via gradient flows
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913089783332864 |
|---|---|
| author | Crucinio, Francesca Romana |
| author_facet | Crucinio, Francesca Romana |
| contents | We consider the problem of sampling from a probability distribution $π$ which admits a density w.r.t. a dominating measure. It is well known that this can be written as an optimisation problem over the space of probability distributions in which we aim to minimise a divergence from $π$. The optimisation problem is normally solved through gradient flows in the space of probability distributions with an appropriate metric. We show that the Kullback--Leibler divergence is the only divergence in the family of Bregman divergences whose gradient flow w.r.t. many popular metrics does not require knowledge of the normalising constant of $π$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04330 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on the unique properties of the Kullback--Leibler divergence for sampling via gradient flows Crucinio, Francesca Romana Methodology Machine Learning Statistics Theory Computation We consider the problem of sampling from a probability distribution $π$ which admits a density w.r.t. a dominating measure. It is well known that this can be written as an optimisation problem over the space of probability distributions in which we aim to minimise a divergence from $π$. The optimisation problem is normally solved through gradient flows in the space of probability distributions with an appropriate metric. We show that the Kullback--Leibler divergence is the only divergence in the family of Bregman divergences whose gradient flow w.r.t. many popular metrics does not require knowledge of the normalising constant of $π$. |
| title | A note on the unique properties of the Kullback--Leibler divergence for sampling via gradient flows |
| topic | Methodology Machine Learning Statistics Theory Computation |
| url | https://arxiv.org/abs/2507.04330 |