Density Ratio Estimation with Conditional Probability Paths
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_ | 1866913889838432256 |
|---|---|
| author | Yu, Hanlin Klami, Arto Hyvärinen, Aapo Korba, Anna Chehab, Omar |
| author_facet | Yu, Hanlin Klami, Arto Hyvärinen, Aapo Korba, Anna Chehab, Omar |
| contents | Density ratio estimation in high dimensions can be reframed as integrating a certain quantity, the time score, over probability paths which interpolate between the two densities. In practice, the time score has to be estimated based on samples from the two densities. However, existing methods for this problem remain computationally expensive and can yield inaccurate estimates. Inspired by recent advances in generative modeling, we introduce a novel framework for time score estimation, based on a conditioning variable. Choosing the conditioning variable judiciously enables a closed-form objective function. We demonstrate that, compared to previous approaches, our approach results in faster learning of the time score and competitive or better estimation accuracies of the density ratio on challenging tasks. Furthermore, we establish theoretical guarantees on the error of the estimated density ratio. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02300 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Density Ratio Estimation with Conditional Probability Paths Yu, Hanlin Klami, Arto Hyvärinen, Aapo Korba, Anna Chehab, Omar Machine Learning Density ratio estimation in high dimensions can be reframed as integrating a certain quantity, the time score, over probability paths which interpolate between the two densities. In practice, the time score has to be estimated based on samples from the two densities. However, existing methods for this problem remain computationally expensive and can yield inaccurate estimates. Inspired by recent advances in generative modeling, we introduce a novel framework for time score estimation, based on a conditioning variable. Choosing the conditioning variable judiciously enables a closed-form objective function. We demonstrate that, compared to previous approaches, our approach results in faster learning of the time score and competitive or better estimation accuracies of the density ratio on challenging tasks. Furthermore, we establish theoretical guarantees on the error of the estimated density ratio. |
| title | Density Ratio Estimation with Conditional Probability Paths |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2502.02300 |