Density Ratio Estimation with Conditional Probability Paths

Hanlin Yu, Arto Klami, Aapo Hyvarinen, Anna Korba, Omar Chehab
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:73146-73174, 2025.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-yu25l, title = {Density Ratio Estimation with Conditional Probability Paths}, author = {Yu, Hanlin and Klami, Arto and Hyvarinen, Aapo and Korba, Anna and Chehab, Omar}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {73146--73174}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/yu25l/yu25l.pdf}, url = {https://proceedings.mlr.press/v267/yu25l.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Density Ratio Estimation with Conditional Probability Paths %A Hanlin Yu %A Arto Klami %A Aapo Hyvarinen %A Anna Korba %A Omar Chehab %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-yu25l %I PMLR %P 73146--73174 %U https://proceedings.mlr.press/v267/yu25l.html %V 267 %X 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.
APA
Yu, H., Klami, A., Hyvarinen, A., Korba, A. & Chehab, O.. (2025). Density Ratio Estimation with Conditional Probability Paths. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:73146-73174 Available from https://proceedings.mlr.press/v267/yu25l.html.

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