Flow-Based Density Ratio Estimation for Intractable Distributions with Applications in Genomics

Egor Antipov, Alessandro Palma, Lorenzo Consoli, Stephan Günnemann, Andrea Dittadi, Fabian J Theis
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:2949-2986, 2026.

Abstract

Estimating density ratios between pairs of intractable data distributions is a core problem in probabilistic modeling, enabling principled comparisons of sample likelihoods under different data-generating processes across conditions. While exact-likelihood models such as normalizing flows offer a promising approach to density ratio estimation, naive evaluations are computationally expensive and prone to discretization errors because they require simulating each distribution’s likelihood independently. In this work, we leverage condition-aware flow matching to derive a single dynamical formulation for tracking density ratios along generative trajectories. We demonstrate competitive performance on simulated benchmarks for closed-form ratio estimation, and show that our method supports versatile tasks in single-cell genomics data analysis, where likelihood-based comparisons of cellular states across experimental conditions enable treatment effect estimation and batch correction evaluation.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-antipov26a, title = {Flow-Based Density Ratio Estimation for Intractable Distributions with Applications in Genomics}, author = {Antipov, Egor and Palma, Alessandro and Consoli, Lorenzo and G\"{u}nnemann, Stephan and Dittadi, Andrea and Theis, Fabian J}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {2949--2986}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/antipov26a/antipov26a.pdf}, url = {https://proceedings.mlr.press/v306/antipov26a.html}, abstract = {Estimating density ratios between pairs of intractable data distributions is a core problem in probabilistic modeling, enabling principled comparisons of sample likelihoods under different data-generating processes across conditions. While exact-likelihood models such as normalizing flows offer a promising approach to density ratio estimation, naive evaluations are computationally expensive and prone to discretization errors because they require simulating each distribution’s likelihood independently. In this work, we leverage condition-aware flow matching to derive a single dynamical formulation for tracking density ratios along generative trajectories. We demonstrate competitive performance on simulated benchmarks for closed-form ratio estimation, and show that our method supports versatile tasks in single-cell genomics data analysis, where likelihood-based comparisons of cellular states across experimental conditions enable treatment effect estimation and batch correction evaluation.} }
Endnote
%0 Conference Paper %T Flow-Based Density Ratio Estimation for Intractable Distributions with Applications in Genomics %A Egor Antipov %A Alessandro Palma %A Lorenzo Consoli %A Stephan Günnemann %A Andrea Dittadi %A Fabian J Theis %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-antipov26a %I PMLR %P 2949--2986 %U https://proceedings.mlr.press/v306/antipov26a.html %V 306 %X Estimating density ratios between pairs of intractable data distributions is a core problem in probabilistic modeling, enabling principled comparisons of sample likelihoods under different data-generating processes across conditions. While exact-likelihood models such as normalizing flows offer a promising approach to density ratio estimation, naive evaluations are computationally expensive and prone to discretization errors because they require simulating each distribution’s likelihood independently. In this work, we leverage condition-aware flow matching to derive a single dynamical formulation for tracking density ratios along generative trajectories. We demonstrate competitive performance on simulated benchmarks for closed-form ratio estimation, and show that our method supports versatile tasks in single-cell genomics data analysis, where likelihood-based comparisons of cellular states across experimental conditions enable treatment effect estimation and batch correction evaluation.
APA
Antipov, E., Palma, A., Consoli, L., Günnemann, S., Dittadi, A. & Theis, F.J.. (2026). Flow-Based Density Ratio Estimation for Intractable Distributions with Applications in Genomics. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:2949-2986 Available from https://proceedings.mlr.press/v306/antipov26a.html.

Related Material