Flow-Based Density Ratio Estimation for Intractable Distributions with Applications in Genomics
This work addresses a core problem in probabilistic modeling for applications like genomics, though it appears incremental as it builds on existing flow-based methods.
The paper tackled the problem of estimating density ratios between intractable distributions by developing a condition-aware flow matching method that avoids costly likelihood integrals, achieving competitive performance on benchmarks and enabling applications in single-cell genomics such as treatment effect estimation and batch correction evaluation.
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 and covariates. While exact-likelihood models such as normalizing flows offer a promising approach to density ratio estimation, naive flow-based evaluations are computationally expensive, as they require simulating costly likelihood integrals for each distribution separately. 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.