Title: One-Step Score-Based Density Ratio Estimation: Solver-Free with Analytic Frames
Primary area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
Keywords: one step, score-based, density ratio estimation, solver-free, analytic frame

Abstract: Score-based density ratio estimation is essential for measuring discrepancies between probability distributions, yet existing methods often suffer from high computational costs. We propose One-Step Score-Based Density Ratio Estimation (OS-DRE), an analytic and efficient framework that eliminates the need for numerical solvers. Our approach is based on a  spatiotemporal decomposition of the time score function, where its temporal component is represented with an RBF-based (radial basis function) analytic frame. This transforms the intractable temporal integral into a closed-form weighted sum, enabling OS-DRE to estimate density ratios with only one function evaluation while preserving high accuracy. Theoretical analysis provides a rigorous truncation error bounds, ensuring provable accuracy with finite bases. Empirical results show that OS-DRE achieves competitive performance while completing density ratio estimation in a single step, effectively resolving the long-standing efficiency–accuracy trade-off in score-based methods.

TL;DR: A solver-free, one-step score-based method for density ratio estimation.