One-Step Score-Based Density Ratio Estimation: Solver-Free with Analytic Frames

Wei Chen, Jiacheng Li, Shigui Li, Zhiqi Lin, JIAN XU, Junmei Yang, John Paisley, Delu Zeng

Keywords: one step, score-based, density ratio estimation, solver-free, analytic frame

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

Abstract: Score-based density ratio estimation is essential for measuring discrepancies between probability distributions, yet existing methods often suffer from high computational costs, requiring many function evaluations to maintain accuracy. 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.

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

Submission Number: 885