Title: Don't Forget Its Variance! The Minimum Path Variance Principle for Accurate and Stable Score-Based Density Ratio Estimation
Primary area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
Keywords: Density ratio estimation, minimum path variance principle, path optimization, Kumaraswamy mixture model

Abstract: Score-based methods have emerged as a powerful framework for density ratio estimation (DRE), but they face an important paradox in that, while theoretically path-independent, their practical performance depends critically on the chosen path schedule. 
	We resolve this issue by proving that tractable training objectives differ from the ideal, ground-truth objective by a crucial, overlooked term: the path variance of the time score.
	To address this, we propose MinPV-DRE (\textbf{Min}imum \textbf{P}ath \textbf{V}ariance DRE), which directly minimizes this missing objective. 
	Our key contribution is the derivation of a closed-form expression for the variance, turning an intractable problem into a tractable optimization. 
	By parameterizing the path with a flexible Kumaraswamy Mixture Model, our method learns a data-adaptive, low-variance path without heuristic selection. 
	This principled optimization of the complete objective yields more accurate and stable estimators, establishing new state-of-the-art results on challenging benchmarks.

TL;DR: MinPV-DRE analytically minimizes the path-dependent variance in score-based density ratio estimation, learning stable, accurate trajectories without heuristic path selection.