提出最小方差路径原则，提升得分函数密度比估计的准确性和稳定性
A Minimum Variance Path Principle for Accurate and Stable Score-Based Density Ratio Estimation
- 通过最小化得分函数路径方差优化训练目标
- 在多个基准上达到新最好性能，方差显著降低
- 适合需要稳定密度比估计的研究者和应用
得分方法在机器学习中表现强大，但存在理论路径无关与实践路径依赖的矛盾。我们证明实践中训练目标与理想目标之间的差异，源于一个被忽视的关键项：得分函数路径方差。为此提出最小方差路径（MVP）原则，以最小化该方差。核心贡献是推导出方差的闭式表达式，使优化可行。通过灵活的Kumaraswamy混合模型参数化路径，方法可自动学习低方差路径，无需人工调参。这种对完整目标的原理性优化，带来了更准确、更稳定的估计器，在挑战性基准上取得新最优结果，并为得分函数插值提供通用框架。
原文摘要 · Abstract (English)
Score-based methods are powerful across machine learning, but they face a paradox: theoretically path-independent, yet practically path-dependent. We resolve this by proving that practical training objectives differ from the ideal, ground-truth objective by a crucial, overlooked term: the path variance of the score function. We propose the MVP (**M**imum **V**ariance **P**ath) Principle to minimize this path variance. Our key contribution is deriving a closed-form expression for the variance, making optimization tractable. By parameterizing the path with a flexible Kumaraswamy Mixture Model, our method learns data-adaptive, low-variance paths without heuristic manual selection. This principled optimization of the complete objective yields more accurate and stable estimators, establishing new state-of-the-art results on challenging benchmarks and providing a general framework for optimizing score-based interpolation. Our code can be found in https://github.com/Hoemr/OpenDRE.git.
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