A Minimum Variance Path Principle for Accurate and Stable Score-Based Density Ratio Estimation
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915997076684800 |
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| author | Chen, Wei Li, Jiacheng Li, Shigui Lin, Zhiqi Yang, Junmei Paisley, John Zeng, Delu |
| author_facet | Chen, Wei Li, Jiacheng Li, Shigui Lin, Zhiqi Yang, Junmei Paisley, John Zeng, Delu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_00834 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Minimum Variance Path Principle for Accurate and Stable Score-Based Density Ratio Estimation Chen, Wei Li, Jiacheng Li, Shigui Lin, Zhiqi Yang, Junmei Paisley, John Zeng, Delu Machine Learning Artificial Intelligence 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. |
| title | A Minimum Variance Path Principle for Accurate and Stable Score-Based Density Ratio Estimation |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2602.00834 |