通过条件路径提升高维密度比估计的效率与精度
Density Ratio Estimation with Conditional Probability Paths
- 引入条件变量构建可闭合求解的目标函数
- 在复杂任务上实现更快收敛和更优估计精度
- 适用于需要高效密度比估计的研究场景
高维密度比估计可转化为对时间得分沿概率路径的积分。实际中需基于两组密度样本估计时间得分，但现有方法计算成本高且精度不足。受生成建模进展启发，本文提出一种基于条件变量的时间得分估计新框架，合理选择条件变量可导出闭式目标函数。实验表明，相比以往方法，本方法能更快学习时间得分，在挑战性任务上达到竞争性或更优的密度比估计精度。此外，本文还建立了估计密度比误差的理论保证。
原文摘要 · Abstract (English)
Density ratio estimation in high dimensions can be reframed as integrating a certain quantity, the time score, over probability paths which interpolate between the two densities. In practice, the time score has to be estimated based on samples from the two densities. However, existing methods for this problem remain computationally expensive and can yield inaccurate estimates. Inspired by recent advances in generative modeling, we introduce a novel framework for time score estimation, based on a conditioning variable. Choosing the conditioning variable judiciously enables a closed-form objective function. We demonstrate that, compared to previous approaches, our approach results in faster learning of the time score and competitive or better estimation accuracies of the density ratio on challenging tasks. Furthermore, we establish theoretical guarantees on the error of the estimated density ratio.
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