发表机构
Simons Institute, University of California Berkeley; Georgia Tech; Google Deepmind（加州大学伯克利分校西蒙斯研究所; 佐治亚理工学院; 谷歌DeepMind）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对仅可访问对数密度的采样问题，提出通过仿射后处理整合多个分数估计以降低偏差和方差，在困难密度上优于计算匹配的基线方法。
AI 中文摘要
仅利用概率密度的对数密度进行采样，是统计学、机器学习和物理科学中的一个基础问题。这一问题在无数据基于分数的扩散文献中得到了研究，该文献通过估计与高斯随机变量卷积产生的密度的分数，并实现逆向随机微分方程来对目标密度进行采样。在此框架下，分数估计器通过马尔可夫链蒙特卡洛、重要性采样或拒绝采样构建。这些估计器通常在混合时间和误差控制可以建立的机制之外运行，并且在估计底层分数时具有较大的偏差和方差。在我们的方法中，我们提出后处理：将固定的计算预算分配给多次评估，在不同点查询估计器，并通过线性组合拟合一个合并估计，以最小化目标位置的偏差和方差。最终值是多个分数估计向量的一种仿射映射。我们表明，与在单点查询的计算匹配的基础估计器相比，这降低了分数估计误差。我们证明了在难以处理的目标密度（如具有大条件数的对数凹密度、多模态密度和高维密度）上，与计算成本匹配的其他分数估计方法相比，样本质量得到了改善。
英文摘要
Sampling from a probability distribution with access only to its log-density is a foundational problem in statistics, machine learning, and the physical sciences. This problem is studied in the data-free score-based diffusion literature, which samples the target density via estimating scores of densities produced by convolution with Gaussian random variables and implementing a reverse SDE. In this framework, score estimators are constructed via Markov chain Monte Carlo, importance sampling, or rejection sampling. The estimators often operate far beyond the regime where mixing time and error control can be established and have large bias and variance when estimating the underlying score. In our method we propose post-processing: splitting a fixed computation budget across multiple evaluations, querying the estimator at different points, and fitting a single pooled estimate via linear combination to minimize bias and variance at a target location. The final value is an affine map of a vector of multiple score estimates. We show this reduces score estimation error when compared to the computation-matched base estimator queried at a single point. We demonstrate improved sample quality over other score estimation methods matched for computation cost on difficult target densities such as log-concave densities with large condition number, multimodal densities, and high-dimensional densities.
