论文标题
基于分数的方法对孤立组件和混合比例的失明
Blindness of score-based methods to isolated components and mixing proportions
论文作者
论文摘要
诸如密度估计和近似贝叶斯推理之类的统计任务通常涉及具有未知标准常数的密度。基于得分的方法（包括得分匹配）是流行技术，因为它们没有标准化常数。尽管这些方法享有理论保证，但鲜为人知的事实是，当兴趣的分布分布具有孤立的组件时，它们表现出实际的故障模式 - 他们无法发现孤立的组件或识别组件之间的正确混合比例。我们使用简单的分布证明了这些发现，并提出了解决这些问题的启发式尝试。我们希望在开发新算法和应用程序时，将理论家和从业者的注意力引起这些问题。
Statistical tasks such as density estimation and approximate Bayesian inference often involve densities with unknown normalising constants. Score-based methods, including score matching, are popular techniques as they are free of normalising constants. Although these methods enjoy theoretical guarantees, a little-known fact is that they exhibit practical failure modes when the unnormalised distribution of interest has isolated components -- they cannot discover isolated components or identify the correct mixing proportions between components. We demonstrate these findings using simple distributions and present heuristic attempts to address these issues. We hope to bring the attention of theoreticians and practitioners to these issues when developing new algorithms and applications.
