基于评分的方法对孤立组分和混合比例的盲性
Blindness of score-based methods to isolated components and mixing proportions
摘要：
诸如密度估计和近似贝叶斯推断的统计任务通常涉及具有未知归一化常数的密度。基于分数的方法，包括分数匹配，是流行的技术，因为它们没有归一化常数。虽然这些方法享有理论保证，但一个鲜为人知的事实是，当感兴趣的非归一化分布具有孤立的成分时，它们会表现出实际的故障模式-它们无法发现孤立的成分或识别成分之间的正确混合比例。我们证明了这些发现使用简单的分布和目前的启发式尝试来解决这些问题。我们希望在开发新的算法和应用程序时，引起理论家和实践者对这些问题的关注。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
