A large family of score-based methods are developed recently to solve unsupervised learning problems including density estimation, statistical testing and variational inference. These methods are attractive because they exploit the derivative of the log density, which is independent of the normaliser, and are thus suitable for tasks involving unnormalised densities. Despite the theoretical guarantees on the performance, here we illustrate a common practical issue suffered by these methods when the unnormalised distribution of interest has isolated components. In particular, we study the behaviour of some popular score-based methods on tasks involving 1-D mixture of Gaussian. These methods fail to identify appropriate mixing proportions when the unnormalised distribution is multimodal. Finally, some directions for finding a remedy are discussed in light of recent successes in specific tasks. We hope to bring the attention of theoreticians and practitioners to this issue when developing new algorithms and applications.

本文研究密度估计和近似贝叶斯推断时，如果密度函数含有未知归一化常数，score-based methods是常用的技术，但是我们发现当含有孤立成分时这些方法会出现实际失效的情况，我们试图通过启发式尝试解决这些问题。

基于得分的方法对孤立成分和混合比例的盲视