分段归一化流
Piecewise Normalizing Flows
AI总结：
针对多模态问题中归一化流基础分布与目标分布拓扑不匹配导致性能差的问题，提出将目标分布划分为拓扑更匹配标准正态分布的簇、再训练系列流的分段归一化流，在标准基准上准确率优于现有学习型采样方法。
摘要：
归一化流是一种通过对基础分布进行可逆变换来建模复杂概率密度的成熟方法。然而，归一化流捕捉目标分布的准确率受基础分布拓扑结构的强烈影响。目标分布与基础分布的拓扑结构不匹配会导致性能不佳，这在多模态问题中是典型情况。已有多项研究尝试修改基础分布的拓扑结构以更好地匹配目标分布，方法包括使用高斯混合模型（Gaussian Mixture Models，Izmailov等人，2020；Ardizzone等人，2020；Hagemann & Neumayer，2021）或学习型接受/拒绝采样（Stimper等人，2022）。我们提出了分段归一化流，该方法将目标分布划分为多个簇，这些簇的拓扑结构与标准正态基础分布更匹配，随后训练一系列流来建模复杂的多模态目标。我们使用若干标准基准验证了分段流的性能，并将其建模多模态分布的准确率与Stimper等人（2022）提出的方法进行了对比。我们发现，在标准基准上，我们的方法始终优于Stimper等人（2022）的方法，具有更高的仿真准确率。
英文摘要：
Normalizing flows are an established approach for modelling complex probability densities through invertible transformations from a base distribution. However, the accuracy with which the target distribution can be captured by the normalizing flow is strongly influenced by the topology of the base distribution. A mismatch between the topology of the target and the base can result in a poor performance, as is typically the case for multi-modal problems. A number of different works have attempted to modify the topology of the base distribution to better match the target, either through the use of Gaussian Mixture Models (Izmailov et al., 2020; Ardizzone et al., 2020; Hagemann & Neumayer, 2021) or learned accept/reject sampling (Stimper et al., 2022). We introduce piecewise normalizing flows which divide the target distribution into clusters, with topologies that better match the standard normal base distribution, and train a series of flows to model complex multi-modal targets. We demonstrate the performance of the piecewise flows using some standard benchmarks and compare the accuracy of the flows to the approach taken in Stimper et al. (2022) for modelling multi-modal distributions. We find that our approach consistently outperforms the approach in Stimper et al. (2022) with a higher emulation accuracy on the standard benchmarks.
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。
