用分步藤耦合实现更灵活的变分推断，自动调节模型复杂度。
Stepwise Variational Inference with Vine Copulas
- 分步构建藤耦合结构，逐层建模潜在变量间复杂依赖关系。
- 基于Rényi散度优化，避免传统方法参数失真问题。
- 自动停止机制省去预设复杂度参数，适合稀疏高斯过程等场景。
我们提出一种基于藤耦合的分步变分推断（stepwise VI with vine copulas）：一种通用的变分推断框架，将藤耦合与新颖的分步参数估计方法结合。藤耦合由嵌套树结构组成，通过增加树层数可建模更复杂的潜变量依赖关系。本文提出按藤结构逐层估计近似后验分布。此外，我们指出传统的反向KL散度无法正确恢复藤耦合模型中的参数，因此采用基于Rényi散度的证据下界。最后，设计了一种直观的终止准则，用于决定是否继续添加新树，从而无需预先设定变分分布的复杂度参数，突破了多数方法的限制。该方法在均值场变分推断（MFVI）与完全潜依赖之间实现平滑插值。在多个应用中，特别是在稀疏高斯过程（sparse Gaussian processes）中，该方法参数效率高且性能优于MFVI。
原文摘要 · Abstract (English)
We propose stepwise variational inference (VI) with vine copulas: a universal VI procedure that combines vine copulas with a novel stepwise estimation procedure of the variational parameters. Vine copulas consist of a nested sequence of trees built from copulas, where more complex latent dependence can be modeled with increasing number of trees. We propose to estimate the vine copula approximate posterior in a stepwise fashion, tree by tree along the vine structure. Further, we show that the usual backward Kullback-Leibler divergence cannot recover the correct parameters in the vine copula model, thus the evidence lower bound is defined based on the Rényi divergence. Finally, an intuitive stopping criterion for adding further trees to the vine eliminates the need to pre-define a complexity parameter of the variational distribution, as required for most other approaches. Thus, our method interpolates between mean-field VI (MFVI) and full latent dependence. In many applications, in particular sparse Gaussian processes, our method is parsimonious with parameters, while outperforming MFVI.
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