连续指标规范化流的变分推断
Variational Inference with Continuously-Indexed Normalizing Flows
摘要：
连续索引流（CIF）最近在各种密度估计任务上实现了对基线归一化流的改进。CIF不具有封闭形式的边缘密度，因此，与标准流不同，不能直接插入到变分推断（VI）方案中，以产生更具表现力的近似后验族。然而，我们在这里展示了如何CIF可以作为辅助VI计划的一部分，以自然的方式制定和训练表达后验近似。我们利用多层CIF的条件独立结构来构建所需的辅助推理模型，我们根据经验证明了模型证据的低方差估计。然后，我们证明了优势的CIF基线流量VI问题时，感兴趣的后验分布具有复杂的拓扑结构，获得改进的结果，在贝叶斯推断和代理极大似然设置。
英文摘要：
Continuously-indexed flows (CIFs) have recently achieved improvements over baseline normalizing flows on a variety of density estimation tasks. CIFs do not possess a closed-form marginal density, and so, unlike standard flows, cannot be plugged in directly to a variational inference (VI) scheme in order to produce a more expressive family of approximate posteriors. However, we show here how CIFs can be used as part of an auxiliary VI scheme to formulate and train expressive posterior approximations in a natural way. We exploit the conditional independence structure of multi-layer CIFs to build the required auxiliary inference models, which we show empirically yield low-variance estimators of the model evidence. We then demonstrate the advantages of CIFs over baseline flows in VI problems when the posterior distribution of interest possesses a complicated topology, obtaining improved results in both the Bayesian inference and surrogate maximum likelihood settings.
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