We consider the problem of learning Variational Autoencoders (VAEs), i.e., a type of deep generative model, from data with missing values. Such data is omnipresent in real-world applications of machine learning because complete data is often impossible or too costly to obtain. We particularly focus on improving a VAE's amortized posterior inference, i.e., the encoder, which in the case of missing data can be susceptible to learning inconsistent posterior distributions regarding the missingness. To this end, we provide a formal definition of posterior consistency and propose an approach for regularizing an encoder's posterior distribution which promotes this consistency. We observe that the proposed regularization suggests a different training objective than that typically considered in the literature when facing missing values. Furthermore, we empirically demonstrate that our regularization leads to improved performance in missing value settings in terms of reconstruction quality and downstream tasks utilizing uncertainty in the latent space. This improved performance can be observed for many classes of VAEs including VAEs equipped with normalizing flows.

通过提出一种正则化方法来提高变分自动编码器（VAEs）对于缺失数据的后验一致性，从而改善了缺失数据条件下的重构质量和利用潜在空间中的不确定性进行下游任务的绩效。

变分自编码器中缺失数据的后验一致性