We consider the problem of handling missing data with deep latent variable
models (DLVMs). First, we present a simple technique to train DLVMs when the
training set contains missing-at-random data. Our approach, called MIWAE, is
based on the importance-weighted autoencoder (IWAE), and maximises a
potentially tight lower bound of the log-likelihood of the observed data.
Compared to the original IWAE, our algorithm does not induce any additional
computational overhead due to the missing data. We also develop Monte Carlo
techniques for single and multiple imputation using a DLVM trained on an
incomplete data set. We illustrate our approach by training a convolutional
DLVM on a static binarisation of MNIST that contains 50% of missing pixels.
Leveraging multiple imputation, a convolutional network trained on these
incomplete digits has a test performance similar to one trained on complete
data. On various continuous and binary data sets, we also show that MIWAE
provides accurate single imputations, and is highly competitive with
state-of-the-art methods.

研究在深度潜变量模型（DLVM）中如何处理缺失数据的问题，提出了一种称为 MIWAE 的基于重要性加权自编码器（IWAE）的方法，可以最大化观察数据的对数似然的潜在下界，通过该方法实现单一和多重插值。在这些不完整的 MNIST 数字上训练的深度卷积 DLVM，通过多重插值，其测试性能与完整数据集训练的网络相似，并且在各种连续和二元数据集上，MIWAE 提供精确的单一插值，并且在最先进方法中非常有竞争力。