Real world datasets often contain entries with missing elements e.g. in a medical dataset, a patient is unlikely to have taken all possible diagnostic tests. Variational Autoencoders (VAEs) are popular generative models often used for unsupervised learning. Despite their widespread use it is unclear how best to apply VAEs to datasets with missing data. We develop a novel latent variable model of a corruption process which generates missing data, and derive a corresponding tractable evidence lower bound (ELBO). Our model is straightforward to implement, can handle both missing completely at random (MCAR) and missing not at random (MNAR) data, scales to high dimensional inputs and gives both the VAE encoder and decoder principled access to indicator variables for whether a data element is missing or not. On the MNIST and SVHN datasets we demonstrate improved marginal log-likelihood of observed data and better missing data imputation, compared to existing approaches.

开发了一种新颖的潜在变量模型，通过生成缺失数据的损坏过程对处理缺失数据集进行了模糊处理，并推导出相应的易于实现、可处理可随机缺失和不随机缺失数据、适用于高维输入、VAE编码器和解码器原则性访问指标变量以确定数据元素是否缺失的可跟踪证据下限(ELBO)。在MNIST和SVHN数据集上，相比现有方法，证明了观测数据的边际对数似然和更好的缺失数据插值提高。

缺失数据下的VAEs