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Deep Learning (DL) methods have dramatically increased in popularity in recent years. While its initial success was demonstrated in the classification and manipulation of image data, there has been significant growth in the application of DL methods to problems in the biomedical sciences. However, the greater prevalence and complexity of missing data in biomedical datasets present significant challenges for DL methods. Here, we provide a formal treatment of missing data in the context of Variational Autoencoders (VAEs), a popular unsupervised DL architecture commonly used for dimension reduction, imputation, and learning latent representations of complex data. We propose a new VAE architecture, NIMIWAE, that is one of the first to flexibly account for both ignorable and non-ignorable patterns of missingness in input features at training time. Following training, samples can be drawn from the approximate posterior distribution of the missing data can be used for multiple imputation, facilitating downstream analyses on high dimensional incomplete datasets. We demonstrate through statistical simulation that our method outperforms existing approaches for unsupervised learning tasks and imputation accuracy. We conclude with a case study of an EHR dataset pertaining to 12,000 ICU patients containing a large number of diagnostic measurements and clinical outcomes, where many features are only partially observed. 

Abstract A primary challenge in the analysis of RNA-seq data is to identify differentially expressed genes or transcripts while controlling for technical biases. Ideally, a statistical testing procedure should incorporate the inherent uncertainty of the abundance estimates arising from the quantification step. Most popular methods for RNA-seq differential expression analysis fit a parametric model to the counts for each gene or transcript, and a subset of methods can incorporate uncertainty. Previous work has shown that nonparametric models for RNA-seq differential expression may have better control of the false discovery rate, and adapt well to new data types without requiring reformulation of a parametric model. Existing nonparametric models do not take into account inferential uncertainty, leading to an inflated false discovery rate, in particular at the transcript level. We propose a nonparametric model for differential expression analysis using inferential replicate counts, extending the existing SAMseq method to account for inferential uncertainty. We compare our method, Swish, with popular differential expression analysis methods. Swish has improved control of the false discovery rate, in particular for transcripts with high inferential uncertainty. We apply Swish to a single-cell RNA-seq dataset, assessing differential expression between sub-populations of cells, and compare its performance to the Wilcoxon test.