Title: Deep unsupervised feature selection. Abstract: Unsupervised feature selection involves finding a small number of highly informative features, in the absence of a specific supervised learning task. Selecting a small number of features is an important problem in many scientific domains with high-dimensional observations. Here, we propose the restricted autoencoder (RAE) framework for selecting features that can accurately reconstruct the rest of the features. We justify our approach through a novel proof that the reconstruction ability of a set of features bounds its performance in downstream supervised learning tasks. Based on this theory, we present a learning algorithm for RAEs that iteratively eliminates features using learned per-feature corruption rates. We apply the RAE framework to two high-dimensional biological datasets—single cell RNA sequencing and microarray gene expression data, which pose important problems in cell biology and precision medicine—and demonstrate that RAEs outperform nine baseline methods, often by a large margin.