Feature selection is a crucial task in settings where data is high-dimensional or acquiring the full set of features is costly. Recent developments in neural network-based embedded feature selection show promising results across a wide range of applications. Concrete Autoencoders (CAEs), considered state-of-the-art in embedded feature selection, may struggle to achieve stable joint optimization, hurting their training time and generalization. In this work, we identify that this instability is correlated with the CAE learning duplicate selections. To remedy this, we propose a simple and effective improvement: Indirectly Parameterized CAEs (IP-CAEs). IP-CAEs learn an embedding and a mapping from it to the Gumbel-Softmax distributions' parameters. Despite being simple to implement, IP-CAE exhibits significant and consistent improvements over CAE in both generalization and training time across several datasets for reconstruction and classification. Unlike CAE, IP-CAE effectively leverages non-linear relationships and does not require retraining the jointly optimized decoder. Furthermore, our approach is, in principle, generalizable to Gumbel-Softmax distributions beyond feature selection.

We introduce the concrete autoencoder, an end-to-end differentiable method for global feature selection, which efficiently identifies a subset of the most informative features and simultaneously learns a neural network to reconstruct the input data from the selected features. Our method is unsupervised, and is based on using a concrete selector layer as the encoder and using a standard neural network as the decoder. During the training phase, the temperature of the concrete selector layer is gradually decreased, which encourages a user-specified number of discrete features to be learned. During test time, the selected features can be used with the decoder network to reconstruct the remaining input features. We evaluate concrete autoencoders on a variety of datasets, where they significantly outperform state-of-the-art methods for feature selection and data reconstruction. In particular, on a large-scale gene expression dataset, the concrete autoencoder selects a small subset of genes whose expression levels can be use to impute the expression levels of the remaining genes. In doing so, it improves on the current widely-used expert-curated L1000 landmark genes, potentially reducing measurement costs by 20%. The concrete autoencoder can be implemented by adding just a few lines of code to a standard autoencoder.