Are score function estimators a viable approach to learning with $k$-subset sampling? Sampling $k$-subsets is a fundamental operation that is not amenable to differentiable parametrization, impeding gradient-based optimization. Previous work has favored approximate pathwise gradients or relaxed sampling, dismissing score function estimators because of their high variance. Inspired by the success of score function estimators in variational inference and reinforcement learning, we revisit them for $k$-subset sampling. We demonstrate how to efficiently compute the distribution's score function using a discrete Fourier transform and reduce the estimator's variance with control variates. The resulting estimator provides both $k$-hot samples and unbiased gradient estimates while being applicable to non-differentiable downstream models, unlike existing methods. We validate our approach experimentally and find that it produces results comparable to those of recent state-of-the-art pathwise gradient estimators across a range of tasks.

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.