Revisiting Score Function Estimators for $k$-Subset Sampling

TL;DR

This paper explores the use of score function estimators for $k$-subset sampling, demonstrating their efficiency, unbiasedness, and applicability to non-differentiable models, with competitive feature selection results.

Contribution

It introduces a novel method to compute score function estimators for $k$-subset sampling using discrete Fourier transforms and variance reduction techniques.

Findings

Efficient computation of $k$-subset distribution's score function.

Unbiased gradient estimates applicable to non-differentiable models.

Competitive feature selection performance.

Abstract

Are score function estimators an underestimated approach to learning with $k$-subset sampling? Sampling $k$-subsets is a fundamental operation in many machine learning tasks that is not amenable to differentiable parametrization, impeding gradient-based optimization. Prior work has focused on relaxed sampling or pathwise gradient estimators. Inspired by the success of score function estimators in variational inference and reinforcement learning, we revisit them within the context of $k$-subset sampling. Specifically, we demonstrate how to efficiently compute the $k$-subset distribution's score function using a discrete Fourier transform, and reduce the estimator's variance with control variates. The resulting estimator provides both exact samples and unbiased gradient estimates while also applying to non-differentiable downstream models, unlike existing methods. Experiments in feature selection show results competitive with current methods, despite weaker assumptions.