Optimised Feature Subset Selection via Simulated Annealing

TL;DR

This paper presents SA-FDR, a simulated annealing-based algorithm for optimal feature subset selection that balances model simplicity and accuracy in high-dimensional classification tasks.

Contribution

SA-FDR introduces a global search approach for $\, ext{l}_0$-norm feature selection using simulated annealing guided by Fisher discriminant ratio, improving over greedy methods.

Findings

SA-FDR selects more compact feature subsets with high accuracy.

It effectively captures inter-feature dependencies missed by greedy methods.

Demonstrates scalability on large datasets with hundreds of thousands of samples.

Abstract

We introduce SA-FDR, a novel algorithm for $\ell_0$-norm feature selection that considers this task as a combinatorial optimisation problem and solves it by using simulated annealing to perform a global search over the space of feature subsets. The optimisation is guided by the Fisher discriminant ratio, which we use as a computationally efficient proxy for model quality in classification tasks. Our experiments, conducted on datasets with up to hundreds of thousands of samples and hundreds of features, demonstrate that SA-FDR consistently selects more compact feature subsets while achieving a high predictive accuracy. This ability to recover informative yet minimal sets of features stems from its capacity to capture inter-feature dependencies often missed by greedy optimisation approaches. As a result, SA-FDR provides a flexible and effective solution for designing interpretable models in high-dimensional settings, particularly when model sparsity, interpretability, and performance are crucial.