Regularized Greedy Column Subset Selection
This work addresses noise sensitivity in feature selection for machine learning practitioners, offering an incremental improvement over existing methods.
The paper tackles the sensitivity to noise in the Column Subset Selection Problem for unsupervised feature selection by proposing a regularized formulation and an efficient greedy algorithm, demonstrating significantly increased robustness and stability in experiments on real and synthetic data.
The Column Subset Selection Problem provides a natural framework for unsupervised feature selection. Despite being a hard combinatorial optimization problem, there exist efficient algorithms that provide good approximations. The drawback of the problem formulation is that it incorporates no form of regularization, and is therefore very sensitive to noise when presented with scarce data. In this paper we propose a regularized formulation of this problem, and derive a correct greedy algorithm that is similar in efficiency to existing greedy methods for the unregularized problem. We study its adequacy for feature selection and propose suitable formulations. Additionally, we derive a lower bound for the error of the proposed problems. Through various numerical experiments on real and synthetic data, we demonstrate the significantly increased robustness and stability of our method, as well as the improved conditioning of its output, all while remaining efficient for practical use.