Consistent Nonparametric Different-Feature Selection via the Sparsest $k$-Subgraph Problem
This addresses the challenge of identifying features that differentiate two probability distributions, which is crucial in scientific and engineering applications, by overcoming limitations of existing methods with restrictive assumptions or computational difficulties.
The paper tackles the problem of two-sample feature selection by formulating it as a sparsest k-subgraph problem, resulting in a nonparametric method that is computationally efficient and provides a consistent estimator under mild conditions, with experimental results showing it outperforms current methods in accuracy and computation time.
Two-sample feature selection is the problem of finding features that describe a difference between two probability distributions, which is a ubiquitous problem in both scientific and engineering studies. However, existing methods have limited applicability because of their restrictive assumptions on data distributoins or computational difficulty. In this paper, we resolve these difficulties by formulating the problem as a sparsest $k$-subgraph problem. The proposed method is nonparametric and does not assume any specific parametric models on the data distributions. We show that the proposed method is computationally efficient and does not require any extra computation for model selection. Moreover, we prove that the proposed method provides a consistent estimator of features under mild conditions. Our experimental results show that the proposed method outperforms the current method with regard to both accuracy and computation time.