Beyond Discrete Selection: Continuous F.mbedding Space Optimization for Generative Feature Selection

The goal of Feature Selection - comprising filter, wrapper, and embedded approaches - is to find the optimal feature subset for designated downstream tasks. Nevertheless, current feature selection methods are limited by: 1) the selection criteria of these methods are varied for different domains, leading them hard to he generalized; 2) the selection performance of these approaches drops significantly when processing high -dimensional feature space coupled with small sample size. In light of these challenges, we pose the question: can selected feature subsets be more robust, accurate, and input dimensionality agnostic? In this paper, we reformulate the feature selection problem as a deep differentiable optimization task and propose a new research perspective: conceptualizing discrete feature subletting as continuous embedding space optimization. We introduce a novel and principled framework that encompasses a sequential encoder, an accuracy evaluator, a sequential decoder, and a gradient ascent optimizer. This comprehensive framework inchides four important steps: preparation of features-accuracy training data, deep feature subset embedding, gradient-optimized search, and feature subset reconstruction. Specifically, we utilize reinforcement feature selection learning to generate diverse and high-quality training data and enhance generalization. By optimizing reconstruction and accuracy losses, we embed feature selection knowledge into a continuous space using an encoderevaluator-decoder model structure. We employ a gradient ascent search algorithm to find better embeddings in the learned embedding space. Furthermore, we reconstruct feature selection solutions using these embeddings and select the feature subset with the highest performance for downstream tasks as the optimal subset. Finally, extensive experimental results demonstrate the effectiveness of our proposed method, showcasing significant enhancements in feature selection robustness and accuracy. To improve the reproducibility of our research, we have released accompanying code and datasets by Dropbox.