Statistical inference for sequential feature selection after domain adaptation

In the context of high-dimensional regression, feature selection methods, such as sequential feature selection (SeqFS), are commonly used to identify relevant features. When data is limited, domain adaptation (DA) becomes crucial. DA is a paradigm that transfers knowledge from a related source domain to a target domain, with the goal of improving generalization performance. Although SeqFS under DA is an important task in machine learning, none of the existing methods can guarantee the reliability of its results. In this paper, we propose a novel statistical inference method for testing the features selected by SeqFS after DA. The key advantage of the proposed method is its capability to control the false positive rate (FPR) below a pre-specified level of guarantee, α (e.g., 0.05). To improve computational efficiency, we introduce a parametric basis tracking mechanism that identifies when the solution of the optimization problem remains unchanged as parameters vary, avoiding the need to repeatedly solve the linear program. Furthermore, our framework can be extended to SeqFS with common model selection criteria such as AIC, BIC, and adjusted R-squared. Extensive experiments on synthetic and real-world datasets validate our theoretical results and demonstrate that our framework achieves superior statistical power with high computational efficiency.