Best-subset selection aims to find a small subset of predictors, so that the resulting linear model is expected to have the most desirable prediction accuracy. It is not only important and imperative in regression analysis but also has far-reaching applications in every facet of research, including computer science and medicine. We introduce a polynomial algorithm, which, under mild conditions, solves the problem. This algorithm exploits the idea of sequencing and splicing to reach a stable solution in finite steps when the sparsity level of the model is fixed but unknown. We define an information criterion that helps the algorithm select the true sparsity level with a high probability. We show that when the algorithm produces a stable optimal solution, that solution is the oracle estimator of the true parameters with probability one. We also demonstrate the power of the algorithm in several numerical studies.
嘉宾介绍
朱俊贤，新加坡国立大学博士后。2021年于中山大学获得博士学位。主要的研究方向是最优子集选择，高维统计，混合模型，随机对照试验。论文发表于PNAS，JMLR，INFORMS Journal on Computing等期刊。
