Analysis of high-dimensional data has led to increased interest in both single index models (SIMs) and best subset selection. SIMs provide an interpretable and flexible modeling framework for high-dimensional data, while best subset selection aims to find a sparse model from a large set of predictors. However, best subset selection in high-dimensional models is known to be computationally intractable. Existing methods tend to relax the selection, but do not yield the best subset solution. In this paper, we directly tackle the intractability by proposing the first provably scalable algorithm for best subset selection in high-dimensional SIMs. Our algorithmic solution enjoys the subset selection consistency and has the oracle property with a high probability. The algorithm comprises a generalized information criterion to determine the support size of the regression coefficients, eliminating the model selection tuning. Moreover, our method does not assume an error distribution or a specific link function and hence is flexible to apply. Extensive simulation results demonstrate that our method is not only computationally efficient but also able to exactly recover the best subset in various settings (e.g., linear regression, Poisson regression, heteroscedastic models).

高维数据的分析引起了对单指数模型和最佳子集选择的日益关注，本文提出了第一个在高维单指数模型中具有可扩展性的证明可规模化的算法来进行最佳子集选择，该算法使用广义信息准则来确定回归系数的支持大小，消除模型选择调优。

单指数模型中最佳子集选择的一致可扩展算法