We introduce a new method for neighbourhood selection in linear structural equation models that improves over classical methods such as best subset selection (BSS) and the Lasso. Our method, called KL-BSS, takes advantage of the existence of underlying structure in SEM -- even when this structure is unknown -- and is easily implemented using existing solvers. Under weaker eigenvalue conditions compared to BSS and the Lasso, KL-BSS can provably recover the support of linear models with fewer samples. We establish both the pointwise and minimax sample complexity for support recovery, which KL-BSS obtains. Extensive experiments on both real and simulated data confirm the improvements offered by KL-BSS. While it is well-known that the Lasso encounters difficulties under structured dependencies, it is less well-known that even BSS runs into trouble as well, and can be substantially improved. These results have implications for structure learning in graphical models, which often relies on neighbourhood selection as a subroutine.

翻译：我们提出了一种在线性结构方程模型中进行邻域选择的新方法，该方法优于经典方法，如最佳子集选择（BSS）和Lasso。我们的方法称为KL-BSS，利用了SEM中存在的潜在结构（即使该结构未知）的优势，并可通过现有求解器轻松实现。在比BSS和Lasso更弱的特征值条件下，KL-BSS能够以更少的样本可证明地恢复线性模型的支持集。我们建立了KL-BSS在支持恢复方面的逐点和极小极大样本复杂度。在真实和模拟数据上的大量实验证实了KL-BSS带来的改进。尽管Lasso在结构化依赖下会遇到困难是众所周知的，但鲜为人知的是，即使是BSS也会遇到问题，并可以得到显著改进。这些结果对图模型中的结构学习具有启示意义，因为图模型通常依赖于邻域选择作为子程序。