KL-BSS: rethinking optimality for neighbourhood selection in structural equation models
提出KL-BSS方法，在线性结构方程模型的邻域选择中优于经典的最佳子集选择（BSS）和Lasso，能在更弱的特征值条件下用更少样本恢复模型支持，实验验证了改进效果。
Abstract 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.