KL-BSS: rethinking optimality for neighbourhood selection in structural equation models
Authors
Paper Information
-
Journal:
Journal of the Royal Statistical Society Series B -
DOI:
10.1093/jrsssb/qkag078 -
Published:
June 03, 2026 -
Added to Tracker:
Jun 04, 2026
Abstract
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.
Author Details
Bryon Aragam
AuthorMing Gao
AuthorWai Ming Tai
AuthorCitation Information
APA Format
Bryon Aragam
,
Ming Gao
&
Wai Ming Tai
(2026)
.
KL-BSS: rethinking optimality for neighbourhood selection in structural equation models.
Journal of the Royal Statistical Society Series B
, 10.1093/jrsssb/qkag078.
BibTeX Format
@article{paper1209,
title = { KL-BSS: rethinking optimality for neighbourhood selection in structural equation models },
author = {
Bryon Aragam
and Ming Gao
and Wai Ming Tai
},
journal = { Journal of the Royal Statistical Society Series B },
year = { 2026 },
doi = { 10.1093/jrsssb/qkag078 },
url = { https://doi.org/10.1093/jrsssb/qkag078 }
}