Variable selection in high-dimensional linear models: partially faithful distributions and the PC-simple algorithm

• 成果类型: Article
• 署名作者: Buehlmann, P.; Kalisch, M.; Maathuis, M. H.
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asq008
• 发表日期: 2010
• 页码: 261278
• 关键词: adaptive lasso; regression; graphs; Consistency; RECOVERY; sparsity; larger

摘要

We consider variable selection in high-dimensional linear models where the number of covariates greatly exceeds the sample size. We introduce the new concept of partial faithfulness and use it to infer associations between the covariates and the response. Under partial faithfulness, we develop a simplified version of the PC algorithm (Spirtes et al., 2000), which is computationally feasible even with thousands of covariates and provides consistent variable selection under conditions on the random design matrix that are of a different nature than coherence conditions for penalty-based approaches like the lasso. Simulations and application to real data show that our method is competitive compared to penalty-based approaches. We provide an efficient implementation of the algorithm in the R-package pcalg.