The Geometry of Algorithms with Orthogonality Constraints
SIAM Journal on Matrix Analysis and Applications
Nonconcave penalized inverse regression in single-index models with high dimensional predictors
Journal of Multivariate Analysis
The Bayesian group-Lasso for analyzing contingency tables
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Optimization algorithms exploiting unitary constraints
IEEE Transactions on Signal Processing
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Chen et al. (2010) [1] propose a unified method-coordinate-independent sparse estimation (CISE)-that is able to simultaneously achieve sparse sufficient dimension reduction and screen out irrelevant and redundant variables efficiently. However, its attractive features depend on the appropriate choice of the tuning parameter. In this note, we re-examine the Bayesian information criterion (BIC) in sufficient dimension reduction and provide a heuristic derivation. Furthermore, the CISE with BIC is shown to be able to identify the true model consistently.