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• Sparsistency of l1-Regularized M-Estimators (pdf, arXiv, software)
  Y. Li, J. Scarlett, P. Ravikumar, V. Cevher.
  In International Conference on Artificial Intelligence and Statistics (AISTATS), 2015. (Oral)
  
  Bibtex:
  
  @inproceedings{li2015sparsisten, author = "Yen-Huan Li AND Jonathan Scarlett AND Pradeep Ravikumar AND Volkan Cevher", title = "Sparsistency of l1-Regularized M-Estimators", booktitle = "International Conference on Artificial Intelligence and Statistics (AISTATS)", year = "2015", abstract = "We consider the model selection consistency or sparsistency of a broad set of ℓ1-regularized M-estimators for linear and non-linear statistical models in a unified fashion. For this purpose, we propose the local structured smoothness condition (LSSC) on the loss function. We provide a general result giving deterministic sufficient conditions for sparsistency in terms of the regularization parameter, ambient dimension, sparsity level, and number of measurements. We show that several important statistical models have M-estimators that indeed satisfy the LSSC, and as a result, the sparsistency guarantees for the corresponding ℓ1-regularized M-estimators can be derived as simple applications of our main theorem." }