On the Model Selection Properties and Uniqueness of the Lasso and Related Estimators

Seminarium: 
Analysis of Large Data Sets
Osoba referująca: 
Ulrike Schneider (Vienna University of Technology)
Data spotkania seminaryjnego: 
czwartek, 14. Listopad 2019 - 14:15
Sala: 
603
Opis: 
We investigate the model selection properties of the Lasso estimator in finite samples with no conditions on the regressor matrix X. We show that which covariates the Lasso estimator may potentially choose in high dimensions (where the number of explanatory variables p exceeds sample size n) depends only on X and the given penalization weights. This set of potential covariates can be determined through a geometric condition on X and may be small enough (less than or equal to n in cardinality). Related to the geometric conditions in our considerations, we also provide a necessary and sufficient condition for uniqueness of the Lasso solutions. Finally, we discuss how these results carry over to other model selection procedures such as the SLOPE