Title: On the model selection properties and uniqueness of the lasso
Authors: Ulrike Schneider - Vienna University of Technology (Austria) [presenting]
Karl Ewald - Vienna University of Technology (Austria)
Abstract: The model selection properties of the lasso estimator are investigated 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), so that the lasso estimator acts as a low-dimensional procedure also in high dimensions. Related to the geometric conditions in our considerations, we also provide a necessary and sufficient condition for uniqueness of the lasso solutions.