Title: On the Model Selection Properties of the Lasso

Abstract: We present an explicit formula for the correspondence between the
Lasso and the least-squares estimator in low dimensions and derive analogous
results for the relationship between the Lasso estimator and the quantity X'y
in high dimensions without any assumptions on the regressor matrix. Given these
results, we also investigate the model selection properties of the Lasso
estimator based on geometric conditions and show that possibly only a subset
of models might be selected, completely independently of the response vector.
Finally, we present a condition for uniqueness of the estimator in this context
that is necessary as well as sufficient.