DASSO: Connections Between the Dantzig Selector and Lasso

We propose a new algorithm, DASSO, for fitting the entire coefficient path of the Dantzig selector with a similar computational cost to the LARS algorithm that is used to compute the Lasso. DASSO efficiently constructs a piecewise linear path through a sequential simplex-like algorithm, which is remarkably similar to LARS. Comparison of the two algorithms sheds new light on the question of how the Lasso and Dantzig selector are related. In addition, we provide theoretical conditions on the design matrix, X , under which the Lasso and Dantzig selector coefficient estimates will be identical for certain tuning parameters. As a consequence, in many instances, we are able to extend the powerful non-asymptotic bounds that have been developed for the Dantzig selector to the Lasso. Finally, through empirical studies of simulated and real world data sets we show that in practice, when the bounds hold for the Dantzig selector, they almost always also hold for the Lasso. Some key words: Dantzig selector; LARS; Lasso; DASSO