The lasso [Tibshirani, 1996] is a popular method for regression that uses an ℓ1 penalty to achieve a sparse solution. In the signal processing literature, the lasso is also known as basis pursuit [Chen et al., 1998]. This idea has been broadly applied, for example to generalized linear models [Tibshirani, 1996] and Cox’s proportional hazard models for survival data [Tibshirani, 1997]. In recent years, there has been an enormous amount of research activity devoted to related regularization methods: The grouped lasso [Yuan and Lin, 2007, Meier et al., 2008], where variables are included or excluded in groups;The Dantzig selector [Candes and Tao, 2007, and discussion], a slightly modified version of the lasso;The elastic net [Zou and Hastie, 2005] for correlated variables, which uses a penalty that is part ℓ1, part ℓ2;ℓ1 regularization paths for generalized linear models [Park and Hastie, 2007];Regularization paths for the support-vector machine [Hastie et al., 2004].The graphical lasso [Friedman et al., 2008] for sparse covariance estimation and undirected graphs
