Geometry and Degrees of Freedom of Linearly Constrained Generalized Lasso
研究了线性约束广义Lasso的拟合唯一性，证明在温和条件下拟合可表示为多面体上的投影，并推导了自由度的公式，可用于模型选择的信息准则。
Abstract The least squares fit in a linear regression is always unique even when the design matrix has rank deficiency. In this paper, we extend this classic result to linearly constrained generalized lasso. It is shown that under a mild condition, the fit can be represented as a projection onto a polytope and, hence, is unique no matter whether design matrix X has full column rank or not. Furthermore, a formula for the degrees of freedom is derived to characterize the effective number of parameters. It directly yields an unbiased estimate of degrees of freedom, which can be incorporated in an information criterion for model selection.