We study the degrees of freedom of the Lasso in the framework of Stein’s unbiased risk estimation (SURE). We show that the number of non-zero coefficients is an unbiased estimate for the degrees of freedom of the Lasso—a conclusion that requires no special assumption on the predictors. Our analysis also provides mathematical support for a related conjecture by Efron et al. (2004). As an applica...

The least absolute shrinkage and selection operator (lasso) and ridge regression produce usually different estimates although input, loss function and parameterization of the penalty are identical. In this paper we look for ridge and lasso models with identical solution set. It turns out, that the lasso model with shrink vector λ and a quadratic penalized model with shrink matrix as outer produ...

The network Lasso is a recently proposed convex optimization method for machine learning from massive network structured datasets, i.e., big data over networks. It is a variant of the well-known least absolute shrinkage and selection operator (Lasso), which is underlying many methods in learning and signal processing involving sparse models. Highly scalable implementations of the network Lasso ...

We provide a principled way for investigators to analyze randomized experiments when the number of covariates is large. Investigators often use linear multivariate regression to analyze randomized experiments instead of simply reporting the difference of means between treatment and control groups. Their aim is to reduce the variance of the estimated treatment effect by adjusting for covariates....

Steady-state visual evoked potential (SSVEP) has been increasingly used for the study of brain–computer interface (BCI). How to recognize SSVEP with shorter time and lower error rate is one of the key points to develop a more efficient SSVEP-based BCI. To achieve this goal, we make use of the sparsity constraint of the least absolute shrinkage and selection operator (LASSO) for the extraction o...