The least absolute shrinkage and selection operator (lasso) has been widely used in regression shrinkage and selection. In this article, we extend its application to the REGression model with AutoRegressive errors (REGAR). Two types of lasso estimators are carefully studied. The first is similar to the traditional lasso estimator with only two tuning parameters (one for regression coefficients ...

We consider the problem of selecting functional variables using the L1 regularization in a functional linear regression model with a scalar response and functional predictors in the presence of outliers. Since the LASSO is a special case of the penalized least squares regression with L1-penalty function it suffers from the heavy-tailed errors and/or outliers in data. Recently, the LAD regressio...

Yuan an Lin (2004) proposed the grouped LASSO, which achieves shrinkage and selection simultaneously, as LASSO does, but works on blocks of covariates. That is, the grouped LASSO provides a model where some blocks of regression coefficients are exactly zero. The grouped LASSO is useful when there are meaningful blocks of covariates such as polynomial regression and dummy variables from categori...

The Lasso is an attractive regularisation method for high dimensional regression. It combines variable selection with an efficient computational procedure. However, the rate of convergence of the Lasso is slow for some sparse high dimensional data, where the number of predictor variables is growing fast with the number of observations. Moreover, many noise variables are selected if the estimato...

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 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 ...

In this paper we consider the problem of grouped variable selection in high-dimensional regression using `1-`q regularization (1 ≤ q ≤ ∞), which can be viewed as a natural generalization of the `1-`2 regularization (the group Lasso). The key condition is that the dimensionality pn can increase much faster than the sample size n, i.e. pn À n (in our case pn is the number of groups), but the numb...

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...