Teneurins are large cell-surface receptors involved in axon guidance. Teneurin-2 (also known as latrophilin-1-associated synaptic surface organizer (Lasso)) interacts across the synaptic cleft with presynaptic latrophilin-1, an adhesion G-protein-coupled receptor that participates in regulating neurotransmitter release. Lasso-latrophilin-1 interaction mediates synapse formation and calcium sign...

The solution path of the 1D fused lasso for an ndimensional input is piecewise linear with O(n) segments [1], [2]. However, existing proofs of this bound do not hold for the weighted fused lasso. At the same time, results for the generalized lasso, of which the weighted fused lasso is a special case, allow Ω(3) segments [3]. In this paper, we prove that the number of segments in the solution pa...

In regression problems where covariates can be naturally grouped, the group Lasso is an attractive method for variable selection since it respects the grouping structure in the data. We study the selection and estimation properties of the group Lasso in high-dimensional settings when the number of groups exceeds the sample size. We provide sufficient conditions under which the group Lasso selec...

Parameterized quadratic programming (Lasso) is a powerful tool for the recovery of sparse signals based on underdetermined observations contaminated by noise. In this paper, we study the problem of simultaneous sparsity pattern recovery and approximation recovery based on the Lasso. An extended Lasso method is proposed with the following main contributions: (1) we analyze the recovery accuracy ...

This paper concerns a class of group-lasso learning problems where the objective function is the sum of an empirical loss and the group-lasso penalty. For a class of loss function satisfying a quadratic majorization condition, we derive a unified algorithm called groupwisemajorization-descent (GMD) for efficiently computing the solution paths of the corresponding group-lasso penalized learning ...

5 The LASSO 9 5.1 Performance of Lasso estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5.2 “Normal equations” for the LASSO solutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5.3 Facts about Lasso solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 This short document presents the Dantzig Selector, first introd...

The application of the lasso is espoused in high-dimensional settings where only a small number of the regression coefficients are believed to be nonzero (i.e., the solution is sparse). Moreover, statistical properties of high-dimensional lasso estimators are often proved under the assumption that the correlation between the predictors is bounded. In this vein, coordinatewise methods, the most ...

We re-examine the original Group Lasso paper of Yuan and Lin (2007). The form of penalty in that paper seems to be designed for problems with uncorrelated features, but the statistical community has adopted it for general problems with correlated features. We show that for this general situation, a Group Lasso with a different choice of penalty matrix is generally more effective. We give insigh...

The least absolute deviation (LAD) regression is a useful method for robust regression, and the least absolute shrinkage and selection operator (lasso) is a popular choice for shrinkage estimation and variable selection. In this article we combine these two classical ideas together to produce LAD-lasso. Compared with the LAD regression, LAD-lasso can do parameter estimation and variable selecti...

Abstract: We study the asymptotic properties of Lasso+mLS and Lasso+ Ridge under the sparse high-dimensional linear regression model: Lasso selecting predictors and then modified Least Squares (mLS) or Ridge estimating their coefficients. First, we propose a valid inference procedure for parameter estimation based on parametric residual bootstrap after Lasso+ mLS and Lasso+Ridge. Second, we der...