Chronic subdural hematoma (CSDH) is characterized by an "old" encapsulated collection of blood and blood breakdown products between the brain and its outermost covering (the dura). Recognized risk factors for development of CSDH are head injury, old age and using anticoagulation medication, but its underlying pathophysiological processes are still unclear. It is assumed that a complex local pro...

We derive the degrees of freedom of the lasso fit, placing no assumptions on the predictor matrix X. Like the well-known result of Zou et al. (2007), which gives the degrees of freedom of the lasso fit when X has full column rank, we express our result in terms of the active set of a lasso solution. We extend this result to cover the degrees of freedom of the generalized lasso fit for an arbitr...

We consider the problem of estimating a function f0 in logistic regression model. We propose to estimate this function f0 by a sparse approximation build as a linear combination of elements of a given dictionary of p functions. This sparse approximation is selected by the Lasso or Group Lasso procedure. In this context, we state non asymptotic oracle inequalities for Lasso and Group Lasso under...

We present a new method which solves a double-barelled LASSO in a convex least squares approach. In the presented method we focus on the scenario where one is interested in (or limited to) a primal (feature) representation for the first view while having a dual (kernel) representation for the second view. DB-LASSO minimises the number of features used in both the primal and dual projections whi...

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...

Abstract: We propose a general family of algorithms for regression estimation with quadratic loss, on the basis of geometrical considerations. These algorithms are able to select relevant functions into a large dictionary. We prove that a lot of methods that have already been studied for this task (LASSO, Dantzig selector, Iterative Feature Selection, among others) belong to our family, and exh...

`2,1-norm is an effective regularization to enforce a simple group sparsity for feature learning. To capture some subtle structures among feature groups, we propose a new regularization called exclusive group `2,1-norm. It enforces the sparsity at the intra-group level by using `2,1-norm, while encourages the selected features to distribute in different groups by using `2 norm at the inter-grou...

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 ...