A classical problem that arises in numerous signal processing applications asks for the reconstruction of an unknown, ksparse signal x0 ∈ R from underdetermined, noisy, linear measurements y = Ax0 + z ∈ R. One standard approach is to solve the following convex program x̂ = arg minx ‖y− Ax‖2+λ‖x‖1, which is known as the `2-LASSO. We assume that the entries of the sensing matrix A and of the noise...

In this paper, we analyze the performance of Lasso-TD, a modification of LSTD in which the projection operator is defined as a Lasso problem. We first show that Lasso-TD is guaranteed to have a unique fixed point and its algorithmic implementation coincides with the recently presented LARS-TD and LC-TD methods. We then derive two bounds on the prediction error of Lasso-TD in the Markov design s...

The regularization path of the Lasso can be shown to be piecewise linear, making it possible to “follow” and explicitly compute the entire path. We analyze in this paper this popular strategy, and prove that its worst case complexity is exponential in the number of variables. We then oppose this pessimistic result to an (optimistic) approximate analysis: We show that an approximate path with at...

Using regression analysis to make inference using data sets that contain a large number of potentially correlated covariates can be difficult. This large number of covariates have become more common in clinical observational studies due to the dramatic improvement in information capturing technology for clinical databases. For instance, in disease diagnosis and treatment, obtaining a number of ...

We consider a joint processing of n independent sparse regression problems. Each is based on a sample (yi1, xi1) . . . , (yim, xim) of m i.i.d. observations from yi1 = x T i1βi+εi1, yi1 ∈ R, xi1 ∈ R, i = 1, . . . , n, and εi1 ∼ N(0, σ), say. p is large enough so that the empirical risk minimizer is not consistent. We consider three possible extensions of the lasso estimator to deal with this pr...

We propose the elastic net, a new regression shrinkage and selection method. Real data and a simulation study show that the elastic net often outperforms the lasso, while it enjoys a similar sparsity of representation. In addition, the elastic net encourages a grouping effect, where strong correlated predictors are kept in the model. The elastic net is particularly useful in the analysis of mic...

The Lunar Architecture Stochastic Simulator and Optimizer (LASSO) is a simulationbased capability, based upon discrete event simulation (DES), for evaluating and optimizing flight element options for lunar transportation architectures. This simulation capability improves the ability to rapidly measure cost, reliability, and schedule impacts of various toplevel architecture decisions and individ...

In this paper, we propose a two-stage variable selection procedure for high dimensional quantile varying coefficient models. The proposed method is based on basis function approximation and LASSO-type penalties.We show that the first stage penalized estimator with LASSO penalty reduces the model from ultra-high dimensional to a model that has size close to the true model, but contains the true ...

In this paper, we consider improved estimation strategies for the parameter vector in multiple regression models with first-order random coefficient autoregressive errors (RCAR(1)). We propose a shrinkage estimation strategy and implement variable selection methods such as lasso and adaptive lasso strategies. The simulation results reveal that the shrinkage estimators perform better than both l...