Related papers: Tuning Parameter Selection for Penalized Estimatio…

High-dimensional data sets are often analyzed and explored via the construction of a latent low-dimensional space which enables convenient visualization and efficient predictive modeling or clustering. For complex data structures, linear…

We study sparse linear regression over a network of agents, modeled as an undirected graph (with no centralized node). The estimation problem is formulated as the minimization of the sum of the local LASSO loss functions plus a quadratic…

In this study, we investigate the bias and variance properties of the debiased Lasso in linear regression when the tuning parameter of the node-wise Lasso is selected to be smaller than in previous studies. We consider the case where the…

Optimization of sensor selection has been studied to monitor complex and large-scale systems with data-driven linear reduced-order modeling. An algorithm for greedy sensor selection is presented under the assumption of correlated noise in…

Inferring network structures remains an interesting question for its importance on the understanding and controlling collective dynamics of complex systems. The existing shrinking methods such as Lasso-type estimation can not suitably…

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…

We study hypothesis testing for penalized estimators in settings where the full marginal distribution of a multivariate response is difficult to specify, such as longitudinal data with correlated measurements or high-dimensional…

Biased stochastic estimators, such as finite-differences for noisy gradient estimation, often contain parameters that need to be properly chosen to balance impacts from the bias and the variance. While the optimal order of these parameters…

In high-dimensional and/or non-parametric regression problems, regularization (or penalization) is used to control model complexity and induce desired structure. Each penalty has a weight parameter that indicates how strongly the structure…

A new reweighted l1-norm penalized least mean square (LMS) algorithm for sparse channel estimation is proposed and studied in this paper. Since standard LMS algorithm does not take into account the sparsity information about the channel…

It is known that the Thresholded Lasso (TL), SCAD or MCP correct intrinsic estimation bias of the Lasso. In this paper we propose an alternative method of improving the Lasso for predictive models with general convex loss functions which…

In this paper, we derive non-asymptotic error bounds for the Lasso estimator when the penalty parameter for the estimator is chosen using $K$-fold cross-validation. Our bounds imply that the cross-validated Lasso estimator has nearly…

We present a new approach to solve the sparse approximation or best subset selection problem, namely find a $k$-sparse vector ${\bf x}\in\mathbb{R}^d$ that minimizes the $\ell_2$ residual $\lVert A{\bf x}-{\bf y} \rVert_2$. We consider a…

Many regularization schemes for high-dimensional regression have been put forward. Most require the choice of a tuning parameter, using model selection criteria or cross-validation schemes. We show that a simple non-negative or…

We consider a two-stage estimation method for linear regression. First, it uses the lasso in Tibshirani (1996) to screen variables and, second, re-estimates the coefficients using the least-squares boosting method in Friedman (2001) on…

This paper studies the asymptotic properties of the penalized least squares estimator using an adaptive group Lasso penalty for the reduced rank regression. The group Lasso penalty is defined in the way that the regression coefficients…

We extend the analysis of investment strategies derived from penalized quantile regression models, introducing alternative approaches to improve state\textendash of\textendash art asset allocation rules. First, we use a post\textendash…

In this paper, we develop an implementation of cross-validation for penalized linear mixed models. While these models have been proposed for correlated high-dimensional data, the current literature implicitly assumes that tuning parameter…

Neural networks are usually not the tool of choice for nonparametric high-dimensional problems where the number of input features is much larger than the number of observations. Though neural networks can approximate complex multivariate…

Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work,…