Related papers: A Greedy Homotopy Method for Regression with Nonco…
We consider a linear regression problem in a high dimensional setting where the number of covariates $p$ can be much larger than the sample size $n$. In such a situation, one often assumes sparsity of the regression vector, \textit i.e.,…
We propose a self-tuning $\sqrt{\mathrm {Lasso}}$ method that simultaneously resolves three important practical problems in high-dimensional regression analysis, namely it handles the unknown scale, heteroscedasticity and (drastic)…
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. Moreover, statistical properties of high-dimensional lasso estimators are often…
We consider the least-square linear regression problem with regularization by the $\ell^1$-norm, a problem usually referred to as the Lasso. In this paper, we first present a detailed asymptotic analysis of model consistency of the Lasso in…
We address the numerical solution of minimal norm residuals of {\it nonlinear} equations in finite dimensions. We take inspiration from the problem of finding a sparse vector solution by using greedy algorithms based on iterative residual…
We propose a new approach to mixed-frequency regressions in a high-dimensional environment that resorts to Group Lasso penalization and Bayesian techniques for estimation and inference. In particular, to improve the prediction properties of…
First-order stochastic methods for solving large-scale non-convex optimization problems are widely used in many big-data applications, e.g. training deep neural networks as well as other complex and potentially non-convex machine learning…
We propose a new class of nonconvex penalty functions, based on data depth functions, for multitask sparse penalized regression. These penalties quantify the relative position of rows of the coefficient matrix from a fixed distribution…
This work presents a new approach to solve the sparse linear regression problem, i.e., to determine a k-sparse vector w in R^d that minimizes the cost ||y - Aw||^2_2. In contrast to the existing methods, our proposed approach splits this…
We propose a new algorithm for recovery of sparse signals from their compressively sensed samples. The proposed algorithm benefits from the strategy of gradual movement to estimate the positions of non-zero samples of sparse signal. We…
We introduce a statistical method that can reconstruct nonlinear genetic models (i.e., including epistasis, or gene-gene interactions) from phenotype-genotype (GWAS) data. The computational and data resource requirements are similar to…
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…
We connect high-dimensional subset selection and submodular maximization. Our results extend the work of Das and Kempe (2011) from the setting of linear regression to arbitrary objective functions. For greedy feature selection, this…
We provide the first global model recovery results for the IRLS (iteratively reweighted least squares) heuristic for robust regression problems. IRLS is known to offer excellent performance, despite bad initializations and data corruption,…
In this paper, we consider the sparse least squares regression problem with probabilistic simplex constraint. Due to the probabilistic simplex constraint, one could not apply the L1 regularization to the considered regression model. To find…
Inverse probability weighted estimators are the oldest and potentially most commonly used class of procedures for the estimation of causal effects. By adjusting for selection biases via a weighting mechanism, these procedures estimate an…
We present a generic coordinate descent solver for the minimization of a nonsmooth convex objective with structure. The method can deal in particular with problems with linear constraints. The implementation makes use of efficient residual…
Many complex disease syndromes such as asthma consist of a large number of highly related, rather than independent, clinical phenotypes, raising a new technical challenge in identifying genetic variations associated simultaneously with…
We introduce c-lasso, a Python package that enables sparse and robust linear regression and classification with linear equality constraints. The underlying statistical forward model is assumed to be of the following form: \[ y = X \beta +…
We introduce and study the Group Square-Root Lasso (GSRL) method for estimation in high dimensional sparse regression models with group structure. The new estimator minimizes the square root of the residual sum of squares plus a penalty…