Related papers: Improved LASSO
Standard likelihood penalties to learn Gaussian graphical models are based on regularising the off-diagonal entries of the precision matrix. Such methods, and their Bayesian counterparts, are not invariant to scalar multiplication of the…
Estimating a covariance matrix is an important task in applications where the number of variables is larger than the number of observations. Shrinkage approaches for estimating a high-dimensional covariance matrix are often employed to…
Convex estimators such as the Lasso, the matrix Lasso and the group Lasso have been studied extensively in the last two decades, demonstrating great success in both theory and practice. Two quantities are introduced, the noise barrier and…
Stein's unbiased risk estimate (SURE) gives an unbiased estimate of the $\ell_2$ risk of any estimator of the mean of a Gaussian random vector. We focus here on the case when the estimator minimizes a quadratic loss term plus a convex…
The propensity score (PS) is often used to control for large numbers of covariates in high-dimensional healthcare database studies. The least absolute shrinkage and selection operator (LASSO) has become the most widely used tool for fitting…
Growth-at-Risk is vital for empirical macroeconomics but is often suspect to quantile crossing due to data limitations. While existing literature addresses this through post-processing of the fitted quantiles, these methods do not correct…
In this paper, we propose an adaptive group lasso procedure to efficiently estimate structural breaks in cointegrating regressions. It is well-known that the group lasso estimator is not simultaneously estimation consistent and model…
Recently, many machine learning and statistical models such as non-linear regressions, the Single Index, Multi-index, Varying Coefficient Index Models and Two-layer Neural Networks can be reduced to or be seen as a special case of a new…
We establish statistical properties of random-weighting methods in LASSO regression under different regularization parameters $\lambda_n$ and suitable regularity conditions. The random-weighting methods in view concern repeated optimization…
We tackle covariance estimation in low-sample scenarios, employing a structured covariance matrix with shrinkage methods. These involve convexly combining a low-bias/high-variance empirical estimate with a biased regularization estimator,…
Effect modification occurs when the effect of the treatment on an outcome varies according to the level of other covariates and often has important implications in decision making. When there are tens or hundreds of covariates, it becomes…
Given data $y$ and $k$ covariates $x$ one problem in linear regression is to decide which in any of the covariates to include when regressing $y$ on the $x$. If $k$ is small it is possible to evaluate each subset of the $x$. If however $k$…
Shuffled linear regression (SLR) seeks to estimate latent features through a linear transformation, complicated by unknown permutations in the measurement dimensions. This problem extends traditional least-squares (LS) and Least Absolute…
In this article we study post-model selection estimators that apply ordinary least squares (OLS) to the model selected by first-step penalized estimators, typically Lasso. It is well known that Lasso can estimate the nonparametric…
Inference for high-dimensional logistic regression models using penalized methods has been a challenging research problem. As an illustration, a major difficulty is the significant bias of the Lasso estimator, which limits its direct…
The estimation of the mean matrix of the multivariate normal distribution is addressed in the high dimensional setting. Efron-Morris-type linear shrinkage estimators based on ridge estimators for the precision matrix instead of the…
In this paper, we propose the application of shrinkage strategies to estimate coefficients in the Bell regression models when prior information about the coefficients is available. The Bell regression models are well-suited for modeling…
The Lasso is a prominent algorithm for variable selection. However, its instability in the presence of correlated variables in the high-dimensional setting is well-documented. Although previous research has attempted to address this issue…
In this work, we address the problem of Hessian inversion bias in distributed second-order optimization algorithms. We introduce a novel shrinkage-based estimator for the resolvent of gram matrices which is asymptotically unbiased, and…
Lasso is a celebrated method for variable selection in linear models, but it faces challenges when the variables are moderately or strongly correlated. This motivates alternative approaches such as using a non-convex penalty, adding a ridge…