Related papers: Assumptionless consistency of the Lasso

Many theoretical results for the lasso require the samples to be iid. Recent work has provided guarantees for the lasso assuming that the time series is generated by a sparse Vector Auto-Regressive (VAR) model with Gaussian innovations.…

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 $k$…

It is more and more frequently the case in applications that the data we observe come from one or more random variables taking values in an infinite dimensional space, e.g. curves. The need to have tools adapted to the nature of these data…

This work performs a non-asymptotic analysis of the generalized Lasso under the assumption of sub-exponential data. Our main results continue recent research on the benchmark case of (sub-)Gaussian sample distributions and thereby explore…

The lasso has become an important practical tool for high dimensional regression as well as the object of intense theoretical investigation. But despite the availability of efficient algorithms, the lasso remains computationally demanding…

Variance estimation in the linear model when $p > n$ is a difficult problem. Standard least squares estimation techniques do not apply. Several variance estimators have been proposed in the literature, all with accompanying asymptotic…

The Lasso regression is a popular regularization method for feature selection in statistics. Prior to computing the Lasso estimator in both linear and generalized linear models, it is common to conduct a preliminary rescaling of the feature…

Conformal prediction is a general method that converts almost any point predictor to a prediction set. The resulting set keeps good statistical properties of the original estimator under standard assumptions, and guarantees valid average…

The Lasso is an attractive technique for regularization and variable selection for high-dimensional data, where the number of predictor variables $p_n$ is potentially much larger than the number of samples $n$. However, it was recently…

In this paper, we investigate seemingly unrelated regression (SUR) models that allow the number of equations (N) to be large, and to be comparable to the number of the observations in each equation (T). It is well known in the literature…

In spite of the wealth of literature on the theoretical properties of the Lasso, there is very little known when the value of the tuning parameter is chosen using the data, even though this is what actually happens in practice. We give a…

Regression analysis is a central topic in statistical modeling, aimed at estimating the relationships between a dependent variable, commonly referred to as the response variable, and one or more independent variables, i.e., explanatory…

The network Lasso (nLasso) has been proposed recently as an efficient learning algorithm for massive networked data sets (big data over networks). It extends the well-known least absolute shrinkage and selection operator (Lasso) from…

The least absolute shrinkage and selection operator (Lasso) is a popular method for high-dimensional statistics. However, it is known that the Lasso often has estimation bias and prediction error. To address such disadvantages, many…

Linear regression is arguably the most widely used statistical method. With fixed regressors and correlated errors, the conventional wisdom is to modify the variance-covariance estimator to accommodate the known correlation structure of the…

Inferring causal relationships or related associations from observational data can be invalidated by the existence of hidden confounding. We focus on a high-dimensional linear regression setting, where the measured covariates are affected…

We propose a new sparse regression method called the component lasso, based on a simple idea. The method uses the connected-components structure of the sample covariance matrix to split the problem into smaller ones. It then solves the…

We consider the problem of estimating and inferring treatment effects in randomized experiments. In practice, stratified randomization, or more generally, covariate-adaptive randomization, is routinely used in the design stage to balance…

Least angle regression (LARS) by Efron et al. (2004) is a novel method for constructing the piece-wise linear path of Lasso solutions. For several years, it remained also as the de facto method for computing the Lasso solution before more…

Least squares linear regression is one of the oldest and widely used data analysis tools. Although the theoretical analysis of the ordinary least squares (OLS) estimator is as old, several fundamental questions are yet to be answered.…