Related papers: Improving Lasso for model selection and prediction

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…

Nowadays, l1 penalized likelihood has absorbed a high amount of consideration due to its simplicity and well developed theoretical properties. This method is known as a reliable method in order to apply in a broad range of applications…

There are many settings where researchers are interested in estimating average treatment effects and are willing to rely on the unconfoundedness assumption, which requires that the treatment assignment be as good as random conditional on…

It is well-known that the statistical performance of Lasso can suffer significantly when the covariates of interest have strong correlations. In particular, the prediction error of Lasso becomes much worse than computationally inefficient…

We propose a new algorithm for estimating NARMAX models with $L_1$ regularization for models represented as a linear combination of basis functions. Due to the $L_1$-norm penalty the Lasso estimation tends to produce some coefficients that…

In additive models with many nonparametric components, a number of regularized estimators have been proposed and proven to attain various error bounds under different combinations of sparsity and fixed smoothness conditions. Some of these…

In high dimension, it is customary to consider Lasso-type estimators to enforce sparsity. For standard Lasso theory to hold, the regularization parameter should be proportional to the noise level, yet the latter is generally unknown in…

The high-dimensional linear model $y = X \beta^0 + \epsilon$ is considered and the focus is put on the problem of recovering the support $S^0$ of the sparse vector $\beta^0.$ We introduce Lasso-Zero, a new $\ell_1$-based estimator whose…

The tuning parameter selection strategy for penalized estimation is crucial to identify a model that is both interpretable and predictive. However, popular strategies (e.g., minimizing average squared prediction error via cross-validation)…

Due to its low computational cost, Lasso is an attractive regularization method for high-dimensional statistical settings. In this paper, we consider multivariate counting processes depending on an unknown function parameter to be estimated…

This paper discusses a class of thresholding-based iterative selection procedures (TISP) for model selection and shrinkage. People have long before noticed the weakness of the convex $l_1$-constraint (or the soft-thresholding) in wavelets…

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…

The construction of coherent prediction models holds great importance in medical research as such models enable health researchers to gain deeper insights into disease epidemiology and clinicians to identify patients at higher risk of…

In high-dimensional statistics, the Lasso is a cornerstone method for simultaneous variable selection and parameter estimation. However, its reliance on the squared loss function renders it highly sensitive to outliers and heavy-tailed…

We propose a generalized debiased Lasso estimator based on a stability principle. When a single column of the design matrix is perturbed, the estimator admits a simple update formula that can be computed from the original solution. Under…

We present upper and lower bounds for the prediction error of the Lasso. For the case of random Gaussian design, we show that under mild conditions the prediction error of the Lasso is up to smaller order terms dominated by the prediction…

Random forests are a statistical learning technique that use bootstrap aggregation to average high-variance and low-bias trees. Improvements to random forests, such as applying Lasso regression to the tree predictions, have been proposed in…

While shrinkage is essential in high-dimensional settings, its use for low-dimensional regression-based prediction has been debated. It reduces variance, often leading to improved prediction accuracy. However, it also inevitably introduces…

The abundance of high-dimensional data in the modern sciences has generated tremendous interest in penalized estimators such as the lasso, scaled lasso, square-root lasso, elastic net, and many others. In this paper, we establish a general…

We develop tools to do valid post-selective inference for a family of model selection procedures, including choosing a model via cross-validated Lasso. The tools apply universally when the following random vectors are jointly asymptotically…