Related papers: Look-Ahead Screening Rules for the Lasso

A new estimator, named S-LASSO, is proposed for the coefficient function of the Function-on-Function linear regression model. The S-LASSO estimator is shown to be able to increase the interpretability of the model, by better locating…

The LASSO estimator is an $\ell_1$-norm penalized least-squares estimator, which was introduced for variable selection in the linear model. When the design matrix satisfies, e.g. the Restricted Isometry Property, or has a small coherence…

We consider the problem of model selection and estimation in sparse high dimensional linear regression models with strongly correlated variables. First, we study the theoretical properties of the dual Lasso solution, and we show that joint…

This paper focusses on "safe" screening techniques for the LASSO problem. Motivated by the need for low-complexity algorithms, we propose a new approach, dubbed "joint" screening test, allowing to screen a set of atoms by carrying out one…

We consider situations where a user feeds her attributes to a machine learning method that tries to predict her best option based on a random sample of other users. The predictor is incentive-compatible if the user has no incentive to…

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…

Laparoscopic Surgery (LS) is a modern surgical technique whereby the surgery is performed through an incision with tools and camera as opposed to conventional open surgery. This promises minimal recovery times and less hemorrhaging. Multi…

In linear models it is common to have situations where several regression coefficients are zero. In these situations a common tool to perform regression is a variable selection operator. One of the most common such operators is the LASSO…

Sparse linear regression is a fundamental problem in high-dimensional statistics, but strikingly little is known about how to efficiently solve it without restrictive conditions on the design matrix. We consider the (correlated) random…

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…

A recently introduced technique for a sparse optimization problem called "safe screening" allows us to identify irrelevant variables in the early stage of optimization. In this paper, we first propose a flexible framework for safe screening…

We consider the linear regression problem. We propose the S-Lasso procedure to estimate the unknown regression parameters. This estimator enjoys sparsity of the representation while taking into account correlation between successive…

Large-scale sequential data is often exposed to some degree of inhomogeneity in the form of sudden changes in the parameters of the data-generating process. We consider the problem of detecting such structural changes in a high-dimensional…

In this paper, we propose a novel method to select significant variables and estimate the corresponding coefficients in multiple-index models with a group structure. All existing approaches for single-index models cannot be extended…

Penalized logistic regression is extremely useful for binary classification with large number of covariates (higher than the sample size), having several real life applications, including genomic disease classification. However, the…

In this paper, we apply shrinkage strategies to estimate regression coefficients efficiently for the high-dimensional multiple regression model, where the number of samples is smaller than the number of predictors. We assume in the sparse…

This thesis studies two problems in modern statistics. First, we study selective inference, or inference for hypothesis that are chosen after looking at the data. The motiving application is inference for regression coefficients selected by…

This article presents a novel methodology for detecting multiple biomarkers in high-dimensional mediation models by utilizing a modified Least Absolute Shrinkage and Selection Operator (LASSO) alongside Pathway LASSO. This approach…

Common high-dimensional methods for prediction rely on having either a sparse signal model, a model in which most parameters are zero and there are a small number of non-zero parameters that are large in magnitude, or a dense signal model,…

Much theoretical and applied work has been devoted to high-dimensional regression with clean data. However, we often face corrupted data in many applications where missing data and measurement errors cannot be ignored. Loh and Wainwright…