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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…

Variable selection in linear regression models has been a problem since hypothesis testing began. Which variables to include or exclude from a model is not an easy task. Techniques such as Forward, Back ward, Stepwise Regression…

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…

We propose the Bayesian adaptive Lasso (BaLasso) for variable selection and coefficient estimation in linear regression. The BaLasso is adaptive to the signal level by adopting different shrinkage for different coefficients. Furthermore, we…

The method of instrumental variables provides a fundamental and practical tool for causal inference in many empirical studies where unmeasured confounding between the treatments and the outcome is present. Modern data such as the genetical…

A reciprocal LASSO (rLASSO) regularization employs a decreasing penalty function as opposed to conventional penalization approaches that use increasing penalties on the coefficients, leading to stronger parsimony and superior model…

This paper develops an approach to inference in a linear regression model when the number of potential explanatory variables is larger than the sample size. The approach treats each regression coefficient in turn as the interest parameter,…

In the multiple changepoint setting, various search methods have been proposed which involve optimising either a constrained or penalised cost function over possible numbers and locations of changepoints using dynamic programming. Such…

Subsampling algorithms for various parametric regression models with massive data have been extensively investigated in recent years. However, all existing studies on subsampling heavily rely on clean massive data. In practical…

Standard approaches for variable selection in linear models are not tailored to deal properly with high-dimensional and incomplete data. Currently, methods dedicated to high-dimensional data handle missing values by ad-hoc strategies, like…

Adaptive collection of data is commonplace in applications throughout science and engineering. From the point of view of statistical inference however, adaptive data collection induces memory and correlation in the samples, and poses…

The problems of Lasso regression and optimal design of experiments share a critical property: their optimal solutions are typically \emph{sparse}, i.e., only a small fraction of the optimal variables are non-zero. Therefore, the…

We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels. Given a sufficiently large (polynomial-size) training set drawn i.i.d. from…

High-dimensional linear regression is a fundamental tool in modern statistics, particularly when the number of predictors exceeds the sample size. The classical Lasso, which relies on the squared loss, performs well under Gaussian noise…

We study computational aspects of a key problem in robust statistics -- the penalized least trimmed squares (LTS) regression problem, a robust estimator that mitigates the influence of outliers in data by capping residuals with large…

In many high dimensional classification or regression problems set in a biological context, the complete identification of the set of informative features is often as important as predictive accuracy, since this can provide mechanistic…

Among techniques for high-dimensional linear regression, Sorted L-One Penalized Estimation (SLOPE) generalizes the LASSO via an adaptive $l_1$ regularization that applies heavier penalties to larger coefficients in the model. To achieve…

The SLOPE estimates regression coefficients by minimizing a regularized residual sum of squares using a sorted-$\ell_1$-norm penalty. The SLOPE combines testing and estimation in regression problems. It exhibits suitable variable selection…

Big data presents potential but unresolved value as a source for analysis and inference. However,selection bias, present in many of these datasets, needs to be accounted for so that appropriate inferences can be made on the target…

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…