Related papers: Consistent group selection in high-dimensional lin…

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…

The sparse group lasso is a high-dimensional regression technique that is useful for problems whose predictors have a naturally grouped structure and where sparsity is encouraged at both the group and individual predictor level. In this…

Lasso-type estimators are routinely used to estimate high-dimensional time series models. The theoretical guarantees established for these estimators typically require the penalty level to be chosen in a suitable fashion often depending on…

A structured variable selection problem is considered in which the covariates, divided into predefined groups, activate according to sparse patterns with few nonzero entries per group. Capitalizing on the concept of atomic norm, a composite…

We propose a new approach to mixed-frequency regressions in a high-dimensional environment that resorts to Group Lasso penalization and Bayesian techniques for estimation and inference. In particular, to improve the prediction properties of…

We consider adaptive estimation and statistical inference for high-dimensional graph-based linear models. In our model, the coordinates of regression coefficients correspond to an underlying undirected graph. Furthermore, the given graph…

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…

Group-based sparsity models are proven instrumental in linear regression problems for recovering signals from much fewer measurements than standard compressive sensing. The main promise of these models is the recovery of "interpretable"…

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…

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…

We consider Bayesian logistic regression models with group-structured covariates. In high-dimensional settings, it is often assumed that only small portion of groups are significant, thus consistent group selection is of significant…

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…

We consider the problem of fitting the parameters of a high-dimensional linear regression model. In the regime where the number of parameters $p$ is comparable to or exceeds the sample size $n$, a successful approach uses an…

The adaptive lasso refers to a class of methods that use weighted versions of the $L_1$-norm penalty, with weights derived from an initial estimate of the parameter vector to be estimated. Irrespective of the method chosen to compute this…

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…

Varying coefficient regression is a flexible technique for modeling data where the coefficients are functions of some effect-modifying parameter, often time or location in a certain domain. While there are a number of methods for variable…

We leverage recent advances in high-dimensional statistics to derive new L2 estimation upper bounds for Lasso and Group Lasso in high-dimensions. For Lasso, our bounds scale as $(k^*/n) \log(p/k^*)$---$n\times p$ is the size of the design…

The choice of the tuning parameter in the Lasso is central to its statistical performance in high-dimensional linear regression. In this work, we study tuning regimes under which the Lasso exhibits suboptimal prediction performance, in the…

Explanatory variables in a predictive regression typically exhibit low signal strength and various degrees of persistence. Variable selection in such a context is of great importance. In this paper, we explore the pitfalls and possibilities…

The sparse group Lasso is a widely used statistical model which encourages the sparsity both on a group and within the group level. In this paper, we develop an efficient augmented Lagrangian method for large-scale non-overlapping sparse…