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We consider the problem of non-parametric regression with a potentially large number of covariates. We propose a convex, penalized estimation framework that is particularly well-suited for high-dimensional sparse additive models. The…

The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from…

We introduce a sparse high-dimensional regression approach that can incorporate prior information on the regression parameters and can borrow information across a set of similar datasets. Prior information may for instance come from…

Sparse additive modeling is a class of effective methods for performing high-dimensional nonparametric regression. In this work we show how shape constraints such as convexity/concavity and their extensions, can be integrated into additive…

Modern network data analysis often involves analyzing network structures alongside covariate features to gain deeper insights into underlying patterns. However, traditional covariate-assisted statistical network models may not adequately…

Sparse covariates are frequent in classification and regression problems and in these settings the task of variable selection is usually of interest. As it is well known, sparse statistical models correspond to situations where there are…

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…

In high dimensional regression, global local shrinkage priors have gained significant traction for their ability to yield sparse estimates, improve parameter recovery, and support accurate predictive modeling. While recent work has explored…

This paper develops a new framework, called modular regression, to utilize auxiliary information -- such as variables other than the original features or additional data sets -- in the training process of linear models. At a high level, our…

A new sparse semiparametric model is proposed, which incorporates the influence of two functional random variables in a scalar response in a flexible and interpretable manner. One of the functional covariates is included through a…

The classical sparse parameter identification methods are usually based on the iterative basis selection such as greedy algorithms, or the numerical optimization of regularized cost functions such as LASSO and Bayesian posterior probability…

Beta regression is commonly employed when the outcome variable is a proportion. Since its conception, the approach has been widely used in applications spanning various scientific fields. A series of extensions have been proposed over time,…

Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. Modern applications in medical imaging generate covariates of more complex form such as multidimensional arrays…

We investigate the problem of statistical inference for logistic regression with high-dimensional covariates in settings where dependence among individuals is induced by an underlying Markov random field. Going beyond the pairwise…

Vector autoregression (VAR) is a fundamental tool for modeling multivariate time series. However, as the number of component series is increased, the VAR model becomes overparameterized. Several authors have addressed this issue by…

A key recent advance in face recognition models a test face image as a sparse linear combination of a set of training face images. The resulting sparse representations have been shown to possess robustness against a variety of distortions…

Area-level models for small area estimation typically rely on areal random effects to shrink design-based direct estimates towards a model-based predictor. Incorporating the spatial dependence of the random effects into these models can…

Reduced-rank regression estimates regression coefficients by imposing a low-rank constraint on the matrix of regression coefficients, thereby accounting for correlations among response variables. To further improve predictive accuracy and…

While Weighted Lasso sparse regression has appealing statistical guarantees that would entail a major real-world impact in finance, genomics, and brain imaging applications, it is typically scarcely adopted due to its complex…

Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…