Related papers: Modelling High-Dimensional Categorical Data Using …

The presence of missing entries in data often creates challenges for pattern recognition algorithms. Traditional algorithms for clustering data assume that all the feature values are known for every data point. We propose a method to…

Two important goals of high-dimensional modeling are prediction and variable selection. In this article, we consider regularization with combined $L_1$ and concave penalties, and study the sampling properties of the global optimum of the…

We present a unified framework for low-rank matrix estimation with nonconvex penalties. We first prove that the proposed estimator attains a faster statistical rate than the traditional low-rank matrix estimator with nuclear norm penalty.…

Various R packages have been developed for the non-convex penalized estimation but they can only be applied to the smoothly clipped absolute deviation (SCAD) or minimax concave penalty (MCP). We develop an R package, entitled ncpen, for the…

This paper consider penalized empirical loss minimization of convex loss functions with unknown non-linear target functions. Using the elastic net penalty we establish a finite sample oracle inequality which bounds the loss of our estimator…

High-dimensional data pose challenges in statistical learning and modeling. Sometimes the predictors can be naturally grouped where pursuing the between-group sparsity is desired. Collinearity may occur in real-world high-dimensional…

We introduce a novel class of variable selection penalties called TWIN, which provides sensible data-adaptive penalization. Under a linear sparsity regime and random Gaussian designs we show that penalties in the TWIN class have a high…

This paper introduces a novel framework for estimation and inference in penalized M-estimators applied to robust high-dimensional linear regression models. Traditional methods for high-dimensional statistical inference, which predominantly…

In high-dimensional model selection problems, penalized simple least-square approaches have been extensively used. This paper addresses the question of both robustness and efficiency of penalized model selection methods, and proposes a…

In traditional logistic regression models, the link function is often assumed to be linear and continuous in predictors. Here, we consider a threshold model that all continuous features are discretized into ordinal levels, which further…

We propose a general framework for reduced-rank modeling of matrix-valued data. By applying a generalized nuclear norm penalty we can directly model low-dimensional latent variables associated with rows and columns. Our framework flexibly…

This paper investigates simple bilevel optimization problems where we minimize an upper-level objective over the optimal solution set of a convex lower-level objective. Existing methods for such problems either only guarantee asymptotic…

Graph-based variational methods have recently shown to be highly competitive for various classification problems of high-dimensional data, but are inherently difficult to handle from an optimization perspective. This paper proposes a convex…

Penalized least squares estimation is a popular technique in high-dimensional statistics. It includes such methods as the LASSO, the group LASSO, and the nuclear norm penalized least squares. The existing theory of these methods is not…

We introduce a new estimator for the vector of coefficients $\beta$ in the linear model $y=X\beta+z$, where $X$ has dimensions $n\times p$ with $p$ possibly larger than $n$. SLOPE, short for Sorted L-One Penalized Estimation, is the…

Under the linear regression framework, we study the variable selection problem when the underlying model is assumed to have a small number of nonzero coefficients (i.e., the underlying linear model is sparse). Non-convex penalties in…

Sorted $\ell_1$ Penalized Estimator (SLOPE) is a relatively new convex regularization method for fitting high-dimensional regression models. SLOPE allows to reduce the model dimension by shrinking some estimates of the regression…

In this paper, we propose to estimate model parameters and identify informative source datasets simultaneously for high-dimensional transfer learning problems with the aid of a non-convex penalty, in contrast to the separate useful dataset…

Modern multivariate machine learning and statistical methodologies estimate parameters of interest while leveraging prior knowledge of the association between outcome variables. The methods that do allow for estimation of relationships do…

Advancements in information technology have enabled the creation of massive spatial datasets, driving the need for scalable and efficient computational methodologies. While offering viable solutions, centralized frameworks are limited by…