Related papers: Robust and Sparse Generalized Linear Models for Hi…

This paper introduces the Bi-linear consensus Alternating Direction Method of Multipliers (Bi-cADMM), aimed at solving large-scale regularized Sparse Machine Learning (SML) problems defined over a network of computational nodes.…

Inference for high-dimensional logistic regression models using penalized methods has been a challenging research problem. As an illustration, a major difficulty is the significant bias of the Lasso estimator, which limits its direct…

Many statistical $M$-estimators are based on convex optimization problems formed by the combination of a data-dependent loss function with a norm-based regularizer. We analyze the convergence rates of projected gradient and composite…

It is known that the Thresholded Lasso (TL), SCAD or MCP correct intrinsic estimation bias of the Lasso. In this paper we propose an alternative method of improving the Lasso for predictive models with general convex loss functions which…

We consider the problem of estimating differences in two multi-attribute Gaussian graphical models (GGMs) which are known to have similar structure, using a penalized D-trace loss function with non-convex penalties. The GGM structure is…

This paper presents GeNI-ADMM, a framework for large-scale composite convex optimization that facilitates theoretical analysis of both existing and new approximate ADMM schemes. GeNI-ADMM encompasses any ADMM algorithm that solves a first-…

Additive models belong to the class of structured nonparametric regression models that do not suffer from the curse of dimensionality. Finding the additive components that are nonzero when the true model is assumed to be sparse is an…

In multi-state models based on high-dimensional data, effective modeling strategies are required to determine an optimal, ideally parsimonious model. In particular, linking covariate effects across transitions is needed to conduct joint…

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…

Confounding can lead to spurious associations. Typically, one must observe confounders in order to adjust for them, but in high-dimensional settings, recent research has shown that it becomes possible to adjust even for unobserved…

Contextual optimization enhances decision quality by leveraging side information to improve predictions of uncertain parameters. However, existing approaches face significant challenges when dealing with multimodal or mixtures of…

Gaussian Mixture Models (GMMs) range among the most frequently used models in machine learning. However, training large, general GMMs becomes computationally prohibitive for datasets that have many data points $N$ of high-dimensionality…

The ordinary least squares estimate in linear regression is sensitive to the influence of errors with large variance, which reduces its robustness, especially when dealing with heavy-tailed errors or outliers frequently encountered in…

Traditional fault diagnosis methods struggle to handle fault data, with complex data characteristics such as high dimensions and large noise. Deep learning is a promising solution, which typically works well only when labeled fault data are…

For high-dimensional linear regression models, we review and compare several estimators of variances $\tau^2$ and $\sigma^2$ of the random slopes and errors, respectively. These variances relate directly to ridge regression penalty…

In this paper, we introduce a novel high-dimensional Factor-Adjusted sparse Partially Linear regression Model (FAPLM), to integrate the linear effects of high-dimensional latent factors with the nonparametric effects of low-dimensional…

Recently, a number of learning-based optimization methods that combine data-driven architectures with the classical optimization algorithms have been proposed and explored, showing superior empirical performance in solving various ill-posed…

Tensor classification is gaining importance across fields, yet handling partially observed data remains challenging. In this paper, we introduce a novel approach to tensor classification with incomplete data, framed within high-dimensional…

Longitudinal data often involve heterogeneity, sparse signals, and contamination from response outliers or high-leverage observations especially in biomedical science. Existing methods usually address only part of this problem, either…

The question of fast convergence in the classical problem of high dimensional linear regression has been extensively studied. Arguably, one of the fastest procedures in practice is Iterative Hard Thresholding (IHT). Still, IHT relies…