Related papers: Ranked Sparsity: A Cogent Regularization Framework…

The Lasso method is known to exhibit instability in the presence of highly correlated features, often leading to an arbitrary selection of predictors. This issue manifests itself in two primary error types: the erroneous omission of…

Reduced-rank regression recognises the possibility of a rank-deficient matrix of coefficients. We propose a novel Bayesian model for estimating the rank of the coefficient matrix, which obviates the need for post-processing steps and allows…

Selection of covariates is crucial in the estimation of average treatment effects given observational data with high or even ultra-high dimensional pretreatment variables. Existing methods for this problem typically assume sparse linear…

Additive models enjoy the flexibility of nonlinear models while still being readily understandable to humans. By contrast, other nonlinear models, which involve interactions between features, are not only harder to fit but also…

This paper concerns with statistical estimation and inference for the ranking problems based on pairwise comparisons with additional covariate information such as the attributes of the compared items. Despite extensive studies, few prior…

Consider the normal linear regression setup when the number of covariates p is much larger than the sample size n, and the covariates form correlated groups. The response variable y is not related to an entire group of covariates in all or…

Finding an unconstrained and statistically interpretable reparameterization of a covariance matrix is still an open problem in statistics. Its solution is of central importance in covariance estimation, particularly in the recent…

Sparse logistic regression is for classification and feature selection simultaneously. Although many studies have been done to solve $\ell_1$-regularized logistic regression, there is no equivalently abundant work on solving sparse logistic…

We consider the problem of estimating high-dimensional covariance matrices of a particular structure, which is a summation of low rank and sparse matrices. This covariance structure has a wide range of applications including factor analysis…

We investigate the rank of random (symmetric) sparse matrices. Our main finding is that with high probability, any dependency that occurs in such a matrix is formed by a set of few rows that contains an overwhelming number of zeros. This…

Sparse regression and classification estimators that respect group structures have application to an assortment of statistical and machine learning problems, from multitask learning to sparse additive modeling to hierarchical selection.…

For statistical inference on regression models with a diverging number of covariates, the existing literature typically makes sparsity assumptions on the inverse of the Fisher information matrix. Such assumptions, however, are often…

Feature selection is important step in machine learning since it has shown to improve prediction accuracy while depressing the curse of dimensionality of high dimensional data. The neural networks have experienced tremendous success in…

In this paper, the estimation problem for sparse reduced rank regression (SRRR) model is considered. The SRRR model is widely used for dimension reduction and variable selection with applications in signal processing, econometrics, etc. The…

Surrogate models are used to alleviate the computational burden in engineering tasks, which require the repeated evaluation of computationally demanding models of physical systems, such as the efficient propagation of uncertainties. For…

The ranking problem is to order a collection of units by some unobserved parameter, based on observations from the associated distribution. This problem arises naturally in a number of contexts, such as business, where we may want to rank…

We investigate the methods that simultaneously enforce sparsity and low-rank structure in a matrix as often employed for sparse phase retrieval problems or phase calibration problems in compressive sensing. We propose a new approach for…

Ranked set sampling (RSS) is a cost-efficient study design that uses inexpensive baseline ranking to select a more informative subset of individuals for full measurement. While RSS is well known to improve precision over simple random…

Sparse representation-based classification (SRC) has been shown to achieve a high level of accuracy in face recognition (FR). However, matching faces captured in unconstrained video against a gallery with a single reference facial still per…

Missing values in datasets are common in applied statistics. For regression problems, theoretical work thus far has largely considered the issue of missing covariates as distinct from missing responses. However, in practice, many datasets…