Related papers: High-Dimensional Sparse Single-Index Regression Vi…
A simple and intuitive method for feature selection consists of choosing the feature subset that maximizes a nonparametric measure of dependence between the response and the features. A popular proposal from the literature uses the…
In statistical learning framework with regressions, interactions are the contributions to the response variable from the products of the explanatory variables. In high-dimensional problems, detecting interactions is challenging due to…
We develop new stochastic gradient methods for efficiently solving sparse linear regression in a partial attribute observation setting, where learners are only allowed to observe a fixed number of actively chosen attributes per example at…
Sliced inverse regression (SIR, Li 1991) is a pioneering work and the most recognized method in sufficient dimension reduction. While promising progress has been made in theory and methods of high-dimensional SIR, two remaining challenges…
Covariance regression offers an effective way to model the large covariance matrix with the auxiliary similarity matrices. In this work, we propose a sparse covariance regression (SCR) approach to handle the potentially high-dimensional…
In this paper, we present a novel framework incorporating a combination of sparse models in different domains. We posit the observed data as generated from a linear combination of a sparse Gaussian Markov model (with a sparse precision…
We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…
In the field of statistical learning and data analysis, estimating precision matrices (i.e., the inverse of covariance matrices) is a critical task, particularly for understanding dependency structures among variables. However, traditional…
This paper introduces a new data-driven methodology for estimating sparse covariance matrices of the random coefficients in logit mixture models. Researchers typically specify covariance matrices in logit mixture models under one of two…
In recent years many sparse linear discriminant analysis methods have been proposed for high-dimensional classification and variable selection. However, most of these proposals focus on binary classification and they are not directly…
The debiased estimator is a crucial tool in statistical inference for high-dimensional model parameters. However, constructing such an estimator involves estimating the high-dimensional inverse Hessian matrix, incurring significant…
The varying-coefficient model is an important nonparametric statistical model that allows us to examine how the effects of covariates vary with exposure variables. When the number of covariates is big, the issue of variable selection…
We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of…
Fitting high-dimensional data involves a delicate tradeoff between faithful representation and the use of sparse models. Too often, sparsity assumptions on the fitted model are too restrictive to provide a faithful representation of the…
Analysis of high-dimensional data has led to increased interest in both single index models (SIMs) and the best-subset selection. SIMs provide an interpretable and flexible modeling framework for high-dimensional data, while the best-subset…
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…
High-dimensional sparse modeling with censored survival data is of great practical importance, as exemplified by modern applications in high-throughput genomic data analysis and credit risk analysis. In this article, we propose a class of…
Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…
Evaluation of statistical dependencies between two data samples is a basic problem of data science/machine learning, and HSIC (Hilbert-Schmidt Information Criterion)~\cite{HSIC} is considered the state-of-art method. However, for size $n$…
This paper proposes a new method for estimating sparse precision matrices in the high dimensional setting. It has been popular to study fast computation and adaptive procedures for this problem. We propose a novel approach, called Sparse…