相关论文: Family-wise error rate control in Gaussian graphic…
Undirected graphical models are powerful tools for uncovering complex relationships among high-dimensional variables. This paper aims to fully recover the structure of an undirected graphical model when the data naturally take matrix form,…
The estimation of a precision matrix is a crucial problem in various research fields, particularly when working with high dimensional data. In such settings, the most common approach is to use the penalized maximum likelihood. The…
It is essential to capture the true probability distribution of uncertain data in the distributionally robust optimization (DRO). The uncertain data presents multimodality in numerous application scenarios, in the sense that the probability…
Distributionally robust optimization (DRO) incorporates robustness against uncertainty in the specification of probabilistic models. This paper focuses on mitigating the curse of dimensionality in data-driven DRO problems with optimal…
Wasserstein distributionally robust optimization (WDRO) strengthens statistical learning under model uncertainty by minimizing the local worst-case risk within a prescribed ambiguity set. Although WDRO has been extensively studied in…
High-dimensional regression often suffers from heavy-tailed noise and outliers, which can severely undermine the reliability of least-squares based methods. To improve robustness, we adopt a non-smooth Wilcoxon score based rank objective…
We consider the least-square linear regression problem with regularization by the $\ell^1$-norm, a problem usually referred to as the Lasso. In this paper, we first present a detailed asymptotic analysis of model consistency of the Lasso in…
The lasso has been studied extensively as a tool for estimating the coefficient vector in the high-dimensional linear model; however, considerably less is known about estimating the error variance in this context. In this paper, we propose…
In this paper, we propose a new estimation procedure for discovering the structure of Gaussian Markov random fields (MRFs) with false discovery rate (FDR) control, making use of the sorted l1-norm (SL1) regularization. A Gaussian MRF is an…
This paper considers a high-dimensional linear regression problem where there are complex correlation structures among predictors. We propose a graph-constrained regularization procedure, named Sparse Laplacian Shrinkage with the Graphical…
Distributional regression aims at estimating the conditional distribution of a targetvariable given explanatory co-variates. It is a crucial tool for forecasting whena precise uncertainty quantification is required. A popular methodology…
High-dimensional predictive models, those with more measurements than observations, require regularization to be well defined, perform well empirically, and possess theoretical guarantees. The amount of regularization, often determined by…
Gaussian graphical model is a graphical representation of the dependence structure for a Gaussian random vector. It is recognized as a powerful tool in different applied fields such as bioinformatics, error-control codes, speech language,…
Wasserstein distributionally robust optimization (DRO) has recently achieved empirical success for various applications in operations research and machine learning, owing partly to its regularization effect. Although connection between…
The popularity of penalized regression in high-dimensional data analysis has led to a demand for new inferential tools for these models. False discovery rate control is widely used in high-dimensional hypothesis testing, but has only…
Distributionally robust optimization (DRO) is a powerful tool for decision making under uncertainty. It is particularly appealing because of its ability to leverage existing data. However, many practical problems call for decision-making…
Graphical Gaussian models with edge and vertex symmetries were introduced by \citet{HojLaur:2008} who also gave an algorithm to compute the maximum likelihood estimate of the precision matrix for such models. In this paper, we take a…
Out-of-distribution (OOD) generalization is a challenging machine learning problem yet highly desirable in many high-stake applications. Existing methods suffer from overly pessimistic modeling with low generalization confidence. As…
Safety is a core challenge of autonomous robot motion planning, especially in the presence of dynamic and uncertain obstacles. Many recent results use learning and deep learning-based motion planners and prediction modules to predict…
Data-driven distributionally robust optimization is a recently emerging paradigm aimed at finding a solution that is driven by sample data but is protected against sampling errors. An increasingly popular approach, known as Wasserstein…