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Related papers: Uncertainty Quantification Under Group Sparsity

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Stochastic gradient descent (SGD) or stochastic approximation has been widely used in model training and stochastic optimization. While there is a huge literature on analyzing its convergence, inference on the obtained solutions from SGD…

Machine Learning · Statistics 2026-04-01 Henry Lam , Zitong Wang

Penalized regression is an attractive framework for variable selection problems. Often, variables possess a grouping structure, and the relevant selection problem is that of selecting groups, not individual variables. The group lasso has…

Computation · Statistics 2016-07-20 Patrick Breheny , Jian Huang

Statistical multispecies models of multiarea marine ecosystems use a variety of data sources to estimate parameters using composite or weighted likelihood functions with associated weighting issues and questions on how to obtain variance…

Applications · Statistics 2012-02-16 Lorna Taylor , Verena M. Trenkel , Vojtech Kupca , Gunnar Stefansson

Modern large scale datasets are often plagued with missing entries. For tabular data with missing values, a flurry of imputation algorithms solve for a complete matrix which minimizes some penalized reconstruction error. However, almost…

Machine Learning · Statistics 2021-01-20 Yuxuan Zhao , Madeleine Udell

The problem of quantifying uncertainty about the locations of multiple change points by means of confidence intervals is addressed. The asymptotic distribution of the change point estimators obtained as the local maximisers of moving sum…

Methodology · Statistics 2022-06-20 Haeran Cho , Claudia Kirch

We study confidence regions and approximate chi-squared tests for variable groups in high-dimensional linear regression. When the size of the group is small, low-dimensional projection estimators for individual coefficients can be directly…

Statistics Theory · Mathematics 2016-02-23 Ritwik Mitra , Cun-Hui Zhang

This paper develops a theory for group Lasso using a concept called strong group sparsity. Our result shows that group Lasso is superior to standard Lasso for strongly group-sparse signals. This provides a convincing theoretical…

Machine Learning · Statistics 2009-03-17 Junzhou Huang , Tong Zhang

An inference procedure is proposed to provide consistent estimators of parameters in a modal regression model with a covariate prone to measurement error. A score-based diagnostic tool exploiting parametric bootstrap is developed to assess…

Methodology · Statistics 2024-07-02 Qingyang Liu , Xianzheng Huang

Despite the popularity of Convolutional Neural Networks (CNN), the problem of uncertainty quantification (UQ) of CNN has been largely overlooked. Lack of efficient UQ tools severely limits the application of CNN in certain areas, such as…

Machine Learning · Computer Science 2026-04-15 Hongfei Du , Emre Barut , Fang Jin

This paper proposes a statistical verification framework using Gaussian processes (GPs) for simulation-based verification of stochastic nonlinear systems with parametric uncertainties. Given a small number of stochastic simulations, the…

Systems and Control · Computer Science 2017-10-03 John F. Quindlen , Ufuk Topcu , Girish Chowdhary , Jonathan P. How

Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…

Statistics Theory · Mathematics 2025-04-02 Guoyu Zhang , Dandan Jiang , Fang Yao

The bootstrap is a popular data-driven method to quantify statistical uncertainty, but for modern high-dimensional problems, it could suffer from huge computational costs due to the need to repeatedly generate resamples and refit models. We…

Methodology · Statistics 2023-06-21 Henry Lam , Zhenyuan Liu

We consider the problem of Bayesian regression with trustworthy uncertainty quantification. We define that the uncertainty quantification is trustworthy if the ground truth can be captured by intervals dependent on the predictive…

Machine Learning · Statistics 2024-07-30 Zhenyuan Yuan , Thinh T. Doan

When dealing with timber structures, the characteristic strength and stiffness of the material are made highly variable and uncertain by the unavoidable, yet hardly predictable, presence of knots and other defects. In this work we apply the…

Numerical Analysis · Mathematics 2022-11-10 Balduzzi Giuseppe , Bonizzoni Francesca , Tamellini Lorenzo

We consider the problem of uncertainty quantification for an unknown low-rank matrix $\mathbf{X}$, given a partial and noisy observation of its entries. This quantification of uncertainty is essential for many real-world problems, including…

Methodology · Statistics 2022-03-28 Henry Shaowu Yuchi , Simon Mak , Yao Xie

Accurate assessment of systematic uncertainties is an increasingly vital task in physics studies, where large, high-dimensional datasets, like those collected at the Large Hadron Collider, hold the key to new discoveries. Common approaches…

Methodology · Statistics 2025-10-02 Alexis Romero , Kyle Cranmer , Daniel Whiteson

How to estimate heterogeneity, e.g. the effect of some variable differing across observations, is a key question in political science. Methods for doing so make simplifying assumptions about the underlying nature of the heterogeneity to…

Methodology · Statistics 2021-03-31 Max Goplerud

Modern artificial intelligence is supported by machine learning models (e.g., foundation models) that are pretrained on a massive data corpus and then adapted to solve a variety of downstream tasks. To summarize performance across multiple…

Machine Learning · Statistics 2025-01-09 Rachel Longjohn , Giri Gopalan , Emily Casleton

This paper develops bootstrap methods for practical statistical inference in panel data quantile regression models with fixed effects. We consider random-weighted bootstrap resampling and formally establish its validity for asymptotic…

Econometrics · Economics 2021-11-08 Antonio F. Galvao , Thomas Parker , Zhijie Xiao

We consider the problem of goodness-of-fit testing for a model that has at least one unknown parameter that cannot be eliminated by transformation. Examples of such problems can be as simple as testing whether a sample consists of…

Methodology · Statistics 2021-04-28 Sean van der Merwe
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