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This paper studies distributionally robust optimization for a rich class of risk measures with ambiguity sets defined by $\phi$-divergences. The risk measures are allowed to be non-linear in probabilities, are represented by Choquet…

Optimization and Control · Mathematics 2025-04-15 Guanyu Jin , Roger J. A. Laeven , Dick den Hertog

We design a general framework for answering adaptive statistical queries that focuses on providing explicit confidence intervals along with point estimates. Prior work in this area has either focused on providing tight confidence intervals…

Machine Learning · Computer Science 2020-03-10 Ryan Rogers , Aaron Roth , Adam Smith , Nathan Srebro , Om Thakkar , Blake Woodworth

We develop a general assumption-lean framework for constructing uniformly valid confidence sets for functionals defined by moment equalities, referred to as $Z$-functionals. Our approach combines self-normalized statistics with a test…

Statistics Theory · Mathematics 2025-07-11 Woonyoung Chang , Arun Kumar Kuchibhotla

This paper presents a novel boundary-optimized fast Fourier extension algorithm for efficient approximation of non-periodic functions. The proposed methodology constructs periodic extensions through strategic utilization of boundary…

Numerical Analysis · Mathematics 2025-08-27 Z. Y. Zhao , Y. F Wang , A. G. Yagola

Decision makers routinely use constrained optimization technology to plan and operate complex systems like global supply chains or power grids. In this context, practitioners must assess how close a computed solution is to optimality in…

Machine Learning · Statistics 2026-03-24 Miao Li , Michael Klamkin , Russell Bent , Pascal Van Hentenryck

Several variants of reweighted risk functionals, such as focal loss, inverse focal loss, and the Area Under the Risk Coverage Curve (AURC), have been proposed for improving model calibration; yet their theoretical connections to calibration…

Computer Vision and Pattern Recognition · Computer Science 2026-01-30 Han Zhou , Sebastian G. Gruber , Teodora Popordanoska , Matthew B. Blaschko

AIMS. The maximum-likelihood method is the standard approach to obtain model fits to observational data and the corresponding confidence regions. We investigate possible sources of bias in the log-likelihood function and its subsequent…

Astrophysics · Physics 2009-11-11 J. Hartlap , P. Simon , P. Schneider

This paper addresses the integration of additional information sources into a Bayesian optimization framework while ensuring that safety constraints are satisfied. The interdependencies between these information sources are modeled using an…

Machine Learning · Computer Science 2025-05-06 Jannis O. Luebsen , Annika Eichler

The theory of convex risk functions has now been well established as the basis for identifying the families of risk functions that should be used in risk averse optimization problems. Despite its theoretical appeal, the implementation of a…

Optimization and Control · Mathematics 2022-07-20 Jonathan Yu-Meng Li

Model Predictive Control evolved as the state of the art paradigm for safety critical control tasks. Control-as-Inference approaches thereof model the constrained optimization problem as a probabilistic inference problem. The constraints…

Optimization and Control · Mathematics 2025-11-21 Jörn Tebbe , Andreas Besginow , Markus Lange-Hegermann

This paper studies the construction of adaptive confidence intervals under Huber's contamination model when the contamination proportion is unknown. For the robust confidence interval of a Gaussian mean, we show that the optimal length of…

Statistics Theory · Mathematics 2025-06-05 Yuetian Luo , Chao Gao

Error bounds, which refer to inequalities that bound the distance of vectors in a test set to a given set by a residual function, have proven to be extremely useful in analyzing the convergence rates of a host of iterative methods for…

Optimization and Control · Mathematics 2015-12-14 Zirui Zhou , Anthony Man-Cho So

Most inverse optimization models impute unspecified parameters of an objective function to make an observed solution optimal for a given optimization problem with a fixed feasible set. We propose two approaches to impute unspecified…

Optimization and Control · Mathematics 2019-07-19 Timothy C. Y. Chan , Neal Kaw

We study the problem of distributional approximations to high-dimensional non-degenerate $U$-statistics with random kernels of diverging orders. Infinite-order $U$-statistics (IOUS) are a useful tool for constructing simultaneous prediction…

Statistics Theory · Mathematics 2019-12-11 Yanglei Song , Xiaohui Chen , Kengo Kato

We propose and analyze algorithms for distributionally robust optimization of convex losses with conditional value at risk (CVaR) and $\chi^2$ divergence uncertainty sets. We prove that our algorithms require a number of gradient…

Optimization and Control · Mathematics 2020-12-14 Daniel Levy , Yair Carmon , John C. Duchi , Aaron Sidford

We study asymptotic frequentist coverage and approximately Gaussian properties of Bayes posterior credible sets in nonlinear inverse problems when a Gaussian prior is placed on the parameter of the PDE. The aim is to ensure valid…

Statistics Theory · Mathematics 2026-04-24 Youngsoo Baek , Katerina Papagiannouli

We consider potentially non-convex optimization problems, for which optimal rates of approximation depend on the dimension of the parameter space and the smoothness of the function to be optimized. In this paper, we propose an algorithm…

Machine Learning · Computer Science 2022-04-12 Blake Woodworth , Francis Bach , Alessandro Rudi

Bootstrap smoothed (bagged) parameter estimators have been proposed as an improvement on estimators found after preliminary data-based model selection. The key result of Efron (2014) is a very convenient and widely applicable formula for a…

Methodology · Statistics 2019-04-29 Paul Kabaila , Christeen Wijethunga

Classical frequentist approaches to inference for the lasso emphasize exact coverage for each feature, which requires debiasing and severs the connection between confidence intervals and the original lasso estimates. To address this, in…

Methodology · Statistics 2025-09-19 Logan Harris , Patrick Breheny

In this paper we develop a concrete and fully implementable approach to the optimization of functionally generated portfolios in stochastic portfolio theory. The main idea is to optimize over a family of rank-based portfolios parameterized…

Portfolio Management · Quantitative Finance 2021-10-12 Steven Campbell , Ting-Kam Leonard Wong