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This paper constructs improved estimators of the means in the Gaussian saturated one-way layout with an ordinal factor. The least squares estimator for the mean vector in this saturated model is usually inadmissible. The hybrid shrinkage…

Statistics Theory · Mathematics 2007-06-13 Rudolf Beran

We describe a novel constructive technique for devising efficient first-order methods for a wide range of large-scale convex minimization settings, including smooth, non-smooth, and strongly convex minimization. The technique builds upon a…

Optimization and Control · Mathematics 2019-06-27 Yoel Drori , Adrien B. Taylor

Bayesian Optimization is the state of the art technique for the optimization of black boxes, i.e., functions where we do not have access to their analytical expression nor its gradients, they are expensive to evaluate and its evaluation is…

Artificial Intelligence · Computer Science 2021-01-13 Eduardo C. Garrido Merchán , Luis C. Jariego Pérez

Sharpness is an almost generic assumption in continuous optimization that bounds the distance from minima by objective function suboptimality. It facilitates the acceleration of first-order methods through restarts. However, sharpness…

Optimization and Control · Mathematics 2024-07-24 Ben Adcock , Matthew J. Colbrook , Maksym Neyra-Nesterenko

Bayesian optimisation is a powerful tool to solve expensive black-box problems, but fails when the stationary assumption made on the objective function is strongly violated, which is the case in particular for ill-conditioned or…

Machine Learning · Statistics 2019-12-06 Victor Picheny , Sattar Vakili , Artem Artemev

We extend the standard notion of self-concordance to non-convex optimization and develop a family of second-order algorithms with global convergence guarantees. In particular, two function classes -- \textit{weakly self-concordant}…

Optimization and Control · Mathematics 2026-04-07 Donald Goldfarb , Lexiao Lai , Tianyi Lin , Jiayu Zhang

When the nonconvex problem is complicated by stochasticity, the sample complexity of stochastic first-order methods may depend linearly on the problem dimension, which is undesirable for large-scale problems. In this work, we propose…

Optimization and Control · Mathematics 2024-10-01 Yue Xie , Jiawen Bi , Hongcheng Liu

Optimization problems involving minimization of a rank-one convex function over constraints modeling restrictions on the support of the decision variables emerge in various machine learning applications. These problems are often modeled…

Optimization and Control · Mathematics 2023-11-29 Soroosh Shafiee , Fatma Kılınç-Karzan

We propose a study of structured non-convex non-concave min-max problems which goes beyond standard first-order approaches. Inspired by the tight understanding established in recent works [Adil et al., 2022, Lin and Jordan, 2022b], we…

Optimization and Control · Mathematics 2023-04-18 Abhijeet Vyas , Brian Bullins

We verify functional a posteriori error estimate for obstacle problem proposed by Repin. Simplification into 1D allows for the construction of a nonlinear benchmark for which an exact solution of the obstacle problem can be derived. Quality…

Numerical Analysis · Mathematics 2016-11-04 Petr Harasim , Jan Valdman

Zeroth-order optimization methods are developed to overcome the practical hurdle of having knowledge of explicit derivatives. Instead, these schemes work with merely access to noisy functions evaluations. One of the predominant approaches…

Optimization and Control · Mathematics 2022-08-22 Wouter Jongeneel

In many optimization problems arising from scientific, engineering and artificial intelligence applications, objective and constraint functions are available only as the output of a black-box or simulation oracle that does not provide…

Optimization and Control · Mathematics 2019-08-15 Jeffrey Larson , Matt Menickelly , Stefan M. Wild

A common problem in data analysis is that the functional form, as well as the parameter values, of the underlying model which should describe a dataset is not known a priori. In these cases some extra uncertainty must be assigned to the…

Data Analysis, Statistics and Probability · Physics 2015-05-20 P. D. Dauncey , M. Kenzie , N. Wardle , G. J. Davies

Deep neural networks do not discriminate between spurious and causal patterns, and will only learn the most predictive ones while ignoring the others. This shortcut learning behaviour is detrimental to a network's ability to generalize to…

Machine Learning · Computer Science 2023-01-11 Thomas Duboudin , Emmanuel Dellandréa , Corentin Abgrall , Gilles Hénaff , Liming Chen

Minimizing finite sums of functions is a central problem in optimization, arising in numerous practical applications. Such problems are commonly addressed using first-order optimization methods. However, these procedures cannot be used in…

Optimization and Control · Mathematics 2025-07-01 Marco Rando , Cheik Traoré , Cesare Molinari , Lorenzo Rosasco , Silvia Villa

We propose leave-out estimators of quadratic forms designed for the study of linear models with unrestricted heteroscedasticity. Applications include analysis of variance and tests of linear restrictions in models with many regressors. An…

Econometrics · Economics 2019-08-28 Patrick Kline , Raffaele Saggio , Mikkel Sølvsten

Recent studies on frequent itemset mining algorithms resulted in significant performance improvements. However, if the minimal support threshold is set too low, or the data is highly correlated, the number of frequent itemsets itself can be…

Databases · Computer Science 2007-05-23 Toon Calders , Bart Goethals

In most practical applications such as recommendation systems, display advertising, and so forth, the collected data often contains missing values and those missing values are generally missing-not-at-random, which deteriorates the…

Machine Learning · Computer Science 2024-05-27 Mingming Ha , Xuewen Tao , Wenfang Lin , Qionxu Ma , Wujiang Xu , Linxun Chen

A linear functional of an object from a convex symmetric set can be optimally estimated, in a worst-case sense, by a linear functional of observations made on the object. This well-known fact is extended here to a nonlinear setting: other…

Functional Analysis · Mathematics 2025-12-25 Simon Foucart

Efficiency criteria for conformal prediction, such as \emph{observed fuzziness} (i.e., the sum of p-values associated with false labels), are commonly used to \emph{evaluate} the performance of given conformal predictors. Here, we…

Machine Learning · Computer Science 2020-05-15 Nicolo Colombo , Vladimir Vovk