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When randomized ensembles such as bagging or random forests are used for binary classification, the prediction error of the ensemble tends to decrease and stabilize as the number of classifiers increases. However, the precise relationship…

Probability · Mathematics 2019-05-01 Miles E. Lopes

It is well known that machine learning methods can be vulnerable to adversarially-chosen perturbations of their inputs. Despite significant progress in the area, foundational open problems remain. In this paper, we address several key…

Machine Learning · Computer Science 2024-10-30 Edgar Dobriban , Hamed Hassani , David Hong , Alexander Robey

This work presents a hybrid approach to solve the maximum stable set problem, using constraint and semidefinite programming. The approach consists of two steps: subproblem generation and subproblem solution. First we rank the variable…

Combinatorics · Mathematics 2007-05-23 W. J. van Hoeve

Safety is a primary concern when applying reinforcement learning to real-world control tasks, especially in the presence of external disturbances. However, existing safe reinforcement learning algorithms rarely account for external…

Machine Learning · Computer Science 2023-10-12 Zeyang Li , Chuxiong Hu , Shengbo Eben Li , Jia Cheng , Yunan Wang

Robust discrete optimization is a highly active field of research where a plenitude of combinations between decision criteria, uncertainty sets and underlying nominal problems are considered. Usually, a robust problem becomes harder to…

Optimization and Control · Mathematics 2022-01-14 Marc Goerigk , Mohammad Khosravi

Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and…

Machine Learning · Computer Science 2021-05-13 Anna-Kathrin Kopetzki , Stephan Günnemann

Simulator imperfection, often known as model error, is ubiquitous in practical data assimilation problems. Despite the enormous efforts dedicated to addressing this problem, properly handling simulator imperfection in data assimilation…

Optimization and Control · Mathematics 2019-08-06 Xiaodong Luo

Deep Neural Networks (DNNs) are often vulnerable to adversarial examples.Several proposed defenses deploy an ensemble of models with the hope that, although the individual models may be vulnerable, an adversary will not be able to find an…

Machine Learning · Computer Science 2020-04-23 Mainuddin Ahmad Jonas , David Evans

This paper presents an initial exploration of stress-assisted diffusion problems in three dimensions within the framework of the virtual element method (VEM). Hilbert spaces enriched with parameter-weighted norms, the extended…

Numerical Analysis · Mathematics 2025-02-05 Andres E. Rubiano

Deep neural networks are vulnerable to adversarial examples - small input perturbations that result in incorrect predictions. We study this problem for models of source code, where we want the network to be robust to source-code…

Machine Learning · Computer Science 2022-08-23 Goutham Ramakrishnan , Jordan Henkel , Zi Wang , Aws Albarghouthi , Somesh Jha , Thomas Reps

Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…

Numerical Analysis · Computer Science 2017-02-15 Roberto Mínguez , Víctor Casero-Alonso

We explore a multiple-stage variant of the min-max robust selection problem with budgeted uncertainty that includes queries. First, one queries a subset of items and gets the exact values of their uncertain parameters. Given this…

Optimization and Control · Mathematics 2025-01-07 Xiaoyu Chen , Marc Goerigk , Michael Poss

In robust optimization, the general aim is to find a solution that performs well over a set of possible parameter outcomes, the so-called uncertainty set. In this paper, we assume that the uncertainty size is not fixed, and instead aim at…

Optimization and Control · Mathematics 2016-06-24 André Chassein , Marc Goerigk

A fundamental problem in robust learning is asymmetry: a learner needs to correctly classify every one of exponentially-many perturbations that an adversary might make to a test-time natural example. In contrast, the attacker only needs to…

Machine Learning · Computer Science 2024-02-14 Saba Ahmadi , Avrim Blum , Omar Montasser , Kevin Stangl

We propose an algorithm to enhance certified robustness of a deep model ensemble by optimally weighting each base model. Unlike previous works on using ensembles to empirically improve robustness, our algorithm is based on optimizing a…

Machine Learning · Statistics 2019-11-01 Huan Zhang , Minhao Cheng , Cho-Jui Hsieh

While deep neural networks have become the go-to approach in computer vision, the vast majority of these models fail to properly capture the uncertainty inherent in their predictions. Estimating this predictive uncertainty can be crucial,…

Machine Learning · Computer Science 2020-04-08 Fredrik K. Gustafsson , Martin Danelljan , Thomas B. Schön

Trustworthy machine learning aims at combating distributional uncertainties in training data distributions compared to population distributions. Typical treatment frameworks include the Bayesian approach, (min-max) distributionally robust…

Machine Learning · Computer Science 2025-05-05 Shixiong Wang , Haowei Wang , Xinke Li , Jean Honorio

Support Vector Machines (SVM) have gathered significant acclaim as classifiers due to their successful implementation of Statistical Learning Theory. However, in the context of multiclass and multilabel settings, the reliance on…

Machine Learning · Computer Science 2023-07-19 Sambhav Jain Reshma Rastogi

Despite the enormous success of machine learning models in various applications, most of these models lack resilience to (even small) perturbations in their input data. Hence, new methods to robustify machine learning models seem very…

Machine Learning · Computer Science 2020-10-30 Fariborz Salehi , Babak Hassibi

Design under uncertainty is a challenging problem, as a systems performance can be highly sensitive to variations in input parameters and model uncertainty. A conventional approach to addressing such problems is robust optimization, which…

Systems and Control · Electrical Eng. & Systems 2025-09-18 Maryam Ghasemzadeh , H M Dilshad Alam Digonta , Anand Balu Nellippallil , Anton van Beek
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