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We study momentum-based first-order optimization algorithms in which the iterations utilize information from the two previous steps and are subject to an additive white noise. This setup uses noise to account for uncertainty in either…

Optimization and Control · Mathematics 2024-06-21 Hesameddin Mohammadi , Meisam Razaviyayn , Mihailo R. Jovanović

We consider a broadband over-the-air computation empowered model aggregation approach for wireless federated learning (FL) systems and propose to leverage an intelligent reflecting surface (IRS) to combat wireless fading and noise. We first…

Information Theory · Computer Science 2023-10-12 Deyou Zhang , Ming Xiao , Zhibo Pang , Lihui Wang , H. Vincent Poor

We study high-probability convergence guarantees of learning on streaming data in the presence of heavy-tailed noise. In the proposed scenario, the model is updated in an online fashion, as new information is observed, without storing any…

Machine Learning · Computer Science 2024-05-02 Aleksandar Armacki , Pranay Sharma , Gauri Joshi , Dragana Bajovic , Dusan Jakovetic , Soummya Kar

A frequently occurring challenge in experimental and numerical observation is how to resolve features, such as spectral peaks - with center, width, height - and derivatives from measured data with unavoidable noise. Therefore, we develop a…

Data Analysis, Statistics and Probability · Physics 2025-10-03 Bert Mulder , Ad Lagendijk , Willem L. Vos

This paper studies the distributed optimization problem under the influence of heavy-tailed gradient noises. Here, a heavy-tailed noise means that the noise does not necessarily satisfy the bounded variance assumption. Instead, it satisfies…

Optimization and Control · Mathematics 2025-05-12 Chao Sun , Huiming Zhang , Bo Chen , Li Yu

High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…

Statistics Theory · Mathematics 2023-05-11 Yinan Shen , Jingyang Li , Jian-Feng Cai , Dong Xia

We present an accelerated and hardware parallelized integral-equation solver for the problem of acoustic scattering by a two-dimensional surface in three-dimensional space. The approach is based, in part, on the novel Interpolated Factored…

Numerical Analysis · Mathematics 2022-11-01 Edwin Jimenez , Christoph Bauinger , Oscar P. Bruno

Hollow-core fibers offer superior loss and latency characteristics compared to solid-core alternatives, yet the geometric complexity of nested antiresonance nodeless fibers (NANFs) makes traditional optimization computationally prohibitive.…

Machine Learning · Computer Science 2026-03-17 Rania A. Eltaieb , Sophie LaRochelle , Leslie A. Rusch

We extend recent computer-assisted design and analysis techniques for first-order optimization over structured functions--known as performance estimation--to apply to structured sets. We prove "interpolation theorems" for smooth and…

Optimization and Control · Mathematics 2024-11-20 Alan Luner , Benjamin Grimmer

The paradigm of learning from automatic annotations driven by pre-trained experts and Foundation Models dominates data-hungry applications. However, it introduces a critical challenge: model-induced label noise. Unlike stochastic noise in…

Machine Learning · Computer Science 2026-05-18 Dayong Ren

Correlated noise sources, particularly magnetic noise, form a risk to future gravitational-wave searches aimed at detecting the gravitational-wave background. Potential noise contamination is investigated by making noise projections which…

We present a multiscale approach for identifying features in ocean beds by solving inverse problems in high frequency seafloor acoustics. The setting is based on Sound Navigation And Ranging (SONAR) imaging used in scientific, commercial,…

Numerical Analysis · Mathematics 2017-04-05 Bjorn Engquist , Christina Frederick , Quyen Huynh , Haomin Zhou

Mixed noise, composed of white Gaussian noise (WGN) and impulsive noise (IN), appears in numerous communication scenarios and can severely degrade system performance. In this paper, we optimize the transmitted constellation under mixed…

Signal Processing · Electrical Eng. & Systems 2025-09-09 Tianfu Qi , Jun Wang

In this paper, we develop connections between two seemingly disparate, but central, models in robust statistics: Huber's epsilon-contamination model and the heavy-tailed noise model. We provide conditions under which this connection…

Machine Learning · Statistics 2019-07-03 Adarsh Prasad , Sivaraman Balakrishnan , Pradeep Ravikumar

Modeling future traffic conditions often relies heavily on complex spatial-temporal neural networks to capture spatial and temporal correlations, which can overlook the inherent noise in the data. This noise, often manifesting as unexpected…

Machine Learning · Computer Science 2023-10-26 Yuanshao Zhu , Yongchao Ye , Xiangyu Zhao , James J. Q. Yu

In the paper, we consider the line spectral estimation problem in an unlimited sensing framework (USF), where a modulo analog-to-digital converter (ADC) is employed to fold the input signal back into a bounded interval before quantization.…

Signal Processing · Electrical Eng. & Systems 2024-08-14 Hongwei Wang , Jun Fang , Hongbin Li , Geert Leus

In this paper we present a new highly efficient calculation method for the far field amplitude pattern that arises from scattering problems governed by the d-dimensional Helmholtz equation and, by extension, Schr\"odinger's equation. The…

Numerical Analysis · Mathematics 2014-06-06 Siegfried Cools , Bram Reps , Wim Vanroose

This paper discusses the error and cost aspects of ill-posed integral equations when given discrete noisy point evaluations on a fine grid. Standard solution methods usually employ discretization schemes that are directly induced by the…

Numerical Analysis · Mathematics 2025-04-04 Michael Griebel , Tim Jahn

This paper proposes a method for estimating a surface that contains a given set of points from noisy measurements. More precisely, by assuming that the surface is described by the zero set of a function in the span of a given set of…

Systems and Control · Electrical Eng. & Systems 2026-04-07 Omar M. Sleem , Sahand Kiani , Constantino M. Lagoa

Predicting flutter remains a key challenge in aeroelastic research, with certain models relying on modal parameters, such as natural frequencies and damping ratios. These models are particularly useful in early design stages or for the…

Systems and Control · Electrical Eng. & Systems 2025-05-19 Gabriele Dessena , Alessandro Pontillo , Marco Civera , Dmitry I. Ignatyev , James F. Whidborne , Luca Zanotti Fragonara