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We study the problem of recovering Gaussian data under adversarial corruptions when the noises are low-rank and the corruptions are on the coordinate level. Concretely, we assume that the Gaussian noises lie in an unknown $k$-dimensional…

Data Structures and Algorithms · Computer Science 2023-11-29 Weihao Kong , Mingda Qiao , Rajat Sen

We examine the performance of the single-mode GKP code and its concatenation with the toric code for a noise model of Gaussian shifts, or displacement errors. We show how one can optimize the tracking of errors in repeated noisy error…

Quantum Physics · Physics 2019-04-02 Christophe Vuillot , Hamed Asasi , Yang Wang , Leonid P. Pryadko , Barbara M. Terhal

We consider finite-dimensional Bayesian linear inverse problems with Gaussian priors and additive Gaussian noise models. The goal of this note is to present a simple derivation of the well-known fact that solving the Bayesian D-optimal…

Statistics Theory · Mathematics 2023-12-27 Alen Alexanderian

We study linear chance-constrained problems where the coefficients follow a Gaussian mixture distribution. We provide mixed-binary quadratic programs that give inner and outer approximations of the chance constraint based on piecewise…

Optimization and Control · Mathematics 2025-11-24 Shibshankar Dey , Sanjay Mehrotra , Anirudh Subramanyam

In this paper, we investigate accelerated first-order methods for smooth convex optimization problems under inexact information on the gradient of the objective. The noise in the gradient is considered to be additive with two possibilities:…

Optimization and Control · Mathematics 2023-01-10 Vasin Artem , Alexander Gasnikov , Pavel Dvurechensky , Vladimir Spokoiny

A continuous-time regression model with a jointly strictly sub-Gaussian random noise is considered in the paper. Upper exponential bounds for probabilities of large deviations of the least squares estimator for the regression parameter are…

Probability · Mathematics 2018-06-12 Alexander V. Ivanov , Igor V. Orlovskyi

In the inverse Gaussian sequence space model with additional noisy observations of the operator, we derive nonasymptotic minimax radii of testing for ellipsoid-type alternatives simultaneously for both the signal detection problem (testing…

Statistics Theory · Mathematics 2020-02-19 Sandra Schluttenhofer , Jan Johannes

This note addresses the question of optimally estimating a linear functional of an object acquired through linear observations corrupted by random noise, where optimality pertains to a worst-case setting tied to a symmetric, convex, and…

Statistics Theory · Mathematics 2023-08-01 Simon Foucart , Grigoris Paouris

This paper considers the linear inverse problem where we wish to estimate a structured signal $x$ from its corrupted observations. When the problem is ill-posed, it is natural to make use of a convex function $f(\cdot)$ that exploits the…

Information Theory · Computer Science 2013-12-06 Samet Oymak , Christos Thrampoulidis , Babak Hassibi

Stochastic programs where the uncertainty distribution must be inferred from noisy data samples are considered. The stochastic programs are approximated with distributionally-robust optimizations that minimize the worst-case expected cost…

Optimization and Control · Mathematics 2024-01-04 Farhad Farokhi

We consider the mixed regression problem with two components, under adversarial and stochastic noise. We give a convex optimization formulation that provably recovers the true solution, and provide upper bounds on the recovery errors for…

Machine Learning · Statistics 2015-02-16 Yudong Chen , Xinyang Yi , Constantine Caramanis

Estimation of a deterministic quantity observed in non-Gaussian additive noise is explored via order statistics approach. More specifically, we study the estimation problem when measurement noises either have positive supports or follow a…

Signal Processing · Electrical Eng. & Systems 2020-07-15 Kamiar Radnosrati , Gustaf Hendeby , Fredrik Gustafsson

This paper studies the problem of discriminating two multivariate Gaussian distributions in a distributed manner. Specifically, it characterizes in a special case the optimal typeII error exponent as a function of the available…

Information Theory · Computer Science 2020-05-15 Pierre Escamilla , Abdellatif Zaidi , Michèle Wigger

We introduce a detailed analysis of the convergence of first-order methods with composite noise (sum of relative and absolute) in gradient for convex and smooth function minimization. This paper illustrates instances of practical problems…

Optimization and Control · Mathematics 2026-03-16 Artem Vasin , Alexander Gasnikov

The advantages of weak measurements, and especially measurements of imaginary weak values, for precision enhancement, are discussed. A situation is considered in which the initial state of the measurement device varies randomly on each run,…

Quantum Physics · Physics 2014-07-16 Yaron Kedem

In this paper we build provably near-optimal, in the minimax sense, estimates of linear forms and, more generally, "$N$-convex functionals" (the simplest example being the maximum of several fractional-linear functions) of unknown "signal"…

Statistics Theory · Mathematics 2019-04-01 Anatoli Juditsky , Arkadi Nemirovski

Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources. As part of a broader effort in scientific machine learning, many recent works have incorporated physical constraints or other a…

Machine Learning · Computer Science 2021-01-07 Laura Swiler , Mamikon Gulian , Ari Frankel , Cosmin Safta , John Jakeman

Variational hybrid quantum-classical optimization represents one of the most promising avenue to show the advantage of nowadays noisy intermediate-scale quantum computers in solving hard problems, such as finding the minimum-energy state of…

Quantum Physics · Physics 2020-11-18 Laura Gentini , Alessandro Cuccoli , Stefano Pirandola , Paola Verrucchi , Leonardo Banchi

Confirmation bias, the tendency to interpret information in a way that aligns with one's preconceptions, can profoundly impact scientific research, leading to conclusions that reflect the researcher's hypotheses even when the observational…

Machine Learning · Statistics 2025-09-09 Amnon Balanov , Tamir Bendory , Wasim Huleihel

We study the problem of super-resolution, where we recover the locations and weights of non-negative point sources from a few samples of their convolution with a Gaussian kernel. It has been shown that exact recovery is possible by…

Optimization and Control · Mathematics 2023-07-06 Stéphane Chrétien , Andrew Thompson , Bogdan Toader