English
Related papers

Related papers: Near-Optimal Estimation of Linear Functionals with…

200 papers

This paper deals with the problem of finding suboptimal values of an unknown function on the basis of measured data corrupted by bounded noise. As a prior, we assume that the unknown function is parameterized in terms of a number of basis…

Optimization and Control · Mathematics 2025-06-10 Jaap Eising , Jorge Cortes

We propose a new recursive estimator for linear dynamical systems under Gaussian process noise and non-Gaussian measurement noise. Specifically, we develop an approximate maximum a posteriori (MAP) estimator using dynamic programming and…

Systems and Control · Electrical Eng. & Systems 2025-09-09 Mohammad Hussein Yoosefian Nooshabadi , Laurent Lessard

This paper proposes a stochastic gradient descent method with an adaptive Gaussian noise term for the global minimization of nearly convex functions, which are nonconvex and possess multiple strict local minimizers. The noise term,…

Optimization and Control · Mathematics 2025-08-05 Chenglong Bao , Liang Chen , Weizhi Shao

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 consider two nonparametric procedures for estimating a concave distribution function based on data corrupted with additive noise generated by a bounded decreasing density on $(0,\infty)$. For the maximum likelihood (ML) estimator and…

Statistics Theory · Mathematics 2009-04-02 Geurt Jongbloed , Frank H. van der Meulen

This note studies a method for the efficient estimation of a finite number of unknown parameters from linear equations, which are perturbed by Gaussian noise. In case the unknown parameters have only few nonzero entries, the proposed…

Systems and Control · Computer Science 2014-05-27 Liang Dai , Kristiaan Pelckmans

Most compressed sensing algorithms do not account for the effect of saturation in noisy compressed measurements, though saturation is an important consequence of the limited dynamic range of existing sensors. The few algorithms that handle…

Machine Learning · Computer Science 2021-02-09 Shuvayan Banerjee , Radhe Srivastava , Ajit Rajwade

The problem of optimal estimation of linear functionals constructed from the unobserved values of a stochastic sequence with periodically stationary increments based on observations of the sequence with stationary noise is considered. For…

Statistics Theory · Mathematics 2021-10-18 Maksym Luz , Mikhail Moklyachuk

In this paper we generalize the estimation-control duality that exists in the linear-quadratic-Gaussian setting. We extend this duality to maximum a posteriori estimation of the system's state, where the measurement and dynamical system…

Optimization and Control · Mathematics 2016-07-12 Robert Bassett , Michael Casey , Roger J-B Wets

This work investigates the parameter estimation performance of super-resolution line spectral estimation using atomic norm minimization. The focus is on analyzing the algorithm's accuracy of inferring the frequencies and complex magnitudes…

Information Theory · Computer Science 2018-10-24 Qiuwei Li , Gongguo Tang

The multivariate linear regression model with shuffled data and additive Gaussian noise arises in various correspondence estimation and matching problems. Focusing on the denoising aspect of this problem, we provide a characterization the…

Machine Learning · Statistics 2017-04-26 Ashwin Pananjady , Martin J. Wainwright , Thomas A. Courtade

Motivated by value function estimation in reinforcement learning, we study statistical linear inverse problems, i.e., problems where the coefficients of a linear system to be solved are observed in noise. We consider penalized estimators,…

Machine Learning · Computer Science 2012-07-03 Bernardo Avila Pires , Csaba Szepesvari

Estimation problems with constrained parameter spaces arise in various settings. In many of these problems, the observations available to the statistician can be modelled as arising from the noisy realization of the image of a random linear…

Statistics Theory · Mathematics 2023-03-23 Reese Pathak , Martin J. Wainwright , Lin Xiao

We consider the problem of recovering of continuous multi-dimensional functions from the noisy observations over the regular grid. Our focus is at the adaptive estimation in the case when the function can be well recovered using a linear…

Statistics Theory · Mathematics 2009-03-06 Anatoli Iouditski , Arkadii S. Nemirovski

The aim of this article is to overview the problem of mean square optimal estimation of linear functionals which depend on unknown values of periodically correlated stochastic process. Estimates are based on observations of this process and…

Statistics Theory · Mathematics 2025-11-24 Iryna Dubovets'ka , Mykhailo Moklyachuk

We study the problem of estimation and testing in logistic regression with class-conditional noise in the observed labels, which has an important implication in the Positive-Unlabeled (PU) learning setting. With the key observation that the…

Methodology · Statistics 2020-08-14 Hyebin Song , Ran Dai , Garvesh Raskutti , Rina Foygel Barber

Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…

Optimization and Control · Mathematics 2017-12-27 Anil Aswani , Zuo-Jun Max Shen , Auyon Siddiq

In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by Poisson noise. A proper data fidelity term (log-likelihood) is introduced to reflect the Poisson statistics of the noise. On…

Applications · Statistics 2011-03-14 François-Xavier Dupé , Jalal Fadili , Jean-Luc Starck

In this paper, we develop convergence analysis of a modified line search method for objective functions whose value is computed with noise and whose gradient estimates are inexact and possibly random. The noise is assumed to be bounded in…

Optimization and Control · Mathematics 2021-03-05 Albert S. Berahas , Liyuan Cao , Katya Scheinberg

In this paper, we propose a novel approach to fit a functional linear regression in which both the response and the predictor are functions of a common variable such as time. We consider the case that the response and the predictor…

Methodology · Statistics 2017-11-15 Behdad Mostafaiy , MohammadReza FaridRohani , Shojaeddin Chenouri