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Motivated by the need for efficient estimation of conditional expectations, we consider a least-squares function approximation problem with heavily polluted data. Existing methods that are effective in the small-noise regime are suboptimal…

Machine Learning · Statistics 2026-05-26 Ben Adcock , Bernhard Hientzsch , Akil Narayan , Yiming Xu

Networked systems usually face different random uncertainties that make the performance of the least-squares (LS) linear filter decline significantly. For this reason, great attention has been paid to the search for other kinds of…

Systems and Control · Electrical Eng. & Systems 2024-08-26 Raquel Caballero-Águila , Josefa Linares-Pérez

Consider a process satisfying a stochastic differential equation with unknown drift parameter, and suppose that discrete observations are given. It is known that a simple least squares estimator (LSE) can be consistent, but numerically…

Statistics Theory · Mathematics 2017-03-17 Yasutaka Shimizu

For the identification of switched systems with a measured switching signal, this work aims to analyze the effect of switching strategies on the estimation error. The data for identification is assumed to be collected from globally…

Systems and Control · Electrical Eng. & Systems 2022-07-26 Shengling Shi , Othmane Mazhar , Bart De Schutter

We assume the direct sum <A> o <B> for the signal subspace. As a result of post- measurement, a number of operational contexts presuppose the a priori knowledge of the LB -dimensional "interfering" subspace <B> and the goal is to estimate…

Applications · Statistics 2017-04-17 Guillaume Bouleux , Rémy Boyer

We consider the problem of linear fitting of noisy data in the case of broad (say $\alpha$-stable) distributions of random impacts ("noise"), which can lack even the first moment. This situation, common in statistical physics of small…

Data Analysis, Statistics and Probability · Physics 2015-05-27 Eugene B. Postnikov , Igor M. Sokolov

This work studies an experimental design problem where {the values of a predictor variable, denoted by $x$}, are to be determined with the goal of estimating a function $m(x)$, which is observed with noise. A linear model is fitted to…

Statistics Theory · Mathematics 2023-05-03 David Azriel

This paper addresses identification of sparse linear and noise-driven continuous-time state-space systems, i.e., the right-hand sides in the dynamical equations depend only on a subset of the states. The key assumption in this study, is…

Systems and Control · Computer Science 2018-04-18 Zuogong Yue , Johan Thunberg , Lennart Ljung , Jorge Goncalves

The problem of fitting experimental data to a given model function $f(t; p_1,p_2,\dots,p_N)$ is conventionally solved numerically by methods such as that of Levenberg-Marquardt, which are based on approximating the Chi-squared measure of…

Optimization and Control · Mathematics 2017-03-14 Alberto Herrera-Gomez , R. Michael Porter

This paper establishes a nearly optimal algorithm for estimating the frequencies and amplitudes of a mixture of sinusoids from noisy equispaced samples. We derive our algorithm by viewing line spectral estimation as a sparse recovery…

Information Theory · Computer Science 2013-04-02 Gongguo Tang , Badri Narayan Bhaskar , Benjamin Recht

In this article we study the asymptotic behaviour of the least square estimator in a linear regression model based on random observation instances. We provide mild assumptions on the moments and dependence structure on the randomly spaced…

Statistics Theory · Mathematics 2021-10-07 Karine Bertin , Soledad Torres , Lauri Viitasaari

Motivated by the prevalence of environments in which data is abundant while resources for storage and/or transmission might be scarce, we study linear regression when predictors, their squares, and responses are subject to single-bit…

Statistics Theory · Mathematics 2026-04-01 Daniel Hill , Martin Slawski

Subsampling methods have been recently proposed to speed up least squares estimation in large scale settings. However, these algorithms are typically not robust to outliers or corruptions in the observed covariates. The concept of influence…

Machine Learning · Statistics 2014-06-20 Brian McWilliams , Gabriel Krummenacher , Mario Lucic , Joachim M. Buhmann

The linear regression models are widely used statistical techniques in numerous practical applications. The standard regression model requires several assumptions about the regres- sors and the error term. The regression parameters are…

Methodology · Statistics 2016-10-23 P. Vellaisamy

The discovery of non-linear causal relationship under additive non-Gaussian noise models has attracted considerable attention recently because of their high flexibility. In this paper, we propose a novel causal inference algorithm called…

Machine Learning · Statistics 2011-03-31 Makoto Yamada , Masashi Sugiyama , Jun Sese

A function of the empirical characteristic function,exists for the stable distribution, which leads to a linear regression and can be used to estimate the parameters. Two approaches are often used, one to find optimal values of t, but these…

Computation · Statistics 2018-11-06 J. Martin van Zyl

The identification of a linear system model from data has wide applications in control theory. The existing work that provides finite sample guarantees for linear system identification typically uses data from a single long system…

Machine Learning · Statistics 2025-05-09 Lei Xin , Baike She , Qi Dou , George Chiu , Shreyas Sundaram

We describe stochastic Newton and stochastic quasi-Newton approaches to efficiently solve large linear least-squares problems where the very large data sets present a significant computational burden (e.g., the size may exceed computer…

Numerical Analysis · Mathematics 2017-02-27 Julianne Chung , Matthias Chung , J. Tanner Slagel , Luis Tenorio

This paper investigates some theoretical properties of the Partial Least Square (PLS) method. We focus our attention on the single component case, that provides a useful framework to understand the underlying mechanism. We provide a…

Statistics Theory · Mathematics 2023-10-17 Luca Castelli , Clément Marteau , Irène Gannaz

Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of…

Statistics Theory · Mathematics 2025-08-04 Jelena Bradic , Victor Chernozhukov , Whitney K. Newey , Yinchu Zhu