English
Related papers

Related papers: Exponential convergence of recursive least squares…

200 papers

This paper determines the range of feasible values of standard error exponents for binary-input memoryless symmetric channels of fixed capacity $C$ and shows that extremes are attained by the binary symmetric and the binary erasure channel.…

Information Theory · Computer Science 2012-12-06 Albert Guillen i Fabregas , Ingmar Land , Alfonso Martinez

The machine learning explosion has created a prominent trend in modern computer hardware towards low precision floating-point operations. In response, there have been growing efforts to use low and mixed precision in general scientific…

Numerical Analysis · Mathematics 2024-03-19 Cody J. Balos , Steven Roberts , David J. Gardner

We show that the points that converge to infinity under iteration of the exponential map form a connected subset of the complex plane.

Dynamical Systems · Mathematics 2010-04-08 Lasse Rempe

Generalized linear mixed models are powerful tools for analyzing clustered data, where the unknown parameters are classically (and most commonly) estimated by the maximum likelihood and restricted maximum likelihood procedures. However,…

Statistics Theory · Mathematics 2023-03-23 Andrea M. Bratsberg , Magne Thoresen , Abhik Ghosh

We provide a recursive method for constructing product formula approximations to exponentials of commutators, giving the first approximations that are accurate to arbitrarily high order. Using these formulas, we show how to approximate…

Quantum Physics · Physics 2013-11-22 Andrew M. Childs , Nathan Wiebe

In this paper, we consider a least-squares (LS)-based distributed algorithm build on a sensor network to estimate an unknown parameter vector of a dynamical system, where each sensor in the network has partial information only but is…

Systems and Control · Electrical Eng. & Systems 2022-12-19 Siyu Xie , Yaqi Zhang , Lei Guo

This paper investigates the finite-sample prediction risk of the high-dimensional least squares estimator. We derive the central limit theorem for the prediction risk when both the sample size and the number of features tend to infinity.…

Machine Learning · Statistics 2020-08-17 Zeng Li , Chuanlong Xie , Qinwen Wang

We study the monotone single index model where a real response variable $Y $ is linked to a $d$-dimensional covariate $X$ through the relationship $E[Y | X] = \Psi_0(\alpha^T_0 X)$ almost surely. Both the ridge function, $\Psi_0$, and the…

Statistics Theory · Mathematics 2018-04-19 F. Balabdaoui , C. Durot , H. Jankowski

The convergence properties of adaptive systems in terms of excitation conditions on the regressor vector are well known. With persistent excitation of the regressor vector in model reference adaptive control the state error and the…

Optimization and Control · Mathematics 2015-11-11 Benjamin M. Jenkins , Anuradha M. Annaswamy , Eugene Lavretsky , Travis E. Gibson

A classical method for risk-sensitive nonlinear control is the iterative linear exponential quadratic Gaussian algorithm. We present its convergence analysis from a first-order optimization viewpoint. We identify the objective that the…

Optimization and Control · Mathematics 2019-10-21 Vincent Roulet , Maryam Fazel , Siddhartha Srinivasa , Zaid Harchaoui

This paper is concerned with the least squares estimator for a basic class of nonlinear autoregressive models, whose outputs are not necessarily to be ergodic. Several asymptotic properties of the least squares estimator have been…

Probability · Mathematics 2019-09-17 Zhaobo Liu , Chanying Li

We consider finite mixtures of generalized linear models with binary output. We prove that cross moment (between the output and the regression variables) until order 3 are sufficient to identify all parameters of the model. We propose a…

Statistics Theory · Mathematics 2020-02-13 Benjamin Auder , Elisabeth Gassiat , Mor Absa Loum

In various areas of applied numerics, the problem of calculating the logarithm of a matrix A emerges. Since series expansions of the logarithm usually do not converge well for matrices far away from the identity, the standard numerical…

Numerical Analysis · Computer Science 2007-07-19 Gernot Schaller

In this work, we consider error detection via simulation for reversible circuit architectures. We rigorously prove that reversibility augments the performance of this simple error detection protocol to a considerable degree. A single…

Hardware Architecture · Computer Science 2023-01-11 Lukas Burgholzer , Robert Wille , Richard Kueng

This paper presents a consensus algorithm for a multi-agent system where each agent has access to its imperfect own state and neighboring state measurements. The measurements are subject to deterministic disturbances and the proposed…

Systems and Control · Computer Science 2014-09-22 Mohammad Zamani , Iman Shames , Valery Ugrinovskii

Fast convergent, accurate, computationally efficient, parallelizable, and robust matrix inversion and parameter estimation algorithms are required in many time-critical and accuracy-critical applications such as system identification,…

Optimization and Control · Mathematics 2020-08-27 Alexander Stotsky

We establish the pointwise convergence of the iterative Lloyd algorithm, also known as $k$-means algorithm, when the quadratic quantization error of the starting grid (with size $N\ge 2$) is lower than the minimal quantization error with…

Probability · Mathematics 2014-01-03 Gilles Pagès , Jun Yu

The Total Least Squares solution of an overdetermined, approximate linear equation $Ax \approx b$ minimizes a nonlinear function which characterizes the backward error. We show that a globally convergent variant of the Gauss--Newton…

Numerical Analysis · Mathematics 2019-11-01 Dario Fasino , Antonio Fazzi

Factor models have been widely used in economics and finance. However, the heavy-tailed nature of macroeconomic and financial data is often neglected in the existing literature. To address this issue and achieve robustness, we propose an…

Methodology · Statistics 2023-03-30 Yong He , Lingxiao Li , Dong Liu , Wen-Xin Zhou

An ensemble method is introduced that utilizes randomization and loss function gradients to compute a prediction. Multiple weakly-correlated estimators approximate the gradient at randomly sampled points on the error surface and are…

Machine Learning · Computer Science 2020-09-15 Nicholas Smith