Related papers: A Tutorial on Linear Least Square Estimation
Line spectral estimation (LSE) from multi snapshot samples is studied utilizing the variational Bayesian methods. Motivated by the recently proposed variational line spectral estimation (VALSE) method for a single snapshot, we develop the…
A numerical method optimizing the coefficients of the semi empirical mass formula or those of similar mass formulas is presented. The optimization is based on the least-squares adjustments method and leads to the resolution of a linear…
The least trimmed squares (LTS) is a reasonable formulation of robust regression whereas it suffers from high computational cost due to the nonconvexity and nonsmoothness of its objective function. The most frequently used FAST-LTS…
Modelling real world systems frequently requires the solution of systems of nonlinear equations. A number of approaches have been suggested and developed for this computational problem. However, it is also possible to attempt solutions…
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…
Developing efficient methods for solving parametric partial differential equations is crucial for addressing inverse problems. This work introduces a Least-Squares-based Neural Network (LS-Net) method for solving linear parametric PDEs. It…
An extension of the Gauss-Newton algorithm is proposed to find local minimizers of penalized nonlinear least squares problems, under generalized Lipschitz assumptions. Convergence results of local type are obtained, as well as an estimate…
In this paper, we study a class of approximation problems, appearing in data approximation and signal processing. The approximations are constructed as combinations of polynomial splines (piecewise polynomials), whose parameters are subject…
In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…
This work provides simple algorithms for multi-class (and multi-label) prediction in settings where both the number of examples n and the data dimension d are relatively large. These robust and parameter free algorithms are essentially…
A novel estimation approach for a general class of semi-parametric multivariate time series models is introduced where the conditional mean is modeled through parametric functions. The focus of the estimation is the conditional mean…
This paper derives a new variational equation for the linear least-squares backward error by expressing the backward error in terms of a generalized eigenvalue problem and using results from indefinite linear algebra. For problems with…
Sparse model estimation is a topic of high importance in modern data analysis due to the increasing availability of data sets with a large number of variables. Another common problem in applied statistics is the presence of outliers in the…
We consider the problem of nonparametric regression under shape constraints. The main examples include isotonic regression (with respect to any partial order), unimodal/convex regression, additive shape-restricted regression, and…
Stochastic nonlinear dynamical systems are ubiquitous in modern, real-world applications. Yet, estimating the unknown parameters of stochastic, nonlinear dynamical models remains a challenging problem. The majority of existing methods…
This paper presents a numerical method to implement the parameter estimation method using response statistics that was recently formulated by the authors. The proposed approach formulates the parameter estimation problem of It\^o drift…
We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the…
Suppose that $\mathbf{y}=\lvert A\mathbf{x_0}\rvert+\eta$ where $\mathbf{x_0} \in \mathbb{R}^d$ is the target signal and $\eta\in \mathbb{R}^m$ is a noise vector. The aim of phase retrieval is to estimate $\mathbf{x_0}$ from $\mathbf{y}$. A…
This paper deals with the consistency of the least squares estimator of a convex regression function when the predictor is multidimensional. We characterize and discuss the computation of such an estimator via the solution of certain…
We introduce a direct numerical treatment of nonlinear higher-index differential-algebraic equations by means of overdetermined polynomial least-squares collocation. The procedure is not much more computationally expensive than standard…