Related papers: Linear Regression without computing pseudo-inverse…

In statistics, researchers use Regression models for data analysis and prediction in many productive sectors (industry, business, academy, etc.). Regression models are mathematical functions representing an approximation of dependent…

The parameter space of nonnegative trigonometric sums (NNTS) models for circular data is the surface of a hypersphere; thus, constructing regression models for a circular-dependent variable using NNTS models can comprise fitting great…

The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…

We propose a new method of estimation in high-dimensional linear regression model. It allows for very weak distributional assumptions including heteroscedasticity, and does not require the knowledge of the variance of random errors. The…

Structure learning methods for covariance and concentration graphs are often validated on synthetic models, usually obtained by randomly generating: (i) an undirected graph, and (ii) a compatible symmetric positive definite (SPD) matrix. In…

For random field theory based multiple comparison corrections In brain imaging, it is often necessary to compute the distribution of the supremum of a random field. Unfortunately, computing the distribution of the supremum of the random…

Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…

We present a geometrical interpretation of linear regression based on vectors in n dimensions (n the number of data points). This is to be used as a didactic tool for teachers when presenting that topic.

Functional linear regression has recently attracted considerable interest. Many works focus on asymptotic inference. In this paper we consider in a non asymptotic framework a simple estimation procedure based on functional Principal…

We develop an estimator for the high-dimensional covariance matrix of a locally stationary process with a smoothly varying trend and use this statistic to derive consistent predictors in non-stationary time series. In contrast to the…

We propose an algebraic combinatorial method for solving large sparse linear systems of equations locally - that is, a method which can compute single evaluations of the signal without computing the whole signal. The method scales only in…

We develop quaternion--native iterative methods for computing the Moore--Penrose (MP) pseudoinverse of quaternion matrices and analyze their convergence. Our starting point is a damped Newton--Schulz (NS) iteration tailored to…

A nonparametric regression setting is considered with a real-valued covariate and responses from a metric space. One may approach this setting via Fr\'echet regression, where the value of the regression function at each point is estimated…

Human inertial thinking schemes can be formed through learning, which are then applied to quickly solve similar problems later. However, when problems are significantly different, inertial thinking generally presents the solutions that are…

In this paper we analyse convergence of projected fixed-point iteration on a Riemannian manifold of matrices with fixed rank. As a retraction method we use `projector splitting scheme'. We prove that the projector splitting scheme converges…

The dramatic growth of big datasets presents a new challenge to data storage and analysis. Data reduction, or subsampling, that extracts useful information from datasets is a crucial step in big data analysis. We propose an orthogonal…

In this work, we consider the inverse problem of reconstructing the internal structure of an object from limited x-ray projections. We use a Gaussian process prior to model the target function and estimate its (hyper)parameters from…

A type of iterative orthogonally accumulated projection methods for solving linear system of equations are proposed in this paper. This type of methods are applications of accumulated projection(AP) technique proposed recently by authors.…

Masked Image Modeling (MIM) is a powerful self-supervised strategy for visual pre-training without the use of labels. MIM applies random crops to input images, processes them with an encoder, and then recovers the masked inputs with a…

We introduce two derivative-free projection methods for large-scale systems of nonlinear monotone equations subject to convex constraints. Both methods incorporate an adaptive spectral parameter into established conjugate gradient…