相关论文: Efficient Batch and Recursive Least Squares for Ma…

Regression analysis is an important instrument to determine the effect of the explanatory variables on response variables. When outliers and bias errors are present, the standard weighted least squares estimator may perform poorly. For this…

The low multilinear rank approximation, also known as the truncated Tucker decomposition, has been extensively utilized in many applications that involve higher-order tensors. Popular methods for low multilinear rank approximation usually…

This paper presents a new method for estimating high dimensional covariance matrices. The method, permuted rank-penalized least-squares (PRLS), is based on a Kronecker product series expansion of the true covariance matrix. Assuming an…

In this paper, we address the problem of robust adaptive beamforming of signals received by a linear array. The challenge associated with the beamforming problem is twofold. Firstly, the process requires the inversion of the usually…

Partial least squares regression (PLSR) has been a popular technique to explore the linear relationship between two datasets. However, most of algorithm implementations of PLSR may only achieve a suboptimal solution through an optimization…

The matrix factor model has drawn growing attention for its advantage in achieving two-directional dimension reduction simultaneously for matrix-structured observations. In this paper, we propose a simple iterative least squares algorithm…

Partial least squares (PLS) is a dimensionality reduction technique introduced in the field of chemometrics and successfully employed in many other areas. The PLS components are obtained by maximizing the covariance between linear…

The least squares (LS) estimator and the best linear unbiased estimator (BLUE) are two well-studied approaches for the estimation of a deterministic but unknown parameter vector. In many applications it is known that the parameter vector…

This paper fortifies the recently introduced hierarchical-optimization recursive least squares (HO-RLS) against outliers which contaminate infrequently linear-regression models. Outliers are modeled as nuisance variables and are estimated…

This paper presents a two-stage online algorithm for recovery of low-rank parameter matrix in non-stationary stochastic systems. The first stage applies the recursive least squares (RLS) estimator combined with its singular value…

Least squares support vector machines are a commonly used supervised learning method for nonlinear regression and classification. They can be implemented in either their primal or dual form. The latter requires solving a linear system,…

Linear least squares (LLS) is perhaps the most common method of data analysis, dating back to Legendre, Gauss and Laplace. Framed as linear regression, LLS is also a backbone of mathematical statistics. Here we report on an unexpected new…

While leverage score sampling provides powerful tools for approximating solutions to large least squares problems, the cost of computing exact scores and sampling often prohibits practical application. This paper addresses this challenge by…

Partial Least Squares (PLS) is a widely used method for data integration, designed to extract latent components shared across paired high-dimensional datasets. Despite decades of practical success, a precise theoretical understanding of its…

We address the recovery of sparse vectors in an overcomplete, linear and noisy multiple measurement framework, where the measurement matrix is known upto a permutation of its rows. We derive sparse Bayesian learning (SBL) based updates for…

Kronecker regression is a highly-structured least squares problem $\min_{\mathbf{x}} \lVert \mathbf{K}\mathbf{x} - \mathbf{b} \rVert_{2}^2$, where the design matrix $\mathbf{K} = \mathbf{A}^{(1)} \otimes \cdots \otimes \mathbf{A}^{(N)}$ is…

We consider the problem of reconstructing rank-one matrices from random linear measurements, a task that appears in a variety of problems in signal processing, statistics, and machine learning. In this paper, we focus on the Alternating…

Performance analysis of $l_0$ norm constrained Recursive least Squares (RLS) algorithm is attempted in this paper. Though the performance pretty attractive compared to its various alternatives, no thorough study of theoretical analysis has…

Iteratively reweighted least square (IRLS) is a popular approach to solve sparsity-enforcing regression problems in machine learning. State of the art approaches are more efficient but typically rely on specific coordinate pruning schemes.…

Convex regression (CR) problem deals with fitting a convex function to a finite number of observations. It has many applications in various disciplines, such as statistics, economics, operations research, and electrical engineering.…