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

Least squares approximation is a technique to find an approximate solution to a system of linear equations that has no exact solution. In a typical setting, one lets $n$ be the number of constraints and $d$ be the number of variables, with…

Model reduction simplifies complex dynamical systems while preserving essential properties. This paper revisits a recently proposed system-theoretic framework for least squares moment matching. It interprets least squares model reduction in…

Bootstrap methods have long been the cornerstone of ensemble learning in machine learning. This paper presents a theoretical analysis of bootstrap techniques applied to the Least Square Support Vector Machine (LSSVM) ensemble in the context…

This study shows how to obtain least-squares solutions to initial and boundary value problems to nonhomogeneous linear differential equations with nonconstant coefficients of any order. However, without loss of generality, the approach has…

We propose randomized least-squares value iteration (RLSVI) -- a new reinforcement learning algorithm designed to explore and generalize efficiently via linearly parameterized value functions. We explain why versions of least-squares value…

We present a reduced basis (RB) method for parametrized linear elliptic partial differential equations (PDEs) in a least-squares finite element framework. A rigorous and reliable error estimate is developed, and is shown to bound the error…

In this paper, we discuss the acceleration of the regularized alternating least square (RALS) algorithm for tensor approximation. We propose a fast iterative method using a Aitken-Stefensen like updates for the regularized algorithm.…

It is shown that the computational efficiency of the discrete least-squares (DLS) approximation of solutions of stochastic elliptic PDEs is improved by incorporating a reduced-basis method into the DLS framework. The goal is to recover the…

We propose iterative projection methods for solving square or rectangular consistent linear systems Ax = b. Existing projection methods use sketching matrices (possibly randomized) to generate a sequence of small projected subproblems, but…

The performance of Least Squares (LS) estimators is studied in isotonic, unimodal and convex regression. Our results have the form of sharp oracle inequalities that account for the model misspecification error. In isotonic and unimodal…

This work presents a model reduction approach to the inverse problem in the application of subsurface flows. For the Bayesian inverse problem, the forward model needs to be repeatedly computed for a large number of samples to get a…

Given a linear regression setting, Iterative Least Trimmed Squares (ILTS) involves alternating between (a) selecting the subset of samples with lowest current loss, and (b) re-fitting the linear model only on that subset. Both steps are…

Markov parameters play a key role in system identification. There exists many algorithms where these parameters are estimated using least-squares in a first, pre-processing, step, including subspace identification and multi-step…

The so-called constrained least mean-square algorithm is one of the most commonly used linear-equality-constrained adaptive filtering algorithms. Its main advantages are adaptability and relative simplicity. In order to gain analytical…

We study the Sparse Plus Low-Rank decomposition problem (SLR), which is the problem of decomposing a corrupted data matrix into a sparse matrix of perturbations plus a low-rank matrix containing the ground truth. SLR is a fundamental…

Variable selection in linear models plays a pivotal role in modern statistics. Hard-thresholding methods such as $l_0$ regularization are theoretically ideal but computationally infeasible. In this paper, we propose a new approach, called…

Bayesian $l_0$-regularized least squares is a variable selection technique for high dimensional predictors. The challenge is optimizing a non-convex objective function via search over model space consisting of all possible predictor…

We introduce a novel semi-supervised version of the least squares classifier. This implicitly constrained least squares (ICLS) classifier minimizes the squared loss on the labeled data among the set of parameters implied by all possible…

In order to improve the performance of Least Mean Square (LMS) based system identification of sparse systems, a new adaptive algorithm is proposed which utilizes the sparsity property of such systems. A general approximating approach on…

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…