相关论文: Tsnnls: A solver for large sparse least squares pr…

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…

Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying…

Nonnegative least squares problems with multiple right-hand sides (MNNLS) arise in models that rely on additive linear combinations. In particular, they are at the core of most nonnegative matrix factorization algorithms and have many…

We describe two algorithms for computing a sparse solution to a least-squares problem where the coefficient matrix can have arbitrary dimensions. We show that the solution vector obtained by our algorithms is close to the solution vector…

Nonnegative (linear) least square problems are a fundamental class of problems that is well-studied in statistical learning and for which solvers have been implemented in many of the standard programming languages used within the machine…

We develop theoretical results that establish a connection across various regression methods such as the non-negative least squares, bounded variable least squares, simplex constrained least squares, and lasso. In particular, we show in…

We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…

In this paper, we propose a sparse least squares (SLS) optimization model for solving multilinear equations, in which the sparsity constraint on the solutions can effectively reduce storage and computation costs. By employing variational…

We propose a new fast algorithm to estimate any sparse generalized linear model with convex or non-convex separable penalties. Our algorithm is able to solve problems with millions of samples and features in seconds, by relying on…

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…

Non-negative least squares (NNLS) problem is one of the most important fundamental problems in numeric analysis. It has been widely used in scientific computation and data modeling. In big data, the limitations of algorithm speed and…

This document is an introduction to the Matlab package SDLS (Semi-Definite Least-Squares) for solving least-squares problems over convex symmetric cones. The package is shortly presented through the addressed problem, a sketch of the…

As enjoying the closed form solution, least squares support vector machine (LSSVM) has been widely used for classification and regression problems having the comparable performance with other types of SVMs. However, LSSVM has two drawbacks:…

We present Sketch 'n Solve, an open-source Python package that implements efficient randomized numerical linear algebra (RandNLA) techniques for solving large-scale least squares problems. While sketch-and-solve algorithms have demonstrated…

The sparse nonlinear programming (SNP) problem has wide applications in signal and image processing, machine learning, pattern recognition, finance and management, etc. However, the computational challenge posed by SNP has not yet been well…

We investigate the solution of low-rank matrix approximation problems using the truncated SVD. For this purpose, we develop and optimize GPU implementations for the randomized SVD and a blocked variant of the Lanczos approach. Our work…

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.…

The idea of unfolding iterative algorithms as deep neural networks has been widely applied in solving sparse coding problems, providing both solid theoretical analysis in convergence rate and superior empirical performance. However, for…

We consider the problem of finding a sparse solution for an underdetermined linear system of equations when the known parameters on both sides of the system are subject to perturbation. This problem is particularly relevant to…

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…