Related papers: Boosted optimal weighted least-squares
The paper addresses the model reduction problem for linear and nonlinear systems using the notion of least squares moment matching. For linear systems, the main idea is to approximate a transfer function by ensuring that the interpolation…
A new exact projective penalty method is proposed for the equivalent reduction of constrained optimization problems to nonsmooth unconstrained ones. In the method, the original objective function is extended to infeasible points by summing…
The modern ability to collect vast quantities of data poses a challenge for parameter estimation problems. When posed as a nonlinear least squares problem fitting a model to data, the cost of each iteration grows linearly with the amount of…
This paper studies the problem of distributed weighted least-squares (WLS) estimation for an interconnected linear measurement network with additive noise. Two types of measurements are considered: self measurements for individual nodes,…
We consider a setting in which it is desired to find an optimal complex vector $\mathbf{x}\in\mathbb{C}^N$ that satisfies $\mathcal{A}(\mathbf{x}) \approx \mathbf{b}$ in a least-squares sense, where $\mathbf{b} \in \mathbb{C}^M$ is a data…
The constrained mock-Chebyshev least squares operator is a linear approximation operator based on an equispaced grid of points. Like other polynomial or rational approximation methods, it was recently introduced in order to defeat the Runge…
This paper aims to select features that contribute most to the pose estimation in VO/VSLAM. Unlike existing feature selection works that are focused on efficiency only, our method significantly improves the accuracy of pose tracking, while…
A sound field reproduction method called weighted pressure matching is proposed. Sound field reproduction is aimed at synthesizing the desired sound field using multiple loudspeakers inside a target region. Optimization-based methods are…
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…
Over the course of the past decade, a variety of randomized algorithms have been proposed for computing approximate least-squares (LS) solutions in large-scale settings. A longstanding practical issue is that, for any given input, the user…
We study the bias-variance tradeoff within a multiscale approximation framework. Our approach uses a given quasi-interpolation operator, which is repeatedly applied within an error-correction scheme over a hierarchical data structure. We…
Outer approximation methods have long been employed to tackle a variety of optimization problems, including linear programming, in the 1960s, and continue to be effective for solving variational inequalities, general convex problems, as…
Many recent problems in signal processing and machine learning such as compressed sensing, image restoration, matrix/tensor recovery, and non-negative matrix factorization can be cast as constrained optimization. Projected gradient descent…
A significant hurdle for analyzing large sample data is the lack of effective statistical computing and inference methods. An emerging powerful approach for analyzing large sample data is subsampling, by which one takes a random subsample…
We study optimization over Riemannian embedded submanifolds, where the objective function is relatively smooth in the ambient Euclidean space. Such problems have broad applications but are still largely unexplored. We introduce two…
In this paper, a novel stochastic extra-step quasi-Newton method is developed to solve a class of nonsmooth nonconvex composite optimization problems. We assume that the gradient of the smooth part of the objective function can only be…
Gradient boosting algorithms construct a regression predictor using a linear combination of ``base learners''. Boosting also offers an approach to obtaining robust non-parametric regression estimators that are scalable to applications with…
We present and analyze an efficient implementation of an iteratively reweighted least squares algorithm for recovering a matrix from a small number of linear measurements. The algorithm is designed for the simultaneous promotion of both a…
We consider polynomial approximation over the interval $[-1,1]$ by regularized weighted discrete least squares methods with $\ell_2-$ or $\ell_1-$regularization, respectively. As the set of nodes we use Gauss quadrature points (which are…
Motivated by the need for the rigorous analysis of the numerical stability of variational least-squares kernel-based methods for solving second-order elliptic partial differential equations, we provide previously lacking stability…