Related papers: OEM for least squares problems
We present a fast algorithm for linear least squares problems governed by hierarchically block separable (HBS) matrices. Such matrices are generally dense but data-sparse and can describe many important operators including those derived…
In this paper, we study the orthogonal least squares (OLS) algorithm for sparse recovery. On the one hand, we show that if the sampling matrix $\mathbf{A}$ satisfies the restricted isometry property (RIP) of order $K + 1$ with isometry…
We construct least squares formulations of PDEs with inhomogeneous essential boundary conditions, where boundary residuals are not measured in unpractical fractional Sobolev norms, but which formulations nevertheless are shown to yield a…
Model selection and sparse recovery are two important problems for which many regularization methods have been proposed. We study the properties of regularization methods in both problems under the unified framework of regularized least…
A l1-norm penalized orthogonal forward regression (l1-POFR) algorithm is proposed based on the concept of leaveone- out mean square error (LOOMSE). Firstly, a new l1-norm penalized cost function is defined in the constructed orthogonal…
In this paper, we propose a framework based on sum-of-squares programming to design iterative first-order optimization algorithms for smooth and strongly convex problems. Our starting point is to develop a polynomial matrix inequality as a…
Reduced basis approximations of Optimal Control Problems (OCPs) governed by steady partial differential equations (PDEs) with random parametric inputs are analyzed and constructed. Such approximations are based on a Reduced Order Model,…
This paper presents an efficient algorithm for the least-squares problem using the point-to-plane cost, which aims to jointly optimize depth sensor poses and plane parameters for 3D reconstruction. We call this least-squares problem…
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…
This paper presents a methodology for solving a geometrically robust least squares problem, which arises in various applications where the model is subject to geometric constraints. The problem is formulated as a minimax optimization…
A large body of research has focused on theory and computation for variable selection techniques for high dimensional data. There has been substantially less work in the big tall data paradigm, where the number of variables may be large,…
Orthogonality constraints are ubiquitous in robust and probabilistic machine learning. Unfortunately, current optimizers are computationally expensive and do not scale to problems with hundreds or thousands of constraints. One notable…
Orthogonal Matching Pursuit (OMP) has been a powerful method in sparse signal recovery and approximation. However, OMP suffers computational issues when the signal has a large number of non-zeros. This paper advances OMP and its extension…
In robot localisation and mapping, outliers are unavoidable when loop-closure measurements are taken into account. A single false-positive loop-closure can have a very negative impact on SLAM problems causing an inferior trajectory to be…
We develop a constructive approach to estimating sparse, high-dimensional linear regression models. The approach is a computational algorithm motivated from the KKT conditions for the $\ell_0$-penalized least squares solutions. It generates…
We consider the minimization of composite objective functions composed of the expectation of quadratic functions and an arbitrary convex function. We study the stochastic dual averaging algorithm with a constant step-size, showing that it…
This paper studies adaptive first-order least-squares finite element methods for second-order elliptic partial differential equations in non-divergence form. Unlike the classical finite element method which uses weak formulations of PDEs…
Greedy algorithms for minimizing L0-norm of sparse decomposition have profound application impact on many signal processing problems. In the sparse coding setup, given the observations $\mathrm{y}$ and the redundant dictionary…
We consider the Orthogonal Least-Squares (OLS) algorithm for the recovery of a $m$-dimensional $k$-sparse signal from a low number of noisy linear measurements. The Exact Recovery Condition (ERC) in bounded noisy scenario is established for…
Here we propose an algorithm, named generalized orthogonal components regression (GOCRE), to explore the relationship between a categorical outcome and a set of massive variables. A set of orthogonal components are sequentially constructed…