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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 introduce a refinement-based Christoffel sampling (RCS) algorithm for least squares approximation in the span of a given, generally non-orthogonal set of functions $\Phi_n = \{\phi_1, \dots, \phi_n\}$. A standard sampling strategy for…
Neural implicit representation is a promising approach for reconstructing surfaces from point clouds. Existing methods combine various regularization terms, such as the Eikonal and Laplacian energy terms, to enforce the learned neural…
Local Polynomial Regression (LPR) and Moving Least Squares (MLS) are closely related nonparametric estimation methods, developed independently in statistics and approximation theory. While statistical LPR analysis focuses on overcoming…
For optimization problems with nonlinear constraints, linearly constrained Lagrangian (LCL) methods sequentially minimize a Lagrangian function subject to linearized constraints. These methods converge rapidly near a solution but may not be…
A least squares semi-supervised local clustering algorithm based on the idea of compressed sensing is proposed to extract clusters from a graph with known adjacency matrix. The algorithm is based on a two-stage approach similar to the one…
Modeling the relationship between vehicle speed and density on the road is a fundamental problem in traffic flow theory. Recent research found that using the least-squares (LS) method to calibrate single-regime speed-density models is…
Current point cloud processing algorithms do not have the capability to automatically extract semantic information from the observed scenes, except in very specialized cases. Furthermore, existing mesh analysis paradigms cannot be directly…
In recent work (Maierhofer & Huybrechs, 2022, Adv. Comput. Math.), the authors showed that least-squares oversampling can improve the convergence properties of collocation methods for boundary integral equations involving operators of…
3D Point clouds (PCs) are commonly used to represent 3D scenes. They can have millions of points, making subsequent downstream tasks such as compression and streaming computationally expensive. PC sampling (selecting a subset of points) can…
A new Levenberg--Marquardt (LM) method for solving nonlinear least squares problems with convex constraints is described. Various versions of the LM method have been proposed, their main differences being in the choice of a damping…
The Constraint-satisfaction problem (CSP) is fundamental in mathematics, physics, and theoretical computer science. Continuous local search (CLS) solvers, as recent advancements, can achieve highly competitive results on certain classes of…
We propose a novel stochastic gradient descent method for solving linear least squares problems with partially observed data. Our method uses submatrices indexed by a randomly selected pair of row and column index sets to update the iterate…
Generalized few-shot 3D point cloud segmentation (GFS-PCS) adapts models to new classes with few support samples while retaining base class segmentation. Existing GFS-PCS methods enhance prototypes via interacting with support or query…
To reduce cost in storing, processing and visualizing a large-scale point cloud, we consider a randomized resampling strategy to select a representative subset of points while preserving application-dependent features. The proposed strategy…
Projected least squares (PLS) is an intuitive and numerically cheap technique for quantum state tomography. The method first computes the least-squares estimator (or a linear inversion estimator) and then projects the initial estimate onto…
We propose a novel point-based representation, Gaussian surfels, to combine the advantages of the flexible optimization procedure in 3D Gaussian points and the surface alignment property of surfels. This is achieved by directly setting the…
The least squares method provides the best-fit curve by minimizing the total squares error. In this work, we provide the modified least squares method based on the fractional orthogonal polynomials that belong to the space $M_{n}^{\lambda}…
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required…
Methods based on partial least squares (PLS) regression, which has recently gained much attention in the analysis of high-dimensional genomic datasets, have been developed since the early 2000s for performing variable selection. Most of…