Related papers: Least Squares Auto-Tuning
Variational Physics-Informed Neural Networks often suffer from poor convergence when using stochastic gradient-descent-based optimizers. By introducing a Least Squares solver for the weights of the last layer of the neural network, we…
Statistical inverse learning aims at recovering an unknown function $f$ from randomly scattered and possibly noisy point evaluations of another function $g$, connected to $f$ via an ill-posed mathematical model. In this paper we blend…
The L-curve method is a well-known heuristic method for choosing the regularization parameter for ill-posed problems by selecting it according to the maximal curvature of the L-curve. In this article, we propose a simplified version that…
Least absolute shrinkage and selection operator (Lasso), a popular method for high-dimensional regression, is now used widely for estimating high-dimensional time series models such as the vector autoregression (VAR). Selecting its tuning…
In navigation activities, kinematic parameters of a mobile vehicle play a significant role. Odometry is most commonly used for dead reckoning. However, the unrestricted accumulation of errors is a disadvantage using this method. As a…
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…
A two-step method for solving planar Laplace problems via rational approximation is introduced. First complex rational approximations to the boundary data are determined by AAA approximation, either globally or locally near each corner or…
Stochastic approximation techniques play an important role in solving many problems encountered in machine learning or adaptive signal processing. In these contexts, the statistics of the data are often unknown a priori or their direct…
We introduce an algorithm for the least squares solution of a rectangular linear system $Ax=b$, in which $A$ may be arbitrarily ill-conditioned. We assume that a complementary matrix $Z$ is known such that $A - AZ^*A$ is numerically low…
The optimization problem that arises out of the least median of squared residuals method in linear regression is analyzed. To simplify the analysis, the problem is replaced by an equivalent one of minimizing the median of absolute…
We consider adaptive system identification problems with convex constraints and propose a family of regularized Least-Mean-Square (LMS) algorithms. We show that with a properly selected regularization parameter the regularized LMS provably…
Bayesian Optimization is the state of the art technique for the optimization of black boxes, i.e., functions where we do not have access to their analytical expression nor its gradients, they are expensive to evaluate and its evaluation is…
In order to function reliably, synthetic molecular circuits require mechanisms that allow them to adapt to environmental disturbances. Least mean squares (LMS) schemes, such as commonly encountered in signal processing and control, provide…
We conduct a study and comparison of superiorization and optimization approaches for the reconstruction problem of superiorized/regularized least-squares solutions of underdetermined linear equations with nonnegativity variable bounds.…
In modern data analysis, random sampling is an efficient and widely-used strategy to overcome the computational difficulties brought by large sample size. In previous studies, researchers conducted random sampling which is according to the…
The goal in the min-\# curve simplification problem is to reduce the number of the vertices of a polygonal curve without changing its shape significantly. We study curve-restricted min-\# simplification of polygonal curves, in which the…
The bottom-left algorithm is a simple heuristic for the Strip Packing Problem. It places the rectangles in the given order at the lowest free position in the strip, using the left most position in case of ties. Despite its simplicity, the…
Functional partial least squares (FPLS) is commonly used for fitting scalar-on-function regression models. For the sake of accuracy, FPLS demands that each realization of the functional predictor is recorded as densely as possible over the…
We describe stochastic Newton and stochastic quasi-Newton approaches to efficiently solve large linear least-squares problems where the very large data sets present a significant computational burden (e.g., the size may exceed computer…
Rough set is one of the important methods for rule acquisition and attribute reduction. The current goal of rough set attribute reduction focuses more on minimizing the number of reduced attributes, but ignores the spatial similarity…