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Extremum seeking (ES) optimization approach has been very popular due to its non-model based analysis and implementation. This approach has been mostly used with gradient based search algorithms. Since least squares (LS) algorithms are…
Least squares approximation is a technique to find an approximate solution to a system of linear equations that has no exact solution. In a typical setting, one lets $n$ be the number of constraints and $d$ be the number of variables, with…
In this paper, we present a low-latency odometry system designed for spinning lidars. Many existing lidar odometry methods wait for an entire sweep from the lidar before processing the data. This introduces a large delay between the first…
This paper is concerned with the design and analysis of least squares solvers for ill-posed PDEs that are conditionally stable. The norms and the regularization term used in the least squares functional are determined by the ingredients of…
In this paper the efficiency of multilevel sparse tensor approximation methods for high-dimensional affine parametric diffusion equations is investigated. Methodologically, the recently presented Sparse Alternating Least Squares (SALS)…
In this paper, we consider a least-squares (LS)-based distributed algorithm build on a sensor network to estimate an unknown parameter vector of a dynamical system, where each sensor in the network has partial information only but is…
The evolution of images with physics-based dynamics is often spatially localized and nonlinear. A switching linear dynamic system (SLDS) is a natural model under which to pose such problems when the system's evolution randomly switches over…
We develop a Recursive $\mathcal{L}_1$-Regularized Least Squares (SPARLS) algorithm for the estimation of a sparse tap-weight vector in the adaptive filtering setting. The SPARLS algorithm exploits noisy observations of the tap-weight…
Object detection has achieved a huge breakthrough with deep neural networks and massive annotated data. However, current detection methods cannot be directly transferred to the scenario where the annotated data is scarce due to the severe…
Invariant linearization criteria of square systems of second-order quadratically semi-linear ordinary differential equations (ODEs) that can be represented as geodesic equations are extended to square systems of ODEs cubically nonlinear in…
Model reduction simplifies complex dynamical systems while preserving essential properties. This paper revisits a recently proposed system-theoretic framework for least squares moment matching. It interprets least squares model reduction in…
This paper studies the weak convergence order of the stochastic theta method for stochastic differential equations (SDEs) driven by time-changed L\'{e}vy noise under global Lipschitz and linear growth conditions. In contrast to classical…
Least-mean squares (LMS) solvers such as Linear / Ridge / Lasso-Regression, SVD and Elastic-Net not only solve fundamental machine learning problems, but are also the building blocks in a variety of other methods, such as decision trees and…
In this paper, we study the problem of finding the least square solutions of over-determined linear algebraic equations over networks in a distributed manner. Each node has access to one of the linear equations and holds a dynamic state. We…
The recent development of more sophisticated spectroscopic methods allows acqui- sition of high dimensional datasets from which valuable information may be extracted using multivariate statistical analyses, such as dimensionality reduction…
An Orthogonal Least Squares (OLS) based feature selection method is proposed for both binomial and multinomial classification. The novel Squared Orthogonal Correlation Coefficient (SOCC) is defined based on Error Reduction Ratio (ERR) in…
We present a novel iterative algorithm for approximating the linear least squares solution with low complexity. After a motivation of the algorithm we discuss the algorithm's properties including its complexity, and we present theoretical…
This work focuses on dimension-reduction techniques for modelling conditional extreme values. Specifically, we investigate the idea that extreme values of a response variable can be explained by nonlinear functions derived from linear…
In regression analysis for deriving scaling laws that occur in various scientific disciplines, usually standard regression methods have been applied, of which ordinary least squares (OLS) is the most popular. In many situations, the…
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…