Related papers: nlstac: Non-Gradient Separable Nonlinear Least Squ…
In this paper, we introduce a new stochastic approximation (SA) type algorithm, namely the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming (SP) problems.…
We propose novel optimal and parameter-free algorithms for computing an approximate solution with small (projected) gradient norm. Specifically, for computing an approximate solution such that the norm of its (projected) gradient does not…
Least squares is by far the simplest and most commonly applied computational method in many fields. In almost all applications, the least squares objective is rarely the true objective. We account for this discrepancy by parametrizing the…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
Radial Basis Function Networks (RBFNs) are used primarily to solve curve-fitting problems and for non-linear system modeling. Several algorithms are known for the approximation of a non-linear curve from a sparse data set by means of RBFNs.…
In this work, a new class of stochastic gradient algorithm is developed based on $q$-calculus. Unlike the existing $q$-LMS algorithm, the proposed approach fully utilizes the concept of $q$-calculus by incorporating time-varying $q$…
We propose a differentiable nonlinear least squares framework to account for uncertainty in relative pose estimation from feature correspondences. Specifically, we introduce a symmetric version of the probabilistic normal epipolar…
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…
A sequential quadratic optimization algorithm for minimizing an objective function defined by an expectation subject to nonlinear inequality and equality constraints is proposed, analyzed, and tested. The context of interest is when it is…
In nonsmooth optimization, a negative subgradient is not necessarily a descent direction, making the design of convergent descent methods based on zeroth-order and first-order information a challenging task. The well-studied bundle methods…
We present a new particle filtering algorithm for nonlinear systems in the discrete-time setting. Our algorithm is based on the Stein variational gradient descent (SVGD) framework, which is a general approach to sample from a target…
Fast Field-Cycling Nuclear Magnetic Resonance relaxometry is a non-destructive technique to investigate molecular dynamics and structure of systems having a wide range of applications such as environment, biology, and food. Besides a…
We consider the problem of ranking $N$ objects starting from a set of noisy pairwise comparisons provided by a crowd of equal workers. We assume that objects are endowed with intrinsic qualities and that the probability with which an object…
Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…
Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required.…
Lane detection is typically tackled with a two-step pipeline in which a segmentation mask of the lane markings is predicted first, and a lane line model (like a parabola or spline) is fitted to the post-processed mask next. The problem with…
Selecting an effective step-size is a fundamental challenge in first-order optimization, especially for problems with non-Euclidean geometries. This paper presents a novel adaptive step-size strategy for optimization algorithms that rely on…
This work provides simple algorithms for multi-class (and multi-label) prediction in settings where both the number of examples n and the data dimension d are relatively large. These robust and parameter free algorithms are essentially…
It is well known that there have been many numerical algorithms for solving nonsmooth minimax problems, numerical algorithms for nonsmooth minimax problems with joint linear constraints are very rare. This paper aims to discuss optimality…
The a posteriori error estimator using the least-squares functional can be used for adaptive mesh refinement and error control even if the numerical approximations are not obtained from the corresponding least-squares method. This suggests…