Related papers: Accelerated and Improved Stabilization for High Or…
Discrete Hahn polynomials (DHPs) and their moments are considered to be one of the efficient orthogonal moments and they are applied in various scientific areas such as image processing and feature extraction. Commonly, DHPs are used as…
In this work (Part I), we study three time-discretization procedures of the Dynamical Low-Rank Approximation (DLRA) of high-dimensional stochastic differential equations (SDEs). Specifically, we consider the Dynamically Orthogonal (DO)…
We proposed a novel dense line spectrum super-resolution algorithm, the DMRA, that leverages dynamical multi-resolution of atoms technique to address the limitation of traditional compressed sensing methods when handling dense point-source…
We present a novel static analysis technique to derive higher moments for program variables for a large class of probabilistic loops with potentially uncountable state spaces. Our approach is fully automatic, meaning it does not rely on…
Geometric moments and moment invariants of image artifacts have many uses in computer vision applications, e.g. shape classification or object position and orientation. Higher order moments are of interest to provide additional feature…
In this work we study the stability regions of linear multistep or multiderivative multistep methods for initial-value problems by using techniques that are straightforward to implement in modern computer algebra systems. In many…
This paper develops a robust angles-only IROD method based on polynomial optimization for arbitrary nonlinear dynamics. First, the relative motion is approximated by high-order Taylor polynomials within the differential algebra framework,…
The dynamical low-rank approximation (DLRA) is used to treat high-dimensional problems that arise in such diverse fields as kinetic transport and uncertainty quantification. Even though it is well known that certain spatial and temporal…
Moment-based distributionally robust optimization (DRO) provides an optimization framework to integrate statistical information with traditional optimization approaches. Under this framework, one assumes that the underlying joint…
We give the first polynomial time and sample $(\epsilon, \delta)$-differentially private (DP) algorithm to estimate the mean, covariance and higher moments in the presence of a constant fraction of adversarial outliers. Our algorithm…
Dose calculations in proton therapy require the fast and accurate solution of a high-dimensional transport equation for a large number of (pencil) beams with different energies and directions. Deterministically solving this transport…
Explicit stabilized methods are highly efficient time integrators for large and stiff systems of ordinary differential equations especially when applied to semi-discrete parabolic problems. However, when local spatial mesh refinement is…
This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…
Randomized methods such as PRM and RRT are widely used in motion planning. However, in some cases, their running-time suffers from inherent instability, leading to ``catastrophic'' performance even for relatively simple instances. We apply…
In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a…
Stochastic gradient descent with momentum (SGDM) is the dominant algorithm in many optimization scenarios, including convex optimization instances and non-convex neural network training. Yet, in the stochastic setting, momentum interferes…
We introduce deterministic perturbation schemes for the recently proposed random directions stochastic approximation (RDSA) [17], and propose new first-order and second-order algorithms. In the latter case, these are the first second-order…
Random projection algorithm is an iterative gradient method with random projections. Such an algorithm is of interest for constrained optimization when the constraint set is not known in advance or the projection operation on the whole…
In this paper, we consider a class of continuous-time, continuous-space stochastic optimal control problems. Building upon recent advances in Markov chain approximation methods and sampling-based algorithms for deterministic path planning,…
In this work, in the context of Linear and Quadratic Programming, we interpret Primal Dual Regularized Interior Point Methods (PDR-IPMs) in the framework of the Proximal Point Method. The resulting Proximal Stabilized IPM (PS-IPM) is…