Related papers: An Improved Frequent Directions Algorithm for Low-…

Stochastic coordinate descent algorithms are efficient methods in which each iterate is obtained by fixing most coordinates at their values from the current iteration, and approximately minimizing the objective with respect to the remaining…

In this paper, we provide a novel algorithm for solving planning and learning problems of Markov decision processes. The proposed algorithm follows a policy iteration-type update by using a rank-one approximation of the transition…

Recently, the regularized functional matching pursuit (RFMP) was introduced as a greedy algorithm for linear ill-posed inverse problems. This algorithm incorporates the Tikhonov-Phillips regularization which implies the necessity of a…

The rational Krylov subspace method (RKSM) and the low-rank alternating directions implicit (LR-ADI) iteration are established numerical tools for computing low-rank solution factors of large-scale Lyapunov equations. In order to generate…

This paper studies a finite-horizon Markov decision problem with information-theoretic constraints, where the goal is to minimize directed information from the controlled source process to the control process, subject to stage-wise cost…

We focus on robust and efficient iterative solvers for the pressure Poisson equation in incompressible Navier-Stokes problems. Preconditioned Krylov subspace methods are popular for these problems, with BiCGStab and GMRES(m) most frequently…

We introduce an algorithm for estimating the trace of a matrix function $f(\mathbf{A})$ using implicit products with a symmetric matrix $\mathbf{A}$. Existing methods for implicit trace estimation of a matrix function tend to treat…

In classical frameworks as the Euclidean space, positive definite kernels as well as their analytic properties are explicitly available and can be incorporated directly in kernel-based learning algorithms. This is different if the…

Iterative phase retrieval algorithms typically employ projections onto constraint subspaces to recover the unknown phases in the Fourier transform of an image, or, in the case of x-ray crystallography, the electron density of a molecule.…

This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as…

Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…

This paper presents a novel frequency-domain approach for path following problem, specifically designed to handle paths described by discrete data. The proposed algorithm utilizes the fast Fourier Transform (FFT) to process the discrete…

We propose a new \textit{randomized Bregman (block) coordinate descent} (RBCD) method for minimizing a composite problem, where the objective function could be either convex or nonconvex, and the smooth part are freed from the global…

We present randomized algorithms based on block Krylov space method for estimating the trace and log-determinant of Hermitian positive semi-definite matrices. Using the properties of Chebyshev polynomial and Gaussian random matrix, we…

We present a new Krylov subspace recycling method for solving a linear system of equations, or a sequence of slowly changing linear systems. Our approach is to reduce the computational overhead of recycling techniques while still benefiting…

Very deep convolutional neural networks offer excellent recognition results, yet their computational expense limits their impact for many real-world applications. We introduce BlockDrop, an approach that learns to dynamically choose which…

While the superior performance of second-order optimization methods such as Newton's method is well known, they are hardly used in practice for deep learning because neither assembling the Hessian matrix nor calculating its inverse is…

Standard numerical algorithms like the fast multipole method or $\mathcal{H}$-matrix schemes rely on low-rank approximations of the underlying kernel function. For high-frequency problems, the ranks grow rapidly as the mesh is refined, and…

Regularized Markov Decision Processes serve as models of sequential decision making under uncertainty wherein the decision maker has limited information processing capacity and/or aversion to model ambiguity. With functional approximation,…

Layer factorization has emerged as a widely used technique for training memory-efficient neural networks. However, layer factorization methods face several challenges, particularly a lack of robustness during the training process. To…