Related papers: Fast Approximation of Rotations and Hessians matri…
This work presents a novel matrix-based method for constructing an approximation Hessian using only function evaluations. The method requires less computational power than interpolation-based methods and is easy to implement in matrix-based…
The aim of this work is to develop a fast algorithm for approximating the matrix function $f(A)$ of a square matrix $A$ that is symmetric and has hierarchically semiseparable (HSS) structure. Appearing in a wide variety of applications,…
As we all known, the nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used in image processing, text compressing and signal processing etc. In this paper, an algorithm for nonnegative matrix…
Hessian operators arising in inverse problems governed by partial differential equations (PDEs) play a critical role in delivering efficient, dimension-independent convergence for both Newton solution of deterministic inverse problems, as…
We introduce a novel method to compute a rank $m$ approximation of the inverse of the Hessian matrix in the distributed regime. By leveraging the differences in gradients and parameters of multiple Workers, we are able to efficiently…
We analyze effective approximation of unitary matrices. In our formulation, a unitary matrix is represented as a product of rotations in two-dimensional subspaces, so-called Givens rotations. Instead of the quadratic dimension dependence…
A common problem in cosmology is to integrate the product of two or more spherical Bessel functions (sBFs) with different configuration-space arguments against the power spectrum or its square, weighted by powers of wavenumber. Naively…
Product quantization (PQ) coupled with a space rotation, is widely used in modern approximate nearest neighbor (ANN) search systems to significantly compress the disk storage for embeddings and speed up the inner product computation.…
Update formulas for the Hessian approximations in quasi-Newton methods such as BFGS can be derived as analytical solutions to certain nearest-matrix problems. In this article, we propose a similar idea for deriving new limited memory…
We study the problem of approximating orthogonal matrices so that their application is numerically fast and yet accurate. We find an approximation by solving an optimization problem over a set of structured matrices, that we call extended…
Generalized matrix approximation plays a fundamental role in many machine learning problems, such as CUR decomposition, kernel approximation, and matrix low rank approximation. Especially with today's applications involved in larger and…
A new fast algebraic method for obtaining an $\mathcal{H}^2$-approximation of a matrix from its entries is presented. The main idea behind the method is based on the nested representation and the maximum-volume principle to select…
Recent Newton-type federated learning algorithms have demonstrated linear convergence with respect to the communication rounds. However, communicating Hessian matrices is often unfeasible due to their quadratic communication complexity. In…
This work introduces the nested-set Hessian approximation, a second-order approximation method that can be used in any derivative-free optimization routine that requires such information. It is built on the foundation of the generalized…
Hough transform is a popular low-level computer vision algorithm. Its computationally effective modification, Fast Hough transform (FHT), makes use of special subsets of image matrix to approximate geometric lines on it. Because of their…
The Hessian matrix has a number of important applications in a variety of different fields, such as optimzation, image processing and statistics. In this paper we focus on the practical aspects of efficiently computing Hessian matrices in…
We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
In recent years, various subspace algorithms have been developed to handle large-scale optimization problems. Although existing subspace Newton methods require fewer iterations to converge in practice, the matrix operations and full…
Estimates of the approximate factor model are increasingly used in empirical work. Their theoretical properties, studied some twenty years ago, also laid the ground work for analysis on large dimensional panel data models with cross-section…