Related papers: Neural incomplete factorization: learning precondi…
Square matrices appear in many machine learning problems and models. Optimization over a large square matrix is expensive in memory and in time. Therefore an economic approximation is needed. Conventional approximation approaches factorize…
We propose $\textsf{ScaledGD($\lambda$)}$, a preconditioned gradient descent method to tackle the low-rank matrix sensing problem when the true rank is unknown, and when the matrix is possibly ill-conditioned. Using overparametrized factor…
Preconditioning is a technique from numerical linear algebra that can accelerate algorithms to solve systems of equations. In this paper, we demonstrate how preconditioning can circumvent a stringent assumption for sign consistency in…
A nonnegative matrix factorization (NMF) can be computed efficiently under the separability assumption, which asserts that all the columns of the given input data matrix belong to the cone generated by a (small) subset of them. The provably…
Matrix factorization techniques have been widely used as a method for collaborative filtering for recommender systems. In recent times, different variants of deep learning algorithms have been explored in this setting to improve the task of…
Large sparse symmetric linear systems appear in several branches of science and engineering thanks to the widespread use of the finite element method (FEM). The fastest sparse linear solvers available implement hybrid iterative methods.…
We propose a penalized likelihood framework for estimating multiple precision matrices from different classes. Most existing methods either incorporate no information on relationships between the precision matrices, or require this…
We propose a generative model for robust tensor factorization in the presence of both missing data and outliers. The objective is to explicitly infer the underlying low-CP-rank tensor capturing the global information and a sparse tensor…
Many problems encountered in science and engineering can be formulated as estimating a low-rank object (e.g., matrices and tensors) from incomplete, and possibly corrupted, linear measurements. Through the lens of matrix and tensor…
A linearly implicit conservative difference scheme is applied to discretize the attractive coupled nonlinear Schr\"odinger equations with fractional Laplacian. Complex symmetric linear systems can be obtained, and the system matrices are…
The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…
Multiresolution Matrix Factorization (MMF) is unusual amongst fast matrix factorization algorithms in that it does not make a low rank assumption. This makes MMF especially well suited to modeling certain types of graphs with complex…
Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing applications, including phase retrieval, blind deconvolution,…
Adaptive regularization methods pre-multiply a descent direction by a preconditioning matrix. Due to the large number of parameters of machine learning problems, full-matrix preconditioning methods are prohibitively expensive. We show how…
Multiresolution Matrix Factorization (MMF) is unusual amongst fast matrix factorization algorithms in that it does not make a low rank assumption. This makes MMF especially well suited to modeling certain types of graphs with complex…
We derive analytical expression of matrix factorization/completion solution by variational Bayes method, under the assumption that observed matrix is originally the product of low-rank dense and sparse matrices with additive noise. We…
Matrix factorization methods are important tools in data mining and analysis. They can be used for many tasks, ranging from dimensionality reduction to visualization. In this paper we concentrate on the use of matrix factorizations for…
We study the solution of large symmetric positive-definite linear systems in a matrix-free setting with a limited iteration budget. We focus on the preconditioned conjugate gradient (PCG) method with spectral preconditioning. Spectral…
The hierarchical interpolative factorization for elliptic partial differential equations is a fast algorithm for approximate sparse matrix inversion in linear or quasilinear time. Its accuracy can degrade, however, when applied to strongly…
Efforts to understand the generalization mystery in deep learning have led to the belief that gradient-based optimization induces a form of implicit regularization, a bias towards models of low "complexity." We study the implicit…