Related papers: A Very Fast Algorithm for Matrix Factorization

Factorization-based gradient descent is a scalable and efficient algorithm for solving low-rank matrix completion. Recent progress in structured non-convex optimization has offered global convergence guarantees for gradient descent under…

We give a number of explicit matrix-algorithms for analysis/synthesis in multi-phase filtering; i.e., the operation on discrete-time signals which allow a separation into frequency-band components, one for each of the ranges of bands, say…

Matrix factorization is one of the best approaches for collaborative filtering, because of its high accuracy in presenting users and items latent factors. The main disadvantages of matrix factorization are its complexity, and being very…

We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural…

High performance computing (HPC) facilities consist of a large number of interconnected computing units (or nodes) that execute highly complex scientific simulations to support scientific research. Monitoring such facilities, in real-time,…

We present a fast direct algorithm for computing symmetric factorizations, i.e. $A = WW^T$, of symmetric positive-definite hierarchical matrices with weak-admissibility conditions. The computational cost for the symmetric factorization…

While deep learning excels in natural image and language processing, its application to high-dimensional data faces computational challenges due to the dimensionality curse. Current large-scale data tools focus on business-oriented…

Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal…

In high-dimensional classification problems, a commonly used approach is to first project the high-dimensional features into a lower dimensional space, and base the classification on the resulting lower dimensional projections. In this…

In this paper, we introduce innovative approaches for accelerating the Jacobi method for matrix diagonalization, specifically through the formulation of large matrix diagonalization as a Semi-Markov Decision Process and small matrix…

For high dimensional data, some of the standard statistical techniques do not work well. So modification or further development of statistical methods are necessary. In this paper, we explore these modifications. We start with the important…

Working with exhaustive search on large dataset is infeasible for several reasons. Recently, developed techniques that made pattern set mining feasible by a general solver with long execution time that supports heuristic search and are…

Nonnegative matrix factorization (NMF) has an established reputation as a useful data analysis technique in numerous applications. However, its usage in practical situations is undergoing challenges in recent years. The fundamental factor…

For most problems in science and engineering we can obtain data sets that describe the observed system from various perspectives and record the behavior of its individual components. Heterogeneous data sets can be collectively mined by data…

Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the…

Predicting unobserved entries of a partially observed matrix has found wide applicability in several areas, such as recommender systems, computational biology, and computer vision. Many scalable methods with rigorous theoretical guarantees…

Recent work in machine learning community proposed multiple methods for performing lossy compression (quantization) of large matrices. This quantization is important for accelerating matrix multiplication (main component of large language…

Modern decision-making scenarios often involve data that is both high-dimensional and rich in higher-order contextual information, where existing bandits algorithms fail to generate effective policies. In response, we propose in this paper…

As datasets grow it becomes infeasible to process them completely with a desired model. For giant datasets, we frame the order in which computation is performed as a decision problem. The order is designed so that partial computations are…

We present a fast randomized algorithm that computes a low rank LU decomposition. Our algorithm uses random projections type techniques to efficiently compute a low rank approximation of large matrices. The randomized LU algorithm can be…