Related papers: Fast Multipole Method as a Matrix-Free Hierarchica…

Low-rank metric learning aims to learn better discrimination of data subject to low-rank constraints. It keeps the intrinsic low-rank structure of datasets and reduces the time cost and memory usage in metric learning. However, it is still…

Constrained low-rank matrix approximations have been known for decades as powerful linear dimensionality reduction techniques to be able to extract the information contained in large data sets in a relevant way. However, such low-rank…

Rank deficient Hankel matrices are at the core of several applications. However, in practice, the coefficients of these matrices are noisy due to e.g. measurements errors and computational errors, so generically the involved matrices are…

Low-rank approximation techniques have become the de facto standard for fine-tuning Large Language Models (LLMs) due to their reduced computational and memory requirements. This paper investigates the effectiveness of these methods in…

The notion of well-separated sets is crucial in fast multipole methods as the main idea is to approximate the interaction between such sets via cluster expansions. We revisit the one-parameter multipole acceptance criterion in a general…

Even in times of deep learning, low-rank approximations by factorizing a matrix into user and item latent factors continue to be a method of choice for collaborative filtering tasks due to their great performance. While deep learning based…

Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, medical imaging, to dimensionality reduction and adaptive filtering. Many modern…

Low-rank approximation and column subset selection are two fundamental and related problems that are applied across a wealth of machine learning applications. In this paper, we study the question of socially fair low-rank approximation and…

Many algorithms in scientific computing and data science take advantage of low-rank approximation of matrices and kernels, and understanding why nearly-low-rank structure occurs is essential for their analysis and further development. This…

Bipartite ranking, which aims to learn a scoring function that ranks positive individuals higher than negative ones from labeled data, is widely adopted in various applications where sample prioritization is needed. Recently, there have…

Low-rank matrices play a fundamental role in modeling and computational methods for signal processing and machine learning. In many applications where low-rank matrices arise, these matrices cannot be fully sampled or directly observed, and…

Neural networks have achieved tremendous success in a large variety of applications. However, their memory footprint and computational demand can render them impractical in application settings with limited hardware or energy resources. In…

Nowadays, low-rank approximations of matrices are an important component of many methods in science and engineering. Traditionally, low-rank approximations are considered in unitary invariant norms, however, recently element-wise…

The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices. These new algorithms attain high practical speed by reducing the dimensionality of intermediate…

In recent years, large language models (LLMs) have achieved strong performance on benchmark tasks, especially in zero or few-shot settings. However, these benchmarks often do not adequately address the challenges posed in the real-world,…

This paper is concerned with the low-rank approximation for large-scale nonsymmetric matrices. Inspired by the classical Nystrom method, which is a popular method to find the low-rank approximation for symmetric positive semidefinite…

Datasets in the fields of climate and environment are often very large and irregularly spaced. To model such datasets, the widely used Gaussian process models in spatial statis- tics face tremendous challenges due to the prohibitive…

In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our…

This article introduces a new fast direct solver for linear systems arising out of wide range of applications, integral equations, multivariate statistics, radial basis interpolation, etc., to name a few. \emph{The highlight of this new…

In many autonomous mapping tasks, the maps cannot be accurately constructed due to various reasons such as sparse, noisy, and partial sensor measurements. We propose a novel map prediction method built upon the recent success of Low-Rank…