Related papers: An $N \log N$ Parallel Fast Direct Solver for Kern…

Efficient and accurate low-rank approximations of multiple data sources are essential in the era of big data. The scaling of kernel-based learning algorithms to large datasets is limited by the O(n^2) computation and storage complexity of…

Despite the outstanding performance of deep neural networks in different applications, they are still computationally extensive and require a great number of memories. This motivates more research on reducing the resources required for…

Given the success of deep learning in classical machine learning, quantum algorithms for traditional neural network architectures may provide one of the most promising settings for quantum machine learning. Considering a fully-connected…

In the iterative solution of dense linear systems from boundary integral equations or systems involving kernel matrices, the main challenges are the expensive matrix-vector multiplication and the storage cost which are usually tackled by…

Computing low-rank approximations of kernel matrices is an important problem with many applications in scientific computing and data science. We propose methods to efficiently approximate and store low-rank approximations to kernel matrices…

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…

In this paper we address the rotation synchronization problem, where the objective is to recover absolute rotations starting from pairwise ones, where the unknowns and the measures are represented as nodes and edges of a graph,…

Quasi-2D Coulomb systems are of fundamental importance and have attracted much attention in many areas nowadays. Their reduced symmetry gives rise to interesting collective behaviors, but also brings great challenges for particle-based…

Non-negative Matrix Factorization(NMF) algorithm can only be used to find low rank approximation of original non-negative data while Concept Factorization(CF) algorithm extends matrix factorization to single non-linear kernel space,…

Recently, convex formulations of low-rank matrix factorization problems have received considerable attention in machine learning. However, such formulations often require solving for a matrix of the size of the data matrix, making it…

Computing $k$-Nearest Neighbors (KNN) is one of the core kernels used in many machine learning, data mining and scientific computing applications. Although kd-tree based $O(\log n)$ algorithms have been proposed for computing KNN, due to…

d-Hitting Set is the NP-hard problem of selecting at most k vertices of a hypergraph so that each hyperedge, all of which have cardinality at most d, contains at least one selected vertex. The applications of d-Hitting Set are, for example,…

We present new algorithms to detect and correct errors in the lower-upper factorization of a matrix, or the triangular linear system solution, over an arbitrary field. Our main algorithms do not require any additional information or…

The low-rank matrix factorization as a L1 norm minimization problem has recently attracted much attention due to its intrinsic robustness to the presence of outliers and missing data. In this paper, we propose a new method, called the…

Given a square, nonsingular matrix of univariate polynomials $\mathbf{F} \in \mathbb{K}[x]^{n \times n}$ over a field $\mathbb{K}$, we give a fast, deterministic algorithm for finding the Hermite normal form of $\mathbf{F}$ with complexity…

In this paper we consider several related online computation problems. First, we study answering sequences of statistical queries arriving online, and being answered immediately when they arrive with differential privacy. Known matrix…

In this paper, we derive a family of fast and stable algorithms for multiplying and inverting $n \times n$ Pascal matrices that run in $O(n log^2 n)$ time and are closely related to De Casteljau's algorithm for B\'ezier curve evaluation.…

If learning methods are to scale to the massive sizes of modern datasets, it is essential for the field of machine learning to embrace parallel and distributed computing. Inspired by the recent development of matrix factorization methods…

We demonstrate that a modification of the classical index calculus algorithm can be used to factor integers. More generally, we reduce the factoring problem to finding an overdetermined system of multiplicative relations in any factor base…

The wide applicability of kernels makes the problem of max-kernel search ubiquitous and more general than the usual similarity search in metric spaces. We focus on solving this problem efficiently. We begin by characterizing the inherent…