Related papers: Randomized Numerical Linear Algebra : A Perspectiv…
The Kaczmarz algorithm is an iterative technique designed to solve consistent linear systems of equations. It falls within the category of row-action methods, focusing on handling one equation per iteration. This characteristic makes it…
The linearized-Laplace approximation (LLA) has been shown to be effective and efficient in constructing Bayesian neural networks. It is theoretically compelling since it can be seen as a Gaussian process posterior with the mean function…
ALAMO is a computational methodology for leaning algebraic functions from data. Given a data set, the approach begins by building a low-complexity, linear model composed of explicit non-linear transformations of the independent variables.…
Symmetric Nonnegative Matrix Factorization (SymNMF) is a technique in data analysis and machine learning that approximates a symmetric matrix with a product of a nonnegative, low-rank matrix and its transpose. To design faster and more…
Deep neural networks (DNNs) often produce overconfident out-of-distribution predictions, motivating Bayesian uncertainty quantification. The Linearized Laplace Approximation (LLA) achieves this by linearizing the DNN and applying Laplace…
We introduce randomized algorithms to Clifford's Geometric Algebra, generalizing randomized linear algebra to hypercomplex vector spaces. This novel approach has many implications in machine learning, including training neural networks to…
The network Lasso (nLasso) has been proposed recently as an efficient learning algorithm for massive networked data sets (big data over networks). It extends the well-known least absolute shrinkage and selection operator (Lasso) from…
A methodology for using random sketching in the context of model order reduction for high-dimensional parameter-dependent systems of equations was introduced in [Balabanov and Nouy 2019, Part I]. Following this framework, we here construct…
Temporal Graph Learning (TGL) has become a prevalent technique across diverse real-world applications, especially in domains where data can be represented as a graph and evolves over time. Although TGL has recently seen notable progress in…
Providing machine learning (ML) over relational data is a mainstream requirement for data analytics systems. While almost all the ML tools require the input data to be presented as a single table, many datasets are multi-table, which forces…
Graph machine learning has been extensively studied in both academic and industry. However, as the literature on graph learning booms with a vast number of emerging methods and techniques, it becomes increasingly difficult to manually…
We consider learning problems over training sets in which both, the number of training examples and the dimension of the feature vectors, are large. To solve these problems we propose the random parallel stochastic algorithm (RAPSA). We…
We propose $\nabla$-RANSAC, a generalized differentiable RANSAC that allows learning the entire randomized robust estimation pipeline. The proposed approach enables the use of relaxation techniques for estimating the gradients in the…
In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we…
Randomized algorithms in numerical linear algebra have proven to be effective in ameliorating issues of scalability when working with large matrices, efficiently producing accurate low-rank approximations. A key remaining challenge,…
We present RandomizedCCA, a randomized algorithm for computing canonical analysis, suitable for large datasets stored either out of core or on a distributed file system. Accurate results can be obtained in as few as two data passes, which…
This paper presents the benefits of using randomized neural networks instead of standard basis functions or deep neural networks to approximate the solutions of optimal stopping problems. The key idea is to use neural networks, where the…
We develop a new efficient sequential approximate leverage score algorithm, SALSA, using methods from randomized numerical linear algebra (RandNLA) for large matrices. We demonstrate that, with high probability, the accuracy of SALSA's…
Neural algorithmic reasoning (NAR) is a growing field that aims to embed algorithmic logic into neural networks by imitating classical algorithms. In this extended abstract, we detail our attempt to build a neural algorithmic reasoner that…
Randomization is a powerful tool that endows algorithms with remarkable properties. For instance, randomized algorithms excel in adversarial settings, often surpassing the worst-case performance of deterministic algorithms with large…