Related papers: New Results on Scrambling Using the Mesh Array

This article presents new properties of the mesh array for matrix multiplication. In contrast to the standard array that requires 3n-2 steps to complete its computation, the mesh array requires only 2n-1 steps. Symmetries of the mesh array…

This note looks at the efficiency of the cross-wired mesh array in the context of matrix multiplication. It is shown that in case of repeated operations, the average number of steps to multiply sets of nxn matrices on a 2D cross-wired mesh…

We propose a new ensemble framework for supervised learning, called machine collaboration (MaC), using a collection of base machines for prediction tasks. Unlike bagging/stacking (a parallel & independent framework) and boosting (a…

The number of ``carries'' when $n$ random integers are added forms a Markov chain [23]. We show that this Markov chain has the same transition matrix as the descent process when a deck of $n$ cards is repeatedly riffle shuffled. This gives…

Matrix multiplication is a fundamental building block for large scale computations arising in various applications, including machine learning. There has been significant recent interest in using coding to speed up distributed matrix…

Stochastic iterative algorithms have gained recent interest in machine learning and signal processing for solving large-scale systems of equations, $Ax=b$. One such example is the Randomized Kaczmarz (RK) algorithm, which acts only on…

Ensembling is a powerful technique for improving the accuracy of machine learning models, with methods like stacking achieving strong results in tabular tasks. In time series forecasting, however, ensemble methods remain underutilized, with…

We introduce \emph{coarse scrambling}, a novel randomization for digital sequences that permutes blocks of digits in a mixed-radix representation. This construction is designed to preserve the powerful $(0,\boldsymbol{e},d)$-sequence…

In this paper, we investigate the randomized algorithms for block matrix multiplication from random sampling perspective. Based on the A-optimal design criterion, the optimal sampling probabilities and sampling block sizes are obtained. To…

The randomized Kaczmarz (RK) method is an iterative method for approximating the least-squares solution of large linear systems of equations. The standard RK method uses sequential updates, making parallel computation difficult. Here, we…

The randomized block Kaczmarz (RBK) method is a widely utilized iterative scheme for solving large-scale linear systems. However, the theoretical analysis and practical effectiveness of this method heavily rely on a good row paving of the…

This survey highlights the recent advances in algorithms for numerical linear algebra that have come from the technique of linear sketching, whereby given a matrix, one first compresses it to a much smaller matrix by multiplying it by a…

Ensembling is among the most popular tools in machine learning (ML) due to its effectiveness in minimizing variance and thus improving generalization. Most ensembling methods for black-box base learners fall under the umbrella of "stacked…

Our work aimed at experimentally assessing the benefits of model ensembling within the context of neural methods for passage reranking. Starting from relatively standard neural models, we use a previous technique named Fast Geometric…

Among recent developments centered around Randomized Kaczmarz (RK), a row-sampling iterative projection method for large-scale linear systems, several adaptions to the method have inspired faster convergence. Focusing solely on…

Covariate-adjusted randomization (CAR) can reduce the risk of covariate imbalance and, when accounted for in analysis, increase the power of a trial. Despite CAR advances, stratified randomization remains the most common CAR method. Matched…

In the last few years several new Random Matrix Models have been proposed and studied. They have found application in various different contexts, ranging from the physics of mesoscopic systems to the chiral transition in lattice gauge…

We give a series of combinatorial results that can be obtained from any two collections (both indexed by $\Z\times \N$) of left and right pointing arrows that satisfy some natural relationship. When applied to certain self-interacting…

Randomized algorithms for very large matrix problems have received a great deal of attention in recent years. Much of this work was motivated by problems in large-scale data analysis, and this work was performed by individuals from many…

Markov Chain Monte Carlo (MCMC) methods for sampling probability density functions (combined with abundant computational resources) have transformed the sciences, especially in performing probabilistic inferences, or fitting models to data.…