Related papers: New Results on Scrambling Using the Mesh Array
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…
The main principle of stacked generalization (or Stacking) is using a second-level generalizer to combine the outputs of base classifiers in an ensemble. In this paper, we investigate different combination types under the stacking…
This note gives a simple analysis of a randomized approximation scheme for matrix multiplication proposed by Sarlos (2006) based on a random rotation followed by uniform column sampling. The result follows from a matrix version of…
Multiplicative random cascade model naturally reproduces the intermittency or multifractality, which is frequently shown among hierarchical complex systems such as turbulence and financial markets. As described herein, we investigate the…
A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination…
Inspired by a common technique for shuffling a deck of cards on a table without riffling, we formalize the pile shuffle and investigate its capabilities as a sorting device. Our study is novel in that we consider pile shuffle in three…
Learned sparse text embeddings have gained popularity due to their effectiveness in top-k retrieval and inherent interpretability. Their distributional idiosyncrasies, however, have long hindered their use in real-world retrieval systems.…
The sampling Kaczmarz-Motzkin (SKM) method is a generalization of the randomized Kaczmarz and Motzkin methods. It first samples some rows of coefficient matrix randomly to build a set and then makes use of the maximum violation criterion…
We analyze the asymptotic behavior of sequences of random variables defined by an initial condition, a stationary and ergodic sequence of random matrices, and an induction formula involving multiplication is the so-called max-plus algebra.…
Large matrices arise in many machine learning and data analysis applications, including as representations of datasets, graphs, model weights, and first and second-order derivatives. Randomized Numerical Linear Algebra (RandNLA) is an area…
Randomized iterative algorithms for solving a factorized linear system, $\mathbf A\mathbf B\mathbf x=\mathbf b$ with $\mathbf A\in{\mathbb{R}}^{m\times \ell}$, $\mathbf B\in{\mathbb{R}}^{\ell\times n}$, and $\mathbf b\in{\mathbb{R}}^m$,…
Enumerating maximal $k$-biplexes (MBPs) of a bipartite graph has been used for applications such as fraud detection. Nevertheless, there usually exists an exponential number of MBPs, which brings up two issues when enumerating MBPs, namely…
This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…
The Kaczmarz algorithm is a well known iterative method for solving overdetermined linear systems. Its randomized version yields provably exponential convergence in expectation. In this paper, we propose two new methods to speed up the…
There has been significant interest and progress recently in algorithms that solve regression problems involving tall and thin matrices in input sparsity time. These algorithms find shorter equivalent of a n*d matrix where n >> d, which…
Motivated by cryptographic applications, we investigate two machine learning approaches to modular multiplication: namely circular regression and a sequence-to-sequence transformer model. The limited success of both methods demonstrated in…
Markov Chain Monte Carlo (MCMC) methods such as Gibbs sampling are finding widespread use in applied statistics and machine learning. These often lead to difficult computational problems, which are increasingly being solved on parallel and…
The purpose of this research report is to present the our learning curve and the exposure to the Machine Learning life cycle, with the use of a Kaggle binary classification data set and taking to explore various techniques from…
When solving linear systems $Ax=b$, $A$ and $b$ are given, but the measurements $b$ often contain corruptions. Inspired by recent work on the quantile-randomized Kaczmarz method, we propose an acceleration of the randomized Kaczmarz method…
We study analytically the performance of a recently proposed algorithm for learning the couplings of a random asymmetric kinetic Ising model from finite length trajectories of the spin dynamics. Our analysis shows the importance of the…