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The success of deep learning hinges on enormous data and large models, which require labor-intensive annotations and heavy computation costs. Subset selection is a fundamental problem that can play a key role in identifying smaller portions…
We present a matrix factorization algorithm that scales to input matrices that are large in both dimensions (i.e., that contains morethan 1TB of data). The algorithm streams the matrix columns while subsampling them, resulting in low…
We study implicit regularization when optimizing an underdetermined quadratic objective over a matrix $X$ with gradient descent on a factorization of $X$. We conjecture and provide empirical and theoretical evidence that with small enough…
This paper describes a new approach, based on linear programming, for computing nonnegative matrix factorizations (NMFs). The key idea is a data-driven model for the factorization where the most salient features in the data are used to…
There are a number of approximation algorithms for NP-hard versions of low rank approximation, such as finding a rank-$k$ matrix $B$ minimizing the sum of absolute values of differences to a given $n$-by-$n$ matrix $A$,…
Matrix factorization is an inference problem that has acquired importance due to its vast range of applications that go from dictionary learning to recommendation systems and machine learning with deep networks. The study of its fundamental…
Clustering algorithms remain valuable tools for grouping and summarizing the most important aspects of data. Example areas where this is the case include image segmentation, dimension reduction, signals analysis, model order reduction,…
Many applications in scientific computing and data science require the computation of a rank-revealing factorization of a large matrix. In many of these instances the classical algorithms for computing the singular value decomposition are…
We propose algorithms for approximate filtering and smoothing in high-dimensional Factorial hidden Markov models. The approximation involves discarding, in a principled way, likelihood factors according to a notion of locality in a factor…
Reducing parameter redundancies in neural network architectures is crucial for achieving feasible computational and memory requirements during training and inference phases. Given its easy implementation and flexibility, one promising…
There has been a recent critical need to study fairness and bias in machine learning (ML) algorithms. Since there is clearly no one-size-fits-all solution to fairness, ML methods should be developed alongside bias mitigation strategies that…
Matrix Factorization (MF) on large scale matrices is computationally as well as memory intensive task. Alternative convergence techniques are needed when the size of the input matrix is higher than the available memory on a Central…
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…
Matrix Factorization plays an important role in machine learning such as Non-negative Matrix Factorization, Principal Component Analysis, Dictionary Learning, etc. However, most of the studies aim to minimize the loss by measuring the…
A new class of matrices based on a parametrization of the Feig-Winograd factorization of 8-point DCT is proposed. Such parametrization induces a matrix subspace, which unifies a number of existing methods for DCT approximation. By solving a…
LU and Cholesky matrix factorization algorithms are core subroutines used to solve systems of linear equations (SLEs) encountered while solving an optimization problem. Standard factorization algorithms are highly efficient but remain…
New algorithms for prime factorization that outperform the existing ones or take advantage of particular properties of the prime factors can have a practical impact on present implementations of cryptographic algorithms that rely on the…
In this paper, we provide novel algorithms with identifiability guarantees for simplex-structured matrix factorization (SSMF), a generalization of nonnegative matrix factorization. Current state-of-the-art algorithms that provide…
Matrix factorization (MF) discovers latent features from observations, which has shown great promises in the fields of collaborative filtering, data compression, feature extraction, word embedding, etc. While many problem-specific…
The problem of approximating a matrix by a low-rank one has been extensively studied. This problem assumes, however, that the whole matrix has a low-rank structure. This assumption is often false for real-world matrices. We consider the…