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Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-01-08 Austin R. Benson , Grey Ballard

A precision matrix is the inverse of a covariance matrix. In this paper, we study the problem of estimating the precision matrix with a known graphical structure under high-dimensional settings. We propose a simple estimator of the…

Statistics Theory · Mathematics 2021-07-15 Thien-Minh Le , Ping-Shou Zhong

Random projection, a dimensionality reduction technique, has been found useful in recent years for reducing the size of optimization problems. In this paper, we explore the use of sparse sub-gaussian random projections to approximate…

Optimization and Control · Mathematics 2024-06-21 Monse Guedes-Ayala , Pierre-Louis Poirion , Lars Schewe , Akiko Takeda

It is often desirable to reduce the dimensionality of a large dataset by projecting it onto a low-dimensional subspace. Matrix sketching has emerged as a powerful technique for performing such dimensionality reduction very efficiently. Even…

Machine Learning · Computer Science 2022-06-15 Michał Dereziński , Feynman Liang , Zhenyu Liao , Michael W. Mahoney

We consider the problem of computationally-efficient prediction from high dimensional and highly correlated predictors in challenging settings where accurate variable selection is effectively impossible. Direct application of penalization…

Statistics Theory · Mathematics 2017-12-08 Minerva Mukhopadhyay , David B. Dunson

Nonparametric tests for equality of multivariate distributions are frequently desired in research. It is commonly required that test-procedures based on relatively small samples of vectors accurately control the corresponding Type I Error…

Methodology · Statistics 2021-01-14 Ablert Vexler , Gregory Gurevich , Li Zou

In this paper, we present novel deterministic algorithms for multiplying two $n \times n$ matrices approximately. Given two matrices $A,B$ we return a matrix $C'$ which is an \emph{approximation} to $C = AB$. We consider the notion of…

Data Structures and Algorithms · Computer Science 2014-08-21 Shiva Manne , Manjish Pal

In this paper, we present a sharp analysis for a class of alternating projected gradient descent algorithms which are used to solve the covariate adjusted precision matrix estimation problem in the high-dimensional setting. We demonstrate…

Information Theory · Computer Science 2022-01-13 Xiao Lv , Wei Cui , Yulong Liu

We introduce a novel method to compute a rank $m$ approximation of the inverse of the Hessian matrix in the distributed regime. By leveraging the differences in gradients and parameters of multiple Workers, we are able to efficiently…

Machine Learning · Computer Science 2017-09-18 Sébastien M. R. Arnold , Chunming Wang

Bayesian methods constitute a popular approach for estimating the conditional independence structure in Gaussian graphical models, since they can quantify the uncertainty through the posterior distribution. Inference in this framework is…

Methodology · Statistics 2026-01-14 Marcus Gehrmann , Håkon Tjelmeland

We consider concave minimization problems over non-convex sets.Optimization problems with this structure arise in sparse principal component analysis. We analyze both a gradient projection algorithm and an approximate Newton algorithm where…

Numerical Analysis · Computer Science 2019-04-09 William W. Hager , Dzung T. Phan , Jia-Jie Zhu

Motivated by economic dispatch and linearly-constrained resource allocation problems, this paper proposes a novel Distributed Approx-Newton algorithm that approximates the standard Newton optimization method. A main property of this…

Numerical Analysis · Computer Science 2017-03-24 Tor Anderson , Chin-Yao Chang , Sonia Martinez

In this paper, we propose a distributed second- order method for reinforcement learning. Our approach is the fastest in literature so-far as it outperforms state-of-the-art methods, including ADMM, by significant margins. We achieve this by…

Optimization and Control · Mathematics 2016-08-08 Rasul Tutunov , Haitham Bou-Ammar , Ali Jadbabaie

We consider solving large scale nonconvex optimisation problems with nonnegativity constraints. Such problems arise frequently in machine learning, such as nonnegative least-squares, nonnegative matrix factorisation, as well as problems…

Optimization and Control · Mathematics 2024-05-22 Oscar Smee , Fred Roosta

This paper considers the low-observability state estimation problem in power distribution networks and develops a decentralized state estimation algorithm leveraging the matrix completion methodology. Matrix completion has been shown to be…

Optimization and Control · Mathematics 2019-10-14 April Sagan , Yajing Liu , Andrey Bernstein

A robust algorithm for non-negative matrix factorization (NMF) is presented in this paper with the purpose of dealing with large-scale data, where the separability assumption is satisfied. In particular, we modify the Linear Programming…

Machine Learning · Statistics 2014-01-10 Jason Gejie Liu , Shuchin Aeron

Finding relative pose between two calibrated images is a fundamental task in computer vision. Given five point correspondences, the classical five-point methods can be used to calculate the essential matrix efficiently. For the case of $N$…

Computer Vision and Pattern Recognition · Computer Science 2020-12-23 Ji Zhao

We consider the problem of computing a positive definite $p \times p$ inverse covariance matrix aka precision matrix $\theta=(\theta_{ij})$ which optimizes a regularized Gaussian maximum likelihood problem, with the elastic-net regularizer…

Statistics Theory · Mathematics 2015-09-02 Yves F. Atchadé , Rahul Mazumder , Jie Chen

This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery…

Machine Learning · Statistics 2016-09-27 Ethan X. Fang , Han Liu , Kim-Chuan Toh , Wen-Xin Zhou

In this paper, we propose new methods to efficiently solve convex optimization problems encountered in sparse estimation, which include a new quasi-Newton method that avoids computing the Hessian matrix and improves efficiency, and we prove…

Optimization and Control · Mathematics 2023-09-06 Ryosuke Shimmura , Joe Suzuki