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Low-rank approximation and column subset selection are two fundamental and related problems that are applied across a wealth of machine learning applications. In this paper, we study the question of socially fair low-rank approximation and…

Machine Learning · Computer Science 2024-12-10 Zhao Song , Ali Vakilian , David P. Woodruff , Samson Zhou

We present a data-driven method for computing approximate forward reachable sets using separating kernels in a reproducing kernel Hilbert space. We frame the problem as a support estimation problem, and learn a classifier of the support as…

Optimization and Control · Mathematics 2020-11-20 Adam J. Thorpe , Kendric R. Ortiz , Meeko M. K. Oishi

Markov decision processes (MDPs) are a well studied framework for solving sequential decision making problems under uncertainty. Exact methods for solving MDPs based on dynamic programming such as policy iteration and value iteration are…

Artificial Intelligence · Computer Science 2015-09-09 Yanping Huang

We propose a computational framework for computing low-rank approximations to the ensemble of solutions of a parametrized system of the form $A(\xi)x(\xi)+g(x(\xi))=b(\xi)$ for multiple parameter values. The central idea is to reinterpret…

Numerical Analysis · Mathematics 2026-04-09 Marco Sutti , Tommaso Vanzan

To accelerate DNNs inference, low-rank approximation has been widely adopted because of its solid theoretical rationale and efficient implementations. Several previous works attempted to directly approximate a pre-trained model by low-rank…

Computer Vision and Pattern Recognition · Computer Science 2020-01-27 Yuhui Xu , Yuxi Li , Shuai Zhang , Wei Wen , Botao Wang , Wenrui Dai , Yingyong Qi , Yiran Chen , Weiyao Lin , Hongkai Xiong

The runtime for Kernel Partial Least Squares (KPLS) to compute the fit is quadratic in the number of examples. However, the necessity of obtaining sensitivity measures as degrees of freedom for model selection or confidence intervals for…

Machine Learning · Statistics 2010-08-13 Nicole Kraemer , Masashi Sugiyama , Mikio Braun

Given a matrix $M\in \mathbb{R}^{m\times n}$, the low rank matrix completion problem asks us to find a rank-$k$ approximation of $M$ as $UV^\top$ for $U\in \mathbb{R}^{m\times k}$ and $V\in \mathbb{R}^{n\times k}$ by only observing a few…

Machine Learning · Computer Science 2024-04-03 Yuzhou Gu , Zhao Song , Junze Yin , Lichen Zhang

This work studies low-rank approximation of a positive semidefinite matrix from partial entries via nonconvex optimization. We characterized how well local-minimum based low-rank factorization approximates a fixed positive semidefinite…

Optimization and Control · Mathematics 2019-04-08 Ji Chen , Xiaodong Li

To enable DNNs on edge devices like mobile phones, low-rank approximation has been widely adopted because of its solid theoretical rationale and efficient implementations. Several previous works attempted to directly approximate a…

Machine Learning · Computer Science 2020-05-01 Yuhui Xu , Yuxi Li , Shuai Zhang , Wei Wen , Botao Wang , Yingyong Qi , Yiran Chen , Weiyao Lin , Hongkai Xiong

Random features is one of the most popular techniques to speed up kernel methods in large-scale problems. Related works have been recognized by the NeurIPS Test-of-Time award in 2017 and the ICML Best Paper Finalist in 2019. The body of…

Machine Learning · Statistics 2021-07-13 Fanghui Liu , Xiaolin Huang , Yudong Chen , Johan A. K. Suykens

The paper deals with the problem of penalized empirical risk minimization over a convex set of linear functionals on the space of Hermitian matrices with convex loss and nuclear norm penalty. Such penalization is often used in low rank…

Statistics Theory · Mathematics 2012-10-11 Vladimir Koltchinskii

Reinforcement learning (RL) algorithms based on high-dimensional function approximation have achieved tremendous empirical success in large-scale problems with an enormous number of states. However, most analysis of such algorithms gives…

Machine Learning · Computer Science 2022-02-17 Jihao Long , Jiequn Han , Weinan E

Reinforcement learning (RL) problems are fundamental in online decision-making and have been instrumental in finding an optimal policy for Markov decision processes (MDPs). Function approximations are usually deployed to handle large or…

Machine Learning · Computer Science 2025-05-20 Jiashuo Jiang , Yiming Zong , Yinyu Ye

We propose a method for low-rank semidefinite programming in application to the semidefinite relaxation of unconstrained binary quadratic problems. The method improves an existing solution of the semidefinite programming relaxation to…

Optimization and Control · Mathematics 2021-12-07 Roman Pogodin , Mikhail Krechetov , Yury Maximov

Sparse reduced rank regression is an essential statistical learning method. In the contemporary literature, estimation is typically formulated as a nonconvex optimization that often yields to a local optimum in numerical computation. Yet,…

Methodology · Statistics 2022-12-06 Canhong Wen , Ruipeng Dong , Xueqin Wang , Weiyu Li , Heping Zhang

We consider classification and regression tasks where we have missing data and assume that the (clean) data resides in a low rank subspace. Finding a hidden subspace is known to be computationally hard. Nevertheless, using a non-proper…

Machine Learning · Computer Science 2015-01-15 Elad Hazan , Roi Livni , Yishay Mansour

Low rank model arises from a wide range of applications, including machine learning, signal processing, computer algebra, computer vision, and imaging science. Low rank matrix recovery is about reconstructing a low rank matrix from…

Numerical Analysis · Mathematics 2018-09-12 Jian-Feng Cai , Ke Wei

Symmetry arises often when learning from high dimensional data. For example, data sets consisting of point clouds, graphs, and unordered sets appear routinely in contemporary applications, and exhibit rich underlying symmetries.…

Optimization and Control · Mathematics 2025-02-06 Mateo Díaz , Dmitriy Drusvyatskiy , Jack Kendrick , Rekha R. Thomas

In this paper we consider the low-rank matrix completion problem with specific application to forecasting in time series analysis. Briefly, the low-rank matrix completion problem is the problem of imputing missing values of a matrix under a…

Methodology · Statistics 2018-02-23 Jonathan Gillard , Konstantin Usevich

Solving symmetric positive definite linear problems is a fundamental computational task in machine learning. The exact solution, famously, is cubicly expensive in the size of the matrix. To alleviate this problem, several linear-time…

Machine Learning · Computer Science 2017-06-02 Filip de Roos , Philipp Hennig