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Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…

Machine Learning · Statistics 2010-09-07 Mehryar Mohri , Ameet Talwalkar

Many problems in machine learning can be solved by rounding the solution of an appropriate linear program (LP). This paper shows that we can recover solutions of comparable quality by rounding an approximate LP solution instead of the ex-…

Numerical Analysis · Computer Science 2013-11-19 Srikrishna Sridhar , Victor Bittorf , Ji Liu , Ce Zhang , Christopher Ré , Stephen J. Wright

We study the \emph{order-finding problem} for Read-once Oblivious Algebraic Branching Programs (ROABPs). Given a polynomial $f$ and a parameter $w$, the goal is to find an order $\sigma$ in which $f$ has an ROABP of \emph{width} $w$. We…

Computational Complexity · Computer Science 2024-12-02 Vishwas Bhargava , Pranjal Dutta , Sumanta Ghosh , Anamay Tengse

The problem of maximizing the $p$-th power of a $p$-norm over a halfspace-presented polytope in $\R^d$ is a convex maximization problem which plays a fundamental role in computational convexity. It has been shown in 1986 that this problem…

Computational Complexity · Computer Science 2013-07-25 Christian Knauer , Stefan König , Daniel Werner

Discrepancy measures how uniformly distributed a point set is with respect to a given set of ranges. There are two notions of discrepancy, namely continuous discrepancy and combinatorial discrepancy. Depending on the ranges, several…

Computational Geometry · Computer Science 2011-03-24 Panos Giannopoulos , Christian Knauer , Magnus Wahlström , Daniel Werner

Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…

Systems and Control · Electrical Eng. & Systems 2023-06-13 Meiyi Li , Soheil Kolouri , Javad Mohammadi

We study the problem of circular seriation, where we are given a matrix of pairwise dissimilarities between $n$ objects, and the goal is to find a {\em circular order} of the objects in a manner that is consistent with their dissimilarity.…

Data Structures and Algorithms · Computer Science 2021-06-11 Santiago Armstrong , Cristóbal Guzmán , Carlos A. Sing-Long

The distance matrix of a dataset $X$ of $n$ points with respect to a distance function $f$ represents all pairwise distances between points in $X$ induced by $f$. Due to their wide applicability, distance matrices and related families of…

Data Structures and Algorithms · Computer Science 2022-10-28 Piotr Indyk , Sandeep Silwal

In the recent literature on machine learning and decision making, calibration has emerged as a desirable and widely-studied statistical property of the outputs of binary prediction models. However, the algorithmic aspects of measuring model…

Machine Learning · Computer Science 2024-06-24 Lunjia Hu , Arun Jambulapati , Kevin Tian , Chutong Yang

We consider the problem of solving a large-scale Quadratically Constrained Quadratic Program. Such problems occur naturally in many scientific and web applications. Although there are efficient methods which tackle this problem, they are…

Machine Learning · Statistics 2017-10-04 Kinjal Basu , Ankan Saha , Shaunak Chatterjee

Various first order approaches have been proposed in the literature to solve Linear Programming (LP) problems, recently leading to practically efficient solvers for large-scale LPs. From a theoretical perspective, linear convergence rates…

Optimization and Control · Mathematics 2024-03-29 Richard Cole , Christoph Hertrich , Yixin Tao , László A. Végh

In this paper, we examine the problem of approximating a general linear dimensionality reduction (LDR) operator, represented as a matrix $A \in \mathbb{R}^{m \times n}$ with $m < n$, by a partial circulant matrix with rows related by…

Machine Learning · Statistics 2015-02-26 Swayambhoo Jain , Jarvis Haupt

A new error bound for the linear complementarity problem is given when the involved matrix is a B-matrix. It is shown that this bound is sharper than some previous bounds [C.Q. Li, Y.T. Li. Note on error bounds for linear complementarity…

Numerical Analysis · Mathematics 2016-03-01 Chaoqian Li , Mengting Gan , Shaorong Yang

This paper is concerned with the problem of exact MAP inference in general higher-order graphical models by means of a traditional linear programming relaxation approach. In fact, the proof that we have developed in this paper is a rather…

Optimization and Control · Mathematics 2026-03-23 Ikhlef Bechar

This paper presents fast first-order methods for solving linear programs (LPs) approximately. We adapt online linear programming algorithms to offline LPs and obtain algorithms that avoid any matrix multiplication. We also introduce a…

Optimization and Control · Mathematics 2024-11-07 Wenzhi Gao , Dongdong Ge , Chunlin Sun , Yinyu Ye

Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient…

Data Structures and Algorithms · Computer Science 2014-11-20 Khaled Elbassioni , Trung Thanh Nguyen

This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…

Data Structures and Algorithms · Computer Science 2026-02-12 Kobe Grobben , Phablo F. S. Moura , Hande Yaman

The study of approximate matching in the Massively Parallel Computations (MPC) model has recently seen a burst of breakthroughs. Despite this progress, however, we still have a far more limited understanding of maximal matching which is one…

Data Structures and Algorithms · Computer Science 2023-10-17 Soheil Behnezhad , MohammadTaghi Hajiaghayi , David G. Harris

We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…

Numerical Analysis · Mathematics 2014-07-01 Gil Shabat , Yaniv Shmueli , Amir Averbuch

Consensus problems for strings and sequences appear in numerous application contexts, ranging from bioinformatics over data mining to machine learning. Closing some gaps in the literature, we show that several fundamental problems in this…

Discrete Mathematics · Computer Science 2019-04-12 Laurent Bulteau , Vincent Froese , Rolf Niedermeier