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Related papers: On the approximation gain for abc-triples

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In this paper, we propose a novel extrapolation coefficient scheme within a new extrapolation term and develop an accelerated proximal gradient algorithm. We establish that the algorithm achieves a sublinear convergence rate. The proposed…

Optimization and Control · Mathematics 2025-10-17 Chengzhi Huang

ABC (approximate Bayesian computation) is a general approach for dealing with models with an intractable likelihood. In this work, we derive ABC algorithms based on QMC (quasi- Monte Carlo) sequences. We show that the resulting ABC…

Computation · Statistics 2018-05-08 Alexander Buchholz , Nicolas Chopin

We propose a novel use of a recent new computational tool for Bayesian inference, namely the Approximate Bayesian Computation (ABC) methodology. ABC is a way to handle models for which the likelihood function may be intractable or even…

Computation · Statistics 2014-03-04 Clara Grazian , Brunero Liseo

Approximate Bayesian computation (ABC) has advanced in two decades from a seminal idea to a practically applicable inference tool for simulator-based statistical models, which are becoming increasingly popular in many research domains. The…

In this paper, we propose a generalized alternating direction method of multipliers (ADMM) with semi-proximal terms for solving a class of convex composite conic optimization problems, of which some are high-dimensional, to moderate…

Optimization and Control · Mathematics 2018-01-17 Yunhai Xiao , Liang Chen , Donghui Li

We consider the problem of classification in a comparison-based setting: given a set of objects, we only have access to triplet comparisons of the form "object $x_i$ is closer to object $x_j$ than to object $x_k$." In this paper we…

Machine Learning · Statistics 2019-05-30 Michaël Perrot , Ulrike von Luxburg

Over the fast few years, the numerical success of the generalized alternating direction method of multipliers (GADMM) proposed by Eckstein \& Bertsekas [Math. Prog., 1992] has inspired intensive attention in analyzing its theoretical…

Optimization and Control · Mathematics 2022-06-09 Han Wang , Peili Li , Yunhai Xiao

In 1987, Orrin Frink introduced the concept of almost Pythagorean triples. He defined them as an ordered triple $(x,y,z)$ that satisfies the equation $x^2+y^2=z^2+1$ where $x,y$ and $z$ are positive integers. In his paper, he showed that…

Number Theory · Mathematics 2015-11-02 John Rafael M. Antalan , Mark D. Tomenes

Given a bounded-above cochain complex of modules over a ring, it is standard to replace it by a projective resolution, and it is classical that doing so can be very useful. Recently, a modified version of this was introduced in triangulated…

Category Theory · Mathematics 2023-12-20 Jesse Burke , Amnon Neeman , Bregje Pauwels

This is a sequel to arXiv:1308.3604. We study applications to limit multiplicity generalizing the results of arXiv:1208.2257.

Number Theory · Mathematics 2018-09-25 Tobias Finis , Erez Lapid

For a graph $G$ spanning a metric space, the dilation of a pair of points is the ratio of their distance in the shortest path graph metric to their distance in the metric space. Given a graph $G$ and a budget $k$, a classic problem is to…

Computational Geometry · Computer Science 2025-06-06 Sariel Har-Peled , Eliot W. Robson

We propose an adaptive proximal gradient method for minimizing the sum of two functions, where one is a simple convex function, and the other belongs to one of the three classes: nonconvex smooth, convex nonsmooth, or convex smooth. The key…

Optimization and Control · Mathematics 2026-05-08 Zimeng Wang , Alp Yurtsever

In this paper we present a first-order method that admits near-optimal convergence rates for convex/concave min-max problems while requiring a simple and intuitive analysis. Similarly to the seminal work of Nemirovski and the recent…

Computer Science and Game Theory · Computer Science 2023-01-18 Volkan Cevher , Georgios Piliouras , Ryann Sim , Stratis Skoulakis

Succinct representations of a graph have been objects of central study in computer science for decades. In this paper, we study the operation called \emph{Distance Preserving Graph Contractions}, which was introduced by Bernstein et al.…

Computational Complexity · Computer Science 2019-12-03 Siddhartha Jain

We obtain a bound on the girth g of a quaternion unit gain graph in terms of the rank r of its adjacency matrix. In particular, we show that g <= r + 2 and characterize all quaternion unit gain graphs for which g = r+2. This extends…

Combinatorics · Mathematics 2024-12-02 Suliman Khan , Edwin R. van Dam

The "short cycle removal" technique was recently introduced by Abboud, Bringmann, Khoury and Zamir (STOC '22) to prove fine-grained hardness of approximation. Its main technical result is that listing all triangles in an $n^{1/2}$-regular…

Data Structures and Algorithms · Computer Science 2023-10-24 Amir Abboud , Karl Bringmann , Nick Fischer

Modern convolutional networks, incorporating rectifiers and max-pooling, are neither smooth nor convex; standard guarantees therefore do not apply. Nevertheless, methods from convex optimization such as gradient descent and Adam are widely…

Machine Learning · Computer Science 2018-06-07 David Balduzzi , Brian McWilliams , Tony Butler-Yeoman

In this master's thesis, we introduce expansion systems as a general framework to describe a large variety of approximation algorithms, such as Taylor approximation, decimal expansion and continued fraction. We consider some basic…

Classical Analysis and ODEs · Mathematics 2012-06-05 V. A. Pessers

Most of the literature on spanners focuses on building the graph from scratch. This paper instead focuses on adding edges to improve an existing graph. A major open problem in this field is: given a graph embedded in a metric space, and a…

Computational Geometry · Computer Science 2022-12-20 Joachim Gudmundsson , Sampson Wong

Bayes linear analysis and approximate Bayesian computation (ABC) are techniques commonly used in the Bayesian analysis of complex models. In this article we connect these ideas by demonstrating that regression-adjustment ABC algorithms…

Methodology · Statistics 2012-12-10 D. J. Nott , Y. Fan , L. Marshall , S. A. Sisson