SIAM journal on mathematics of data science最新文献_第3页

Convergence of a Constrained Vector Extrapolation Scheme 约束向量外推方案的收敛性

SIAM journal on mathematics of data science Pub Date : 2022-07-11 DOI: 10.1137/21m1428030

Mathieu Barré, Adrien B. Taylor, A. d’Aspremont

引用次数: 2

Numerical Considerations and a New Implementation for Invariant Coordinate Selection 不变坐标选择的数值考虑与新实现

SIAM journal on mathematics of data science Pub Date : 2022-07-05 DOI: 10.1137/22M1498759

A. Archimbaud, Z. Drmač, K. Nordhausen, Una Radojicic, A. Ruiz-Gazen

引用次数: 0

Data-Driven Mirror Descent with Input-Convex Neural Networks 基于输入凸神经网络的数据驱动镜像下降

SIAM journal on mathematics of data science Pub Date : 2022-06-14 DOI: 10.1137/22m1508613

Hongwei Tan, Subhadip Mukherjee, Junqi Tang, C. Schonlieb

{"title":"Data-Driven Mirror Descent with Input-Convex Neural Networks","authors":"Hongwei Tan, Subhadip Mukherjee, Junqi Tang, C. Schonlieb","doi":"10.1137/22m1508613","DOIUrl":"https://doi.org/10.1137/22m1508613","url":null,"abstract":"Learning-to-optimize is an emerging framework that seeks to speed up the solution of certain optimization problems by leveraging training data. Learned optimization solvers have been shown to outperform classical optimization algorithms in terms of convergence speed, especially for convex problems. Many existing data-driven optimization methods are based on parameterizing the update step and learning the optimal parameters (typically scalars) from the available data. We propose a novel functional parameterization approach for learned convex optimization solvers based on the classical mirror descent (MD) algorithm. Specifically, we seek to learn the optimal Bregman distance in MD by modeling the underlying convex function using an input-convex neural network (ICNN). The parameters of the ICNN are learned by minimizing the target objective function evaluated at the MD iterate after a predetermined number of iterations. The inverse of the mirror map is modeled approximately using another neural network, as the exact inverse is intractable to compute. We derive convergence rate bounds for the proposed learned mirror descent (LMD) approach with an approximate inverse mirror map and perform extensive numerical evaluation on various convex problems such as image inpainting, denoising, learning a two-class support vector machine (SVM) classifier and a multi-class linear classifier on fixed features.","PeriodicalId":74797,"journal":{"name":"SIAM journal on mathematics of data science","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47238537","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 7

Speedy Categorical Distributional Reinforcement Learning and Complexity Analysis 快速分类分布强化学习与复杂性分析

SIAM journal on mathematics of data science Pub Date : 2022-06-01 DOI: 10.1137/20m1364436

Markus Böck, C. Heitzinger

引用次数: 2

Wasserstein-Based Projections with Applications to Inverse Problems 基于wasserstein的投影及其在逆问题中的应用

SIAM journal on mathematics of data science Pub Date : 2022-05-05 DOI: 10.1137/20m1376790

Howard Heaton, Samy Wu Fung, A. Lin, S. Osher, W. Yin

引用次数: 12

Nonbacktracking spectral clustering of nonuniform hypergraphs 非均匀超图的非回溯谱聚类

SIAM journal on mathematics of data science Pub Date : 2022-04-27 DOI: 10.48550/arXiv.2204.13586

Philip S. Chodrow, Nicole Eikmeier, Jamie Haddock

{"title":"Nonbacktracking spectral clustering of nonuniform hypergraphs","authors":"Philip S. Chodrow, Nicole Eikmeier, Jamie Haddock","doi":"10.48550/arXiv.2204.13586","DOIUrl":"https://doi.org/10.48550/arXiv.2204.13586","url":null,"abstract":"Spectral methods offer a tractable, global framework for clustering in graphs via eigenvector computations on graph matrices. Hypergraph data, in which entities interact on edges of arbitrary size, poses challenges for matrix representations and therefore for spectral clustering. We study spectral clustering for nonuniform hypergraphs based on the hypergraph nonbacktracking operator. After reviewing the definition of this operator and its basic properties, we prove a theorem of Ihara-Bass type which allows eigenpair computations to take place on a smaller matrix, often enabling faster computation. We then propose an alternating algorithm for inference in a hypergraph stochastic blockmodel via linearized belief-propagation which involves a spectral clustering step again using nonbacktracking operators. We provide proofs related to this algorithm that both formalize and extend several previous results. We pose several conjectures about the limits of spectral methods and detectability in hypergraph stochastic blockmodels in general, supporting these with in-expectation analysis of the eigeinpairs of our studied operators. We perform experiments in real and synthetic data that demonstrate the benefits of hypergraph methods over graph-based ones when interactions of different sizes carry different information about cluster structure.","PeriodicalId":74797,"journal":{"name":"SIAM journal on mathematics of data science","volume":"11 1","pages":"251-279"},"PeriodicalIF":0.0,"publicationDate":"2022-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81460300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 13

An improved central limit theorem and fast convergence rates for entropic transportation costs 熵运输成本的一个改进的中心极限定理和快速收敛速率

SIAM journal on mathematics of data science Pub Date : 2022-04-19 DOI: 10.48550/arXiv.2204.09105

E. Barrio, Alberto González-Sanz, Jean-Michel Loubes, Jonathan Niles-Weed

引用次数: 22

Statistical Analysis of Random Objects Via Metric Measure Laplacians 基于度量拉普拉斯算子的随机物体的统计分析

SIAM journal on mathematics of data science Pub Date : 2022-04-13 DOI: 10.1137/22m1491022

Gilles Mordant, A. Munk

引用次数: 1

Approximation of Lipschitz Functions using Deep Spline Neural Networks 利用深度样条神经网络逼近Lipschitz函数

SIAM journal on mathematics of data science Pub Date : 2022-04-13 DOI: 10.48550/arXiv.2204.06233

Sebastian Neumayer, Alexis Goujon, Pakshal Bohra, M. Unser

引用次数: 14

A Nonlinear Matrix Decomposition for Mining the Zeros of Sparse Data 一种用于稀疏数据零点挖掘的非线性矩阵分解

SIAM journal on mathematics of data science Pub Date : 2022-04-07 DOI: 10.1137/21m1405769

L. Saul

{"title":"A Nonlinear Matrix Decomposition for Mining the Zeros of Sparse Data","authors":"L. Saul","doi":"10.1137/21m1405769","DOIUrl":"https://doi.org/10.1137/21m1405769","url":null,"abstract":". We describe a simple iterative solution to a widely recurring problem in multivariate data analysis: given a sparse nonnegative matrix X , how to estimate a low-rank matrix Θ such that X ≈ f ( Θ ), where f is an elementwise nonlinearity? We develop a latent variable model for this problem and consider those sparsifying nonlinearities, popular in neural networks, that map all negative values to zero. The model seeks to explain the variability of sparse high-dimensional data in terms of a smaller number of degrees of freedom. We show that exact inference in this model is tractable and derive an expectation-maximization (EM) algorithm to estimate the low-rank matrix Θ . Notably, we do not parameterize Θ as a product of smaller matrices to be alternately optimized; instead, we estimate Θ directly via the singular value decomposition of matrices that are repeatedly inferred (at each iteration of the EM algorithm) from the model’s posterior distribution. We use the model to analyze large sparse matrices that arise from data sets of binary, grayscale, and color images. In all of these cases, we find that the model discovers much lower-rank decompositions than purely linear approaches.","PeriodicalId":74797,"journal":{"name":"SIAM journal on mathematics of data science","volume":"147 7 1","pages":"431-463"},"PeriodicalIF":0.0,"publicationDate":"2022-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83112621","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3