Found. Trends Mach. Learn.最新文献

Tensor Regression 张量的回归

Found. Trends Mach. Learn. Pub Date : 2023-08-22 DOI: 10.1561/2200000087

Jiani Liu, Ce Zhu, Zhen Long, Yipeng Liu

{"title":"Tensor Regression","authors":"Jiani Liu, Ce Zhu, Zhen Long, Yipeng Liu","doi":"10.1561/2200000087","DOIUrl":"https://doi.org/10.1561/2200000087","url":null,"abstract":"Regression analysis is a key area of interest in the field of data analysis and machine learning which is devoted to exploring the dependencies between variables, often using vectors. The emergence of high dimensional data in technologies such as neuroimaging, computer vision, climatology and social networks, has brought challenges to traditional data representation methods. Tensors, as high dimensional extensions of vectors, are considered as natural representations of high dimensional data. In this book, the authors provide a systematic study and analysis of tensor-based regression models and their applications in recent years. It groups and illustrates the existing tensor-based regression methods and covers the basics, core ideas, and theoretical characteristics of most tensor-based regression methods. In addition, readers can learn how to use existing tensor-based regression methods to solve specific regression tasks with multiway data, what datasets can be selected, and what software packages are available to start related work as soon as possible. Tensor Regression is the first thorough overview of the fundamentals, motivations, popular algorithms, strategies for efficient implementation, related applications, available datasets, and software resources for tensor-based regression analysis. It is essential reading for all students, researchers and practitioners of working on high dimensional data.","PeriodicalId":431372,"journal":{"name":"Found. Trends Mach. Learn.","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128073646","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

Tutorial on Amortized Optimization 平摊优化教程

Found. Trends Mach. Learn. Pub Date : 2022-02-01 DOI: 10.1561/9781638282099

Brandon Amos

引用次数: 7

Machine Learning for Automated Theorem Proving: Learning to Solve SAT and QSAT 自动定理证明的机器学习:学习解决SAT和QSAT

Found. Trends Mach. Learn. Pub Date : 2021-10-26 DOI: 10.1561/2200000081

S. Holden

引用次数: 11

A unifying tutorial on Approximate Message Passing 关于近似消息传递的统一教程

Found. Trends Mach. Learn. Pub Date : 2021-05-05 DOI: 10.1561/2200000092

Oliver Y. Feng, R. Venkataramanan, Cynthia Rush, R. Samworth

引用次数: 44

Reinforcement Learning, Bit by Bit 一点一点的强化学习

Found. Trends Mach. Learn. Pub Date : 2021-03-06 DOI: 10.1561/2200000097

Xiuyuan Lu, Benjamin Van Roy, V. Dwaracherla, M. Ibrahimi, Ian Osband, Zheng Wen

引用次数: 51

Data Analytics on Graphs Part I: Graphs and Spectra on Graphs 图上的数据分析第一部分:图和图上的谱

Found. Trends Mach. Learn. Pub Date : 2020-12-30 DOI: 10.1561/2200000078-1

L. Stanković, D. Mandic, M. Daković, M. Brajović, Bruno Scalzo, Shengxi Li, A. Constantinides

{"title":"Data Analytics on Graphs Part I: Graphs and Spectra on Graphs","authors":"L. Stanković, D. Mandic, M. Daković, M. Brajović, Bruno Scalzo, Shengxi Li, A. Constantinides","doi":"10.1561/2200000078-1","DOIUrl":"https://doi.org/10.1561/2200000078-1","url":null,"abstract":"The area of Data Analytics on graphs promises a paradigm shift, as we approach information processing of new classes of data which are typically acquired on irregular but structured domains (such as social networks, various ad-hoc sensor networks). Yet, despite the long history of Graph Theory, current approaches tend to focus on aspects of optimisation of graphs themselves rather than on eliciting strategies relevant to the objective application of the graph paradigm, such as detection, estimation, statistical and probabilistic inference, clustering and separation from signals and data acquired on graphs. In order to bridge this gap, we first revisit graph topologies from a Data Analytics point of view, to establish a taxonomy of graph networks through a linear algebraic formalism of graph topology (vertices, connections, directivity). This serves as a basis for spectral Ljubiša Stanković, Danilo Mandic, Miloš Daković, Miloš Brajović, Bruno Scalzo, Shengxi Li and Anthony G. Constantinides (2020), “Data Analytics on Graphs Part I: Graphs and Spectra on Graphs”, Foundations and Trends © in Machine Learning: Vol. 13, No. 1, pp 1–157. DOI: 10.1561/2200000078-1.","PeriodicalId":431372,"journal":{"name":"Found. Trends Mach. Learn.","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124544804","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: 23

Data Analytics on Graphs Part III: Machine Learning on Graphs, from Graph Topology to Applications 图上的数据分析第三部分:图上的机器学习，从图拓扑到应用

Found. Trends Mach. Learn. Pub Date : 2020-12-30 DOI: 10.1561/2200000078-3

L. Stanković, D. Mandic, M. Daković, M. Brajović, Bruno Scalzo, Shengxi Li, A. Constantinides

引用次数: 34

Data Analytics on Graphs Part II: Signals on Graphs 图上的数据分析第二部分:图上的信号

Found. Trends Mach. Learn. Pub Date : 2020-12-30 DOI: 10.1561/2200000078-2

L. Stanković, D. Mandic, M. Daković, M. Brajović, Bruno Scalzo, Shengxi Li, A. Constantinides

引用次数: 24

Spectral Methods for Data Science: A Statistical Perspective 数据科学的光谱方法:统计学视角

Found. Trends Mach. Learn. Pub Date : 2020-12-15 DOI: 10.1561/2200000079

Yuxin Chen, Yuejie Chi, Jianqing Fan, Cong Ma

{"title":"Spectral Methods for Data Science: A Statistical Perspective","authors":"Yuxin Chen, Yuejie Chi, Jianqing Fan, Cong Ma","doi":"10.1561/2200000079","DOIUrl":"https://doi.org/10.1561/2200000079","url":null,"abstract":"Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In a nutshell, spectral methods refer to a collection of algorithms built upon the eigenvalues (resp. singular values) and eigenvectors (resp. singular vectors) of some properly designed matrices constructed from data. A diverse array of applications have been found in machine learning, data science, and signal processing. Due to their simplicity and effectiveness, spectral methods are not only used as a stand-alone estimator, but also frequently employed to initialize other more sophisticated algorithms to improve performance. \u0000While the studies of spectral methods can be traced back to classical matrix perturbation theory and methods of moments, the past decade has witnessed tremendous theoretical advances in demystifying their efficacy through the lens of statistical modeling, with the aid of non-asymptotic random matrix theory. This monograph aims to present a systematic, comprehensive, yet accessible introduction to spectral methods from a modern statistical perspective, highlighting their algorithmic implications in diverse large-scale applications. In particular, our exposition gravitates around several central questions that span various applications: how to characterize the sample efficiency of spectral methods in reaching a target level of statistical accuracy, and how to assess their stability in the face of random noise, missing data, and adversarial corruptions? In addition to conventional $ell_2$ perturbation analysis, we present a systematic $ell_{infty}$ and $ell_{2,infty}$ perturbation theory for eigenspace and singular subspaces, which has only recently become available owing to a powerful \"leave-one-out\" analysis framework.","PeriodicalId":431372,"journal":{"name":"Found. Trends Mach. Learn.","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131488777","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: 111

Divided Differences, Falling Factorials, and Discrete Splines: Another Look at Trend Filtering and Related Problems 可分差、下降阶乘和离散样条:趋势过滤和相关问题的另一个视角

Found. Trends Mach. Learn. Pub Date : 2020-03-09 DOI: 10.1561/2200000099

R. Tibshirani

引用次数: 13