Mathematical Theories of Machine Learning - Theory and Applications
暫譯: 機器學習的數學理論 - 理論與應用

Shi, Bin, Iyengar, S. S.

Mathematical Theories of Machine Learning - Theory and Applications

商品描述

This book studies mathematical theories of machine learning. The first part of the book explores the optimality and adaptivity of choosing step sizes of gradient descent for escaping strict saddle points in non-convex optimization problems. In the second part, the authors propose algorithms to find local minima in nonconvex optimization and to obtain global minima in some degree from the Newton Second Law without friction. In the third part, the authors study the problem of subspace clustering with noisy and missing data, which is a problem well-motivated by practical applications data subject to stochastic Gaussian noise and/or incomplete data with uniformly missing entries. In the last part, the authors introduce an novel VAR model with Elastic-Net regularization and its equivalent Bayesian model allowing for both a stable sparsity and a group selection.

商品描述(中文翻譯)

本書研究機器學習的數學理論。書的第一部分探討在非凸優化問題中，選擇梯度下降步長以逃離嚴格鞍點的最優性和適應性。第二部分，作者提出算法以在非凸優化中尋找局部最小值，並從牛頓第二定律中獲得某種程度的全局最小值，且不考慮摩擦。第三部分，作者研究帶有噪聲和缺失數據的子空間聚類問題，這是一個受到實際應用數據影響的問題，數據受到隨機高斯噪聲和/或均勻缺失條目的不完整數據的影響。最後一部分，作者介紹了一種具有彈性網路正則化的新型 VAR 模型及其等效的貝葉斯模型，允許同時實現穩定的稀疏性和群組選擇。

作者簡介

Bin Shi is a Ph.D. candidate in the School of Computing and Information Sciences at FIU under the supervision of Professor Sitharama S. Iyengar. His preliminary research focuses on the theory of machine learning, especially on optimization. Bin Shi received his B.S. of Applied Math from Ocean University of China, China in 2006, Master of Pure Mathematics from Fudan University, China in 2011 and Master of Theoretical Physics from University of Massachusetts Dartmouth in 2015. His research interests focus on statistical machine learning and optimization, some theoretical computer science.

Dr. S.S. Iyengar is the Distinguished University Professor, Ryder Professor of Computer Science and Director of the School of Computing and Information Sciences at Florida International University (FIU), Miami. He is also the founding director of the Discovery Lab. Prior to joining FIU, Dr. Iyengar was the Roy Paul Daniel's Distinguished Professor and Chairman of the Computer Science department for over 20 years at Lousiana State University. He has also worked as a visiting scientist at Oak Ridge National Lab, Jet Propulsion Lab, Satish Dhawan Professor at IISc and Homi Bhabha Professor at IGCAR, Kalpakkam and University of Paris and visited Tsinghua University, Korea Advanced Institute of Science and Technology (KAIST) etc. Professor Iyengar is an IEEE Distinguished Visitor, SIAM Distinguished Lecturer, and ACM National Lecturer and has won many other awards like Distinguished Research Master's award, Hub Cotton award of Faculty Excellence (LSU), Rain Maker awards (LSU), Florida Information Technology award (IT2), Distinguished Research award from Tunisian Mathematical Society etc. During the last four decades, he has supervised over 55 Ph.D. students, 100 Master's students, and many undergraduate students who are now faculty at Major Universities worldwide or Scientists or Engineers at National Labs/Industries around the world. He has published more than 500 research papers, has authored/co-authored and edited 22 books. His books are published by MIT Press, John Wiley, and Sons, CRC Press, Prentice Hall, Springer Verlag, IEEE Computer Society Press, etc. One of his books titled \Introduction to Parallel Algorithms" has been translated to Chinese.

作者簡介(中文翻譯)

施斌是佛羅里達國際大學（FIU）計算與資訊科學學院的博士候選人，指導教授為Sitharama S. Iyengar教授。他的初步研究專注於機器學習理論，特別是優化方面。施斌於2006年獲得中國海洋大學應用數學學士學位，2011年獲得中國復旦大學純數學碩士學位，2015年獲得美國麻省達特茅斯大學理論物理碩士學位。他的研究興趣集中在統計機器學習和優化，以及一些理論計算機科學領域。

S.S. Iyengar博士是佛羅里達國際大學（FIU）計算與資訊科學學院的傑出大學教授、計算機科學的Ryder教授及學院主任。他也是Discovery Lab的創始主任。在加入FIU之前，Iyengar博士在路易斯安那州立大學擔任Roy Paul Daniel's傑出教授及計算機科學系主任超過20年。他還曾在橡樹嶺國家實驗室、噴氣推進實驗室擔任訪問科學家，並在印度科學研究所擔任Satish Dhawan教授及在IGCAR、Kalpakkam和巴黎大學擔任Homi Bhabha教授，並曾訪問清華大學、韓國科學技術院（KAIST）等。Iyengar教授是IEEE傑出訪客、SIAM傑出講師及ACM全國講師，並獲得許多其他獎項，如傑出研究碩士獎、路易斯安那州立大學教職員卓越獎（Hub Cotton award）、路易斯安那州立大學雨水製造者獎（Rain Maker awards）、佛羅里達資訊技術獎（IT2）、突尼西亞數學學會的傑出研究獎等。在過去的四十年中，他指導了超過55名博士生、100名碩士生，以及許多本科生，這些學生如今在全球主要大學擔任教職或在國家實驗室/工業界擔任科學家或工程師。他已發表超過500篇研究論文，並撰寫/合著及編輯了22本書籍。他的書籍由MIT Press、John Wiley & Sons、CRC Press、Prentice Hall、Springer Verlag、IEEE Computer Society Press等出版。其中一本名為《Introduction to Parallel Algorithms》的書籍已被翻譯成中文。

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