Foundations of Machine Learning and AI: Geometry, Probability and Optimization
暫譯: 機器學習與人工智慧基礎：幾何、機率與優化

這本書從線性代數到機率與統計學習建立了一條單一且一致的路徑，這是現代資料科學、人工智慧（AI）和機器學習（ML）的雙支柱。書中同樣重視幾何（矩陣、光譜、投影）和不確定性（隨機性、估計、泛化），使讀者能夠從基本原則推導演算法並在大規模上穩健地實現它們。在整個過程中，幾何圖像（投影、角度、光譜）和機率論證（風險、集中、泛化）並行發展。每個概念都以真實的機器學習應用案例為動機，例如使用主成分分析（PCA）去噪、回歸中的病態條件、通過驗證曲線選擇正則化，或使用草圖加速大型最小二乘法。

Dr. Pradeep Singh is serving as an Assistant Professor (Grade--I) at the Indian Institute of Information Technology Surat, where he also serves as Associate Dean (R&D). He is faculty in the Department of Mathematics and Computational Sciences, and joint faculty in the Department of Computer Science & Engineering. His research spans Geometric Deep Learning, Neuro-symbolic AI, and Dynamical Systems. His research has appeared in premier venues, including IEEE Transactions; Knowledge-Based Systems; Neurocomputing; Chaos, Solitons & Fractals; and ECAI, contributing to the wider dialogue in AI and dynamical-systems research. He has authored multiple books: the Springer monographs Deep Learning Through the Prism of Tensors and The Geometry of Intelligence: Foundations of Transformer Networks, and the McGraw-Hill text Machine Learning and Artificial Intelligence. He earned his Ph.D. (2022) and Master's degree from IIT Delhi, specializing in Symbolic Systems, and a Bachelor's degree in Data Science from IIT Madras. Dr Singh secured All-India Rank 1 in GATE 2020, JAM 2015, and CSIR-NET 2019. He has also received highly competitive awards, including the National Board for Higher Mathematics (NBHM) Master's, Doctoral, and Post-Doctoral Fellowships awarded by the Department of Atomic Energy, India. In 2019, he was one of only two researchers nationwide to receive the Dr Shyama Prasad Mukherjee (SPM) Fellowship in Mathematics from CSIR, India. He is also a recipient of the prestigious Human Frontier Science Program Postdoctoral Fellowship, an international fellowship supporting frontier cross-disciplinary research.

Dr. Balasubramanian Raman received his Ph.D. from IIT Madras and his B.Sc. and M.Sc. in Mathematics from the University of Madras. He is a Professor and the Head of the Department of Computer Science and Engineering at IIT Roorkee, as well as the iHUB Divyasampark Chair Professor. He is also a Joint Faculty member in the Mehta Family School of Data Science and Artificial Intelligence at IIT Roorkee. With over 200 research papers published in reputed journals and conferences, his research interests span Machine Learning, Image and Video Processing, Computer Vision, and Pattern Recognition. Dr. Raman has served as a Guest Professor and Visiting Researcher at prestigious institutions such as Osaka Metropolitan University, Curtin University, the University of Cyberjaya, and the University of Windsor. He has held postdoctoral positions at Rutgers University and the University of Missouri-Columbia. Under his coaching, teams have achieved notable rankings in the ACM International Collegiate Programming Contest (ICPC) World Finals. He has been recognized with several awards, including the BOYSCAST Fellowship and the Ramkumar Prize for Outstanding Teaching and Research.

Dr. Pradeep Singh 目前擔任印度信息技術學院蘇拉特分校的助理教授（I級），同時擔任副院長（研究與發展）。他是數學與計算科學系的教員，並且在計算機科學與工程系擔任聯合教員。他的研究範疇包括幾何深度學習（Geometric Deep Learning）、神經符號人工智慧（Neuro-symbolic AI）和動態系統（Dynamical Systems）。他的研究成果發表於多個頂尖期刊，包括 IEEE Transactions、Knowledge-Based Systems、Neurocomputing、Chaos, Solitons & Fractals 以及 ECAI，為人工智慧和動態系統研究的廣泛對話做出了貢獻。他著有多本書籍，包括 Springer 的專著《Deep Learning Through the Prism of Tensors》和《The Geometry of Intelligence: Foundations of Transformer Networks》，以及 McGraw-Hill 的教材《Machine Learning and Artificial Intelligence》。他於 2022 年獲得博士學位，並在德里印度理工學院獲得碩士學位，專攻符號系統（Symbolic Systems），並在馬德拉斯印度理工學院獲得數據科學的學士學位。Dr. Singh 在 2020 年 GATE 考試中獲得全印度第一名，並在 2015 年 JAM 和 2019 年 CSIR-NET 考試中也取得優異成績。他還獲得了多項競爭激烈的獎項，包括由印度原子能部頒發的全國高等數學委員會（NBHM）碩士、博士及博士後獎學金。2019 年，他是全國僅有的兩位獲得 CSIR 頒發的 Dr. Shyama Prasad Mukherjee（SPM）數學獎學金的研究人員之一。他還是享有盛譽的人類前沿科學計劃博士後獎學金的獲得者，該獎學金支持前沿跨學科研究。

Dr. Balasubramanian Raman 於馬德拉斯印度理工學院獲得博士學位，並在馬德拉斯大學獲得數學的學士及碩士學位。他是印度理工學院魯爾基分校計算機科學與工程系的教授及系主任，同時擔任 iHUB Divyasampark 椅教授。他也是印度理工學院魯爾基分校梅赫塔家族數據科學與人工智慧學校的聯合教員。他在知名期刊和會議上發表了超過 200 篇研究論文，研究興趣涵蓋機器學習（Machine Learning）、影像與視頻處理（Image and Video Processing）、計算機視覺（Computer Vision）和模式識別（Pattern Recognition）。Dr. Raman 曾在大阪市立大學、科廷大學、賽伯賈亞大學和溫莎大學等知名機構擔任客座教授和訪問研究員。他曾在羅格斯大學和密蘇里大學哥倫比亞分校擔任博士後職位。在他的指導下，團隊在 ACM 國際大學程式設計競賽（ICPC）世界總決賽中取得了顯著的排名。他獲得了多項獎項，包括 BOYSCAST 獎學金和 Ramkumar 獎，以表彰其卓越的教學和研究。