Mathematical Pictures at a Data Science Exhibition (Paperback)

This text provides deep and comprehensive coverage of the mathematical background for data science, including machine learning, optimal recovery, compressed sensing, optimization, and neural networks. In the past few decades, heuristic methods adopted by big tech companies have complemented existing scientific disciplines to form the new field of Data Science. This text embarks the readers on an engaging itinerary through the theory supporting the field. Altogether, twenty-seven lecture-length chapters with exercises provide all the details necessary for a solid understanding of key topics in data science. While the book covers standard material on machine learning and optimization, it also includes distinctive presentations of topics such as reproducing kernel Hilbert spaces, spectral clustering, optimal recovery, compressed sensing, group testing, and applications of semidefinite programming. Students and data scientists with less mathematical background will appreciate the appendices that provide more background on some of the more abstract concepts.

本書提供了深入且全面的數學背景知識，適用於資料科學中的機器學習、最佳恢復、壓縮感知、優化和神經網絡等領域。在過去的幾十年中，大型科技公司採用的啟發式方法已經補充了現有的科學學科，形成了新興的資料科學領域。本書帶領讀者踏上一段引人入勝的旅程，深入探討支持該領域的理論。全書共有二十七個講座長度的章節，並附有練習題，提供了所有必要的細節，以確保對資料科學的關鍵主題有扎實的理解。雖然本書涵蓋了機器學習和優化的標準內容，但還包括了獨特的主題介紹，如再生核希爾伯特空間、頻譜聚類、最佳恢復、壓縮感知、群體測試以及半定規劃的應用。對於數學背景較少的學生和資料科學家來說，附錄提供了更多關於一些抽象概念的背景知識，這將受到他們的讚賞。