Mathematical Foundations of Data Science

This textbook aims to point out the most important principles of data analysis from the mathematical point of view. Specifically, it selected these questions for exploring: Which are the principles necessary to understand the implications of an application, and which are necessary to understand the conditions for the success of methods used? Theory is presented only to the degree necessary to apply it properly, striving for the balance between excessive complexity and oversimplification. Its primary focus is on principles crucial for application success.

Topics and features:

• Focuses on approaches supported by mathematical arguments, rather than sole computing experiences
• Investigates conditions under which numerical algorithms used in data science operate, and what performance can be expected from them
• Considers key data science problems: problem formulation including optimality measure; learning and generalization in relationships to training set size and number of free parameters; and convergence of numerical algorithms
• Examines original mathematical disciplines (statistics, numerical mathematics, system theory) as they are specifically relevant to a given problem
• Addresses the trade-off between model size and volume of data available for its identification and its consequences for model parametrization
• Investigates the mathematical principles involves with natural language processing and computer vision
• Keeps subject coverage intentionally compact, focusing on key issues of each topic to encourage full comprehension of the entire book

Although this core textbook aims directly at students of computer science and/or data science, it will be of real appeal, too, to researchers in the field who want to gain a proper understanding of the mathematical foundations "beyond" the sole computing experience.

Tomas Hrycej is a pioneer in the field of artificial intelligence and neural networks, having worked in this field since the 1980s. As an example of his pioneering deeds, he worked in the 1990s at Daimler Research on self-driving cars. In his doctoral thesis, he dealt with modular learning concepts in neural networks. His most important research stations were Daimler AG, Bosch GmbH, the University of Passau and currently the University of St. Gallen. He is the author of three monographs: Neurocontrol - Towards an Industrial Control Methodology, Modular Learning in Neural Networks (both Wiley-Interscience) and Robust Control ("Robuste Regelung", Springer), as well as about 60 publications in journals and conference proceedings.

Bernhard Bermeitinger is a research assistant at the Chair of Data Science and Natural Language Processing and is currently working on his PhD in Deep Learning.

Matthias Cetto is a visiting researcher at the Chair of Data Science and Natural Language Processing and conducts research in the field of Natural Language Processing.
Siegfried Handschuh is a Full professor of Data Science and Natural Language Processing at the Institute of Computer Science at the University of St. Gallen, Switzerland. He received his PhD from the University of Karlsruhe (now: Karlsruhe Institute of Technology), Germany. His PhD thesis was in Collaboration with Stanford University as part of the American DARPA DAML project. Siegfried spend eight year in Ireland, where he led the Knowledge Discovery Unit at the Insight Centre for Data Analytics in Galway. He worked with multinational companies such as HP, SAP, IBM, Motorola and Elsevier Publishing. He also conducted research on the Digital Aristotle initiative, a project by Microsoft co-funder Paul Allen. He has published over 300 scientific papers and is highly cited with an h-index of 41 (according to Google Scholar). This makes him one of the top-ranked Computer Scientists in Switzerland.

Tomas Hrycej是人工智慧和神經網路領域的先驅者，自1980年代以來一直在這個領域工作。作為他開拓性工作的一個例子，他在1990年代在戴姆勒研究部門工作，研究自動駕駛汽車。在他的博士論文中，他探討了神經網路中的模塊化學習概念。他最重要的研究機構包括戴姆勒股份公司、博世有限公司、帕索大學和目前的聖加倫大學。他是三本專著的作者：《神經控制-邁向工業控制方法論》、《神經網路中的模塊化學習》（均由Wiley-Interscience出版）和《魯棒控制》（Springer出版），以及約60篇期刊和會議論文。

Bernhard Bermeitinger是數據科學和自然語言處理主席的研究助理，目前正在進行深度學習的博士研究。

Matthias Cetto是數據科學和自然語言處理主席的訪問研究員，從事自然語言處理領域的研究。
Siegfried Handschuh是瑞士聖加倫大學計算機科學研究所的數據科學和自然語言處理的全職教授。他在德國卡爾斯魯厄大學（現卡爾斯魯厄理工學院）獲得博士學位。他的博士論文是在美國DARPA DAML計劃的一部分，與斯坦福大學合作完成的。Siegfried在愛爾蘭度過了八年，在那裡他領導了加爾韋的洞察數據分析中心的知識發現單位。他曾與惠普、SAP、IBM、摩托羅拉和Elsevier Publishing等跨國公司合作。他還參與了由微軟聯合創始人保羅·艾倫發起的Digital Aristotle計劃的研究。他發表了300多篇科學論文，並且在Google Scholar上的h指數為41，是瑞士排名靠前的計算機科學家之一。