Название: Mathematical Foundations of Data Science
Автор: Tomas Hrycej, Bernhard Bermeitinger, Matthias Cetto, Siegfried Handschuh
Издательство: Springer
Серия: Texts in Computer Science
Год: 2023
Страниц: 219
Язык: английский
Формат: pdf (true)
Размер: 10.1 MB

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.

Data Science is a rapidly expanding field with increasing relevance. There are correspondingly numerous textbooks about the topic. They usually focus on various Data Science methods. In a growing field, there is a danger that the number of methods grows, too, in a pace that it is difficult to compare their specific merits and application focus.

To cope with this method avalanche, the user is left alone with the judgment about the method selection. He or she can be helped only if some basic principles such as fitting model to data, generalization, and abilities of numerical algorithms are thoroughly explained, independently from the methodical approach. Unfortunately, these principles are hardly covered in the textbook variety. This book would like to close this gap.

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. This book is appropriate for advanced undergraduate or master’s students in Computer Science, Artificial Intelligence, statistics or related quantitative subjects, as well as people from other disciplines who want to solve Data Science tasks. Elements of this book can be used earlier, e.g., in introductory courses for Data Science, engineering, and science students who have the required mathematical background.

We developed this book to support a semester course in Data Science, which is the first course in our Data Science specialization in Computer Science. To give you an example of how we use this book in our own lectures, our Data Science course consists of two parts:

• In the first part, a general framework for solving Data Science tasks is described, with a focus on facts that can be supported by mathematical and statistical arguments. This part is covered by this book.

• In the second part of the course, concrete methods from multivariate statistics and Machine Learning are introduced. For this part, many well-known Springer textbooks are available (e.g., those by Hastie and Tibshirani or Bishop), which are used to accompany this part of the course. We did not intend to duplicate this voluminous work in our book.