Mathematical Foundations of Data Science / by Tomas Hrycej, Bernhard Bermeitinger, Matthias Cetto, Siegfried Handschuh.

Format:

Book

Author/Creator:

Hrycej, Tomas., Author.

Bermeitinger, Bernhard., Author.

Cetto, Matthias., Author.

Handschuh, Siegfried, Author.

Contributor:

SpringerLink (Online service)

Series:

Computer Science (SpringerNature-11645)

Texts in computer science 1868-095X

Texts in Computer Science, 1868-095X

Language:

English

Subjects (All):

Artificial intelligence-Data processing.

Computer science-Mathematics.

Discrete mathematics.

Computer arithmetic and logic units.

Data Science.

Discrete Mathematics in Computer Science.

Mathematical Applications in Computer Science.

Arithmetic and Logic Structures.

Local Subjects:

Data Science.

Discrete Mathematics in Computer Science.

Mathematical Applications in Computer Science.

Arithmetic and Logic Structures.

Physical Description:

1 online resource (XIII, 213 pages) : 108 illustrations, 98 illustrations in color.

Edition:

1st ed. 2023.

Contained In:

Springer Nature eBook

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2023.

System Details:

text file PDF

Summary:

Although it is widely recognized that analyzing large volumes of data by intelligent methods may provide highly valuable insights, the practical success of data science has led to the development of a sometimes confusing variety of methods, approaches and views. This practical 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 parameterization Investigates the mathematical principles involved 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.

Contents:

1. Data Science and its Tasks

2. Application Specific Mappings and Measuring the Fit to Data

3. Data Processing by Neural Networks

4. Learning and Generalization

5. Numerical Algorithms for Network Learning

6. Specific Problems of Natural Language Processing

7. Specific Problems of Computer Vision.

Other Format:

Printed edition:

ISBN:

978-3-031-19074-2

9783031190742

Access Restriction:

Restricted for use by site license.