Название: Algorithmic Mathematics in Machine LearningАвтор: Bastian Bohn, Jochen Garcke, Michael Griebel
Издательство: SIAM (Society for Industrial and Applied Mathematics)
Серия: Data Science Book Series
Год: 2024
Страниц: 235
Язык: английский
Формат: pdf (true)
Размер: 25.5 MB
This unique book explores several well-known Machine Learning and data analysis algorithms from a mathematical and programming perspective. The authors present Machine Learning methods, review the underlying mathematics, and provide programming exercises to deepen the reader's understanding; accompany application areas with exercises that explore the unique characteristics of real-world data sets (e.g., image data for pedestrian detection, biological cell data); and provide new terminology and background information on mathematical concepts, as well as exercises, in “info-boxes” throughout the text.
Machine Learning itself is a subarea of Artificial Intelligence (AI) and a related subject to data mining (DM). As a core topic, AI is concerned with all aspects of machine intelligence, i.e., with cases where a (real or virtual) artificial device is able to take actions to achieve a given goal by using information, e.g., from sensors, on the surrounding environment in which it lives. The term data mining, on the other hand, is usually used to describe methodologies with the goal of detecting statistical trends or relations within or in between different data sets. Oftentimes, ML and DM are used somewhat ambiguously. To better distinguish these two areas, ML is typically used when the goal is to predict certain values or outcomes from given data, whereas DM is used when there is no prediction sought, but rather a statistical analysis of the data.
In this book, we explore several well-known Machine Learning and data analysis algorithms from both a mathematical perspective and a programming perspective. These two aspects will always serve as the main guidelines throughout all chapters and tasks. In this way, we want to specifically address readers with a background in mathematics, who are interested in both the mathematical foundation of the most commonly used modern-day Machine Learning algorithms and the practical knowledge on implementing and using them. Furthermore, we will apply the algorithms to real-world data sets to get an intuition on the specific needs in different relevant applications. In particular, we will get to know use-cases and data sets from the fields of hand-written digit recognition, pedestrian detection in images, and biological single-cell analysis, for instance.
Most chapters of this book will be accompanied by a variety of programming exercises, which are intended to be solved in Jupyter notebooks. There, we also provide templates for some of the programming exercises. We assume that the reader is familiar with basic Python tools and libraries. However, we also provide a brief tutorial on the most important Python and NumPy concepts. Moreover, we will learn how to use the Machine Learning libraries Scikit-Learn and Keras. The latter serves as an interface to Tensor Flow.
Algorithmic Mathematics in Machine Learning is intended for mathematicians, computer scientists, and practitioners who have a basic mathematical background in analysis and linear algebra, but little or no knowledge of Machine Learning and related algorithms. Researchers in the natural sciences and engineers interested in acquiring the mathematics needed to apply the most popular Machine Learning algorithms will also find this book useful.
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