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Fundamental Mathematical Concepts for Machine Learning in Science

  • Textbook
  • © 2024

Overview

Authors:
  1. Umberto Michelucci

    1. TOELT.AI, Dübendorf, Switzerland

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  • Clearly explains the mathematical underpinnings essential for a robust understanding of machine learning algorithms
  • Coverage is tailored to students and researchers in all natural science areas, in addition to computer scientists
  • Accessible yet rigorous mathematical approach supplemented with website https://fmcmls-book.org/ and instructor manual

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About this book

This book is for individuals with a scientific background who aspire to apply machine learning within various natural science disciplines—such as physics, chemistry, biology, medicine, psychology and many more. It elucidates core mathematical concepts in an accessible and straightforward manner, maintaining rigorous mathematical integrity. For readers more versed in mathematics, the book includes advanced sections that are not prerequisites for the initial reading. It ensures concepts are clearly defined and theorems are proven where it's pertinent. Machine learning transcends the mere implementation and training of algorithms; it encompasses the broader challenges of constructing robust datasets, model validation, addressing imbalanced datasets, and fine-tuning hyperparameters. These topics are thoroughly examined within the text, along with the theoretical foundations underlying these methods. Rather than concentrating on particular algorithms this book focuses on the comprehensive concepts and theories essential for their application. It stands as an indispensable resource for any scientist keen on integrating machine learning effectively into their research.

Numerous texts delve into the technical execution of machine learning algorithms, often overlooking the foundational concepts vital for fully grasping these methods. This leads to a gap in using these algorithms effectively across diverse disciplines. For instance, a firm grasp of calculus is imperative to comprehend the training processes of algorithms and neural networks, while linear algebra is essential for the application and efficient training of various algorithms, including neural networks. Absent a solid mathematical base, machine learning applications may be, at best, cursory, or at worst, fundamentally flawed. This book lays the foundation for a comprehensive understanding of machine learning algorithms and approaches.

 

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xvii
    Download chapter PDF

  2. Introduction

    • Umberto Michelucci
    Pages 1-8

  3. Machine Learning: History and Terminology

    • Umberto Michelucci
    Pages 9-20

  4. Calculus and Optimisation for Machine Learning

    • Umberto Michelucci
    Pages 21-62

  5. Linear Algebra

    • Umberto Michelucci
    Pages 63-98

  6. Statistics and Probability for Machine Learning

    • Umberto Michelucci
    Pages 99-135

  7. Sampling Theory (a.k.a. Creating a Dataset Properly)

    • Umberto Michelucci
    Pages 137-151

  8. Model Validation and Selection

    • Umberto Michelucci
    Pages 153-184

  9. Unbalanced Datasets and Machine Learning Metrics

    • Umberto Michelucci
    Pages 185-212

  10. Hyper-parameter Tuning

    • Umberto Michelucci
    Pages 213-227

  11. Feature Importance and Selection

    • Umberto Michelucci
    Pages 229-242

  12. Back Matter

    Pages 243-249
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Authors and Affiliations

  • TOELT.AI, Dübendorf, Switzerland

    Umberto Michelucci

About the author

Umberto Michelucci has a PhD in Machine Learning and Physics from the University of Portsmouth. He is the cofounder and Chief AI scientist of TOELT LLC, a company aiming to develop new and modern teaching, coaching, and research methods for AI to make AI technologies and research accessible to every company and everyone. He’s an expert in numerical simulation, statistics, data science, and machine learning. In addition to several years of research experience at the George Washington University (USA) and the University of Augsburg (DE), he has 15 years of practical experience in the fields of data warehouse, data science, and machine learning. His first book, Applied Deep Learning—A Case-Based Approach to Understanding Deep Neural Networks, was published by Apress in 2018. He followed with Convolutional and Recurrent Neural Networks Theory and Applications in 2019. He’s very active in research in the field of artificial intelligence. He publishes his research results regularly in leading journals and gives regular talks at international conferences. Umberto studied physics and mathematics. Sharing is caring—for that, he is a lecturer at the ZHAW University of Applied Sciences for deep learning and neural networks theory and applications. He’s also responsible at Helsana Versicherung AG for research and collaborations with universities in the area of AI. He is also a Google Developer Expert in Machine Learning based in Switzerland.

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