MATHEMATICAL FOUNDATIONS OF MACHINE LEARNING: Unveiling the Mathematical Essence of Machine Learning (2024 Guide for Beginners)

By DAVID MACKAY

"Mathematical Foundations of Machine Learning" delves into the fundamental mathematical concepts that underpin the field of machine learning, providing a comprehensive exploration of the mathematical principles behind algorithms and models. Whether you're a data scientist, researcher, or enthusiast seeking a deeper understanding of the mathemati

• Language: English
• Publisher: DAVID MACKAY
• Release date: Mar 2, 2024
• ISBN: 9783689440053

DAVID MACKAY

David Mackay is a renowned mathematician and computer scientist based in London. With a wealth of experience in both academia and industry, Mackay has been instrumental in advancing the field of machine learning. He has authored numerous research papers and books, making complex mathematical concepts accessible to a wide audience.

Book preview

Introduction

Congratulations on your purchase of Mathematical Foundations of Machine Learning: Study Deep Learning through Data Science. Thank you for choosing this book.

The upcoming chapters delve into fundamental machine learning concepts and the significance of machine learning in addressing contemporary business challenges. The first chapter provides a comprehensive explanation of the four main types of machine learning algorithms available today, emphasizing the importance of machine learning. It covers representation, evaluation, and optimization as the three core concepts of machine learning. Additionally, the chapter introduces the concept of Statistical Learning, a descriptive statistics-based machine learning framework categorized as supervised or unsupervised.

In the second chapter, titled Machine Learning Algorithms, you will explore the development and application of popular supervised machine learning algorithms. Detailed insights into linear regression, logistic regression, and Naïve Bayes classification algorithms are provided. Moving on to the third chapter, Neural Network Learning Models, a comprehensive guide is presented for successfully developing neural network models. This includes building data pipelines and adopting specific neural network training approaches. The chapter outlines an end-to-end process for creating machine learning models, focusing on neural network models, and explores the components and functions of Artificial Neural Network and Perceptron models. Various applications of these advanced machine learning models for solving everyday business problems are also covered.

In the fourth chapter, Learning Through Uniform Convergence, the overlap of machine learning with statistics is examined. The borrowed statistical concept of Uniform Convergence is explored, allowing developers to assess the learnability of a problem based on data sample size using empirical risk minimizers. The chapter delves into Vapnik’s 1995 concept of the General Setting of Learning, central to machine learning development. A statistical explanation of the impact of Uniform Convergence on learnability with finite classes is provided, along with a discussion on potential learnability without Uniform Convergence.

The final chapter offers a comprehensive overview of cutting-edge data science technologies such as data mining and artificial intelligence. It details the Team Data Science Process (TDSP) lifecycle for structured data science projects, explaining various deliverables at each stage. The chapter explores how businesses leverage data science in decision-making and distinguishes between Business Intelligence and Data Science technology. Real-life examples are incorporated to enhance understanding, along with descriptions of multiple tools for further exploration and selective implementation in business.

While there are numerous books on this subject, thank you once again for choosing this one! Every effort has been made to ensure it is filled with useful information. Enjoy your reading!

Chapter 1: Introduction to Machine Learning

The concept of Artificial Intelligence Technology is rooted in the idea that computers can be engineered to demonstrate human-like intelligence and replicate human reasoning and learning abilities. This involves adapting to new inputs and carrying out tasks without requiring human intervention. The principle of artificial intelligence encompasses machine learning.

Machine Learning Technology (ML) refers to the concept of Artificial Intelligence Technology, primarily focusing on the designed capacity of computers to learn explicitly and self-train. This involves identifying information patterns to improve the underlying algorithm and making autonomous decisions without human involvement. The term machine learning was coined in 1959 by the pioneering professor of gaming and artificial intelligence, Arthur Samuel, during his tenure at IBM.

Machine learning posits that contemporary computers can be trained using targeted training datasets, easily tailored to create the required functionality. It employs a pattern-recognition method where past interactions and outcomes are recorded and revisited in a way that corresponds to its present position. Due to the need to process vast volumes of data, with fresh data constantly flowing in, machines must adapt to new data without being explicitly programmed by a person, considering the iterative aspect of machine learning.

Machine learning has close relations with the field of Statistics, focused on generating predictions using advanced computing tools and technologies. The research of mathematical optimization provides machine learning with techniques, theories, and implementation areas. In its application to address business issues, machine learning is also referred to as predictive analytics. In ML, the target is known as the label, while in statistics, it’s called the dependent variable. A variable in statistics is known as a feature in ML. Furthermore, feature creation in ML is referred to as transformation in statistics.

ML technology is closely related to data mining and optimization. ML and data mining often utilize the same techniques with significant overlap. ML focuses on generating predictions based on predefined characteristics of the given training data, while data mining identifies unknown characteristics in a large volume of data. Data mining uses many ML techniques but with distinct objectives. Machine learning also uses data mining techniques through unsupervised learning algorithms or as a pre-processing phase to enhance the prediction accuracy of the model.

The intersection of these two research areas stems from the fundamental assumptions they operate with. In machine learning, efficiency is generally assessed in terms of the model’s ability to reproduce known knowledge, while in knowledge discovery and information mining (KDD), the primary task is to discover new information. An uninformed or unsupervised technique, evaluated based on known information, will be easily outperformed by other supervised techniques. Conversely, supervised techniques cannot be used in a typical KDD task due to the lack of training data.

Data optimization is another area closely linked to machine learning. Various learning issues can be formulated as the minimization of certain loss function on a training dataset. Loss functions are derived as the difference between