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This book delves into the intricate relationship between mathematics and Machine Learning, providing readers with a comprehensive understanding of the mathematical concepts that underpin modern AI. From linear algebra and calculus to probability theory and statistics, each chapter explores a different mathematical topic and its application in machine learning. Throughout the book, readers will learn about fundamental concepts such as regression, classification, clustering, and Deep Learning, as well as advanced topics like reinforcement learning, GANs, and quantum machine learning. With a focus on both theoretical foundations and practical applications, "Machine Learning Mathematics" is an indispensable resource for anyone looking to deepen their understanding of the mathematical principles that drive contemporary AI algorithms.
This book aims to bridge the gap between mathematics and Machine Learning, showcasing the critical role of mathematics in solving complex data-driven tasks. Each chapter presents key mathematical concepts, accompanied by clear explanations and Python code samples, ensuring that readers can grasp the underlying principles. From matrix operations and optimization techniques to probability distributions and statistical inference, the book covers a wide range of mathematical topics that are essential for understanding Machine Learning algorithms. Additionally, the book explores various Machine Learning techniques, including linear regression, logistic regression, decision trees, neural networks, and more. By incorporating mathematical rigour into the discussion of Machine Learning, this book equips readers with the tools they need to effectively analyze and implement Machine Learning algorithms in practice.
1 Introduction to Machine Learning and Mathemat ics
2 Linear Algebra Review
3 Calculus for Machine Learning
4 Probability Theory
Descriptive Statistics
6 Simple Linear Regression
7 Multiple Linear Regression
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9 Gradient Descent
10 Gradient Descent Variants
11 Ordinary Least Squares (OLS)
12 Ordinary Least Squares (OLS)
13 Bayesian Inference
14 Naive Bayes Classifier
15 K-Nearest Neighbors (K-NN)
16 Decision Trees
17 Random Forests
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30 Transfer Learning
31 Hyperparameter Tuning
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50 Topological Data Analysis (TDA)
51 Spiking Neural Networks (SNN)
52 Federated Learning
53 Quantum Machine Learning