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Mathematics of Machine Learning

Mathematics of Machine Learning

By : Tivadar Danka
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Mathematics of Machine Learning

Mathematics of Machine Learning

By: Tivadar Danka

Overview of this book

Mathematics of Machine Learning provides a rigorous yet accessible introduction to the mathematical underpinnings of machine learning, designed for engineers, developers, and data scientists ready to elevate their technical expertise. With this book, you’ll explore the core disciplines of linear algebra, calculus, and probability theory essential for mastering advanced machine learning concepts. PhD mathematician turned ML engineer Tivadar Danka—known for his intuitive teaching style that has attracted 100k+ followers—guides you through complex concepts with clarity, providing the structured guidance you need to deepen your theoretical knowledge and enhance your ability to solve complex machine learning problems. Balancing theory with application, this book offers clear explanations of mathematical constructs and their direct relevance to machine learning tasks. Through practical Python examples, you’ll learn to implement and use these ideas in real-world scenarios, such as training machine learning models with gradient descent or working with vectors, matrices, and tensors. By the end of this book, you’ll have gained the confidence to engage with advanced machine learning literature and tailor algorithms to meet specific project requirements.
Table of Contents (36 chapters)
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2
Part 1: Linear Algebra
11
References
12
Part 2: Calculus
19
References
20
Part 3: Multivariable Calculus
24
References
25
Part 4: Probability Theory
29
References
30
Part 5: Appendix
31
Other Books You May Enjoy
32
Index

7.5 Computing eigenvalues

In the last chapter, we reached the singular value decomposition, one of the pinnacle results of linear algebra. We laid out the theoretical groundwork to get us to this point.

However, one thing is missing: computing the singular value decomposition in practice. Without this, we can’t reap all the rewards this powerful tool offers. In this section, we’ll develop two methods for this purpose. One offers a deep insight into the behavior of eigenvectors, but it doesn’t work in practice. The other offers excellent performance, but it is hard to understand what is happening behind the formulas. Let’s start with the first one, illuminating how the eigenvectors determine the effects of a linear transformation!

7.5.1 Power iteration for calculating the eigenvectors of real symmetric matrices

If you recall, we discovered the singular value decomposition by tracing the problem back to the spectral decomposition of symmetric matrices. In...

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