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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

17.4 Summary

Although this chapter was short and sweet, we took quite a big step by dissecting the fine details of gradient descent in high dimensions. The chapter’s brevity is a testament to the power of vectorization: same formulas, code, and supercharged functionality. It’s quite unbelievable, but the simple algorithm

xn+1 = xn − h∇f (xn)

is behind most of the neural network models. Yes, even state-of-the-art ones.

This lies on the same theoretical foundations as the univariate case, but instead of checking the positivity of the second derivatives, we have to study the full Hessian matrix Hf. To be more precise, we have learned that a critical point f(a) = 0 is

  1. a local minimum if all the eigenvalues of Hf(a) are positive,
  2. and a local maximum if all the eigenvalues of Hf(a) are negative.

Deep down, this is the reason why gradient descent works. And with this, we have finished our study of calculus, both in single and multiple variables.

Take a deep breath and relax a bit. We...

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Mathematics of Machine Learning
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