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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

16
Derivatives and Gradients

Now that we understand why multivariate functions and high-dimensional spaces are more complex than the single-variable case we studied earlier, it’s time to see how to do things in the general case.

To recap quickly, our goal in machine learning is to optimize functions with millions of variables. For instance, think about a neural network N(x,w) trained for binary classification, where

  • x n is the input data,
  • w m is the vector compressing all of the weight parameters,
  • and N(x,w) [0,1] is the prediction, representing the probability of belonging to the positive class.

In the case of, say, binary cross-entropy loss, we have the loss function

 d L(w ) = − ∑ y log N (x ,w ), i i k=1

where xi is the i-th data point with ground truth yi ∈{0,1}. See, I told you that we have to write much more in multivariable calculus. (We’ll talk about binary cross-entropy loss in Chapter 20.)

Training the neural network is the same as finding a...

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Mathematics of Machine Learning
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