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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. *Email sign-up and proof of purchase required
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

8.1 The directed graph of a nonnegative matrix

If you look carefully at Figure 8.1, you can probably figure out how to construct a weighted graph from a matrix. Just compare each row and the outgoing edge weights for nodes.

Each row is a node, and each element represents a directed and weighted edge. Edges of zero elements are omitted. The element in the i-th row and j-th column corresponds to an edge going from i to j. The resulting graph is called the directed graph (or digraph) of the matrix.

To unwrap the definition a bit, let’s check out the previous graph of the matrix

 ⌊ ⌋ 0.5 1 0 | | 3×3 A = |⌈0.2 0 2.2|⌉ ∈ ℝ . 1.8 2 0

Here’s the first row, corresponding to the edges coming out from the first node.

PIC

Figure 8.2: The first row corresponds to the edges coming out from the first node

Similarly, the first column corresponds to the edges coming into the first node.

PIC

Figure 8.3: The first column corresponds to the edges coming into the first node

Now, we can put all of this together. Figure 8.4...

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Mathematics of Machine Learning
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