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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

3 (2)
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

20.1 Discrete random variables

Let’s play a simple game. I toss a coin, and if it comes up heads, you win $1 . If it is tails, you lose $2 .

Up until now, we were dealing with questions like the probability of winning. Say, for the coin toss, whether you win or lose, we have

P(heads) = P(tails) = 1. 2

Despite the equal chances of winning and losing, should you play this game? Let’s find out.

After n rounds, your earnings can be calculated by the number of heads times $1 minus the number of tails times $2 . If we divide total earnings by n, we obtain your average winnings per round. That is,

 total-winnings- your average winnings = n 1⋅#heads − 2⋅#tails = -------------------- n = 1⋅ #heads − 2⋅ #tails, n n

where #heads and #tails denote the number of heads and tails respectively.

Recall the frequentist interpretation of probability from Section 18.2.7? According to our intuition, we should have

 lim #heads- = P(heads) = 1, n→ ∞ n 2 #tails- 1- lni→m∞ n = P(tails) = 2.

This means that if you play long enough, your average winnings per round is

your average winnings = 1⋅P (heads)− 2 ⋅P(tails) = − 1. 2

So, as you are losing half a dollar per round on average, you definitely shouldn’t play this game.

Let’s formalize...

CONTINUE READING
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