You're reading from Mathematics of Machine Learning Master linear algebra, calculus, and probability for machine learning

Product type Paperback

Published in May 2025

Publisher Packt

ISBN-13 9781837027873

Length 730 pages

Edition 1st Edition

Concepts

Machine Learning

Author (1):

Tivadar Danka

View More author details

Table of Contents (36) Chapters

Introduction

Part 1: Linear Algebra FREE CHAPTER

1 Vectors and Vector Spaces

2 The Geometric Structure of Vector Spaces

3 Linear Algebra in Practice

4 Linear Transformations

5 Matrices and Equations

6 Eigenvalues and Eigenvectors

7 Matrix Factorizations

8 Matrices and Graphs

References

Part 2: Calculus

9 Functions

10 Numbers, Sequences, and Series

11 Topology, Limits, and Continuity

12 Differentiation

13 Optimization

14 Integration

References

Part 3: Multivariable Calculus

15 Multivariable Functions

16 Derivatives and Gradients

17 Optimization in Multiple Variables

References

Part 4: Probability Theory

18 What is Probability?

19 Random Variables and Distributions

20 The Expected Value

References

Part 5: Appendix

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Index

Appendix A It’s Just Logic

1. Appendix B The Structure of Mathematics

2. Appendix C Basics of Set Theory

3. Appendix D Complex Numbers

17.5 Problems

Problem 1. Let y ∈ℝⁿ be an arbitrary vector. The general version of the famous mean-squared error is defined by

n MSE (x) = 1-∑ (x − y )2. n i i i=1

Compute its gradient and implement it using the MultivariateFunction base class!

Problem 2. Let f : ℝ² →ℝ be the function defined by

2 2 f(x,y) = (2x − y)(y − x ).

Does f have a local extremum in x = (0,0)?

Problem 3. Use the previously implemented gradient_descent function to find the minimum of

2 2 f(x,y) = sin(x+ y)+ x y .

Experiment with various learning rates and initial values!

Problem 4. In the problem section of Chapter 13, we saw the improved version of gradient descent, called gradient descent with momentum. We can do the same in multiple variables: define

dn+1 = αdn − hf ′(xn), xn+1 = xn + dn,

where d₀ = 0 and x₀ is arbitrary. Implement it!

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