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15 Math Concepts Every Data Scientist Should Know

You're reading from   15 Math Concepts Every Data Scientist Should Know Understand and learn how to apply the math behind data science algorithms

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Product type Paperback
Published in Aug 2024
Publisher Packt
ISBN-13 9781837634187
Length 510 pages
Edition 1st Edition
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Author (1):
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David Hoyle David Hoyle
Author Profile Icon David Hoyle
David Hoyle
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Table of Contents (21) Chapters Close

Preface 1. Part 1: Essential Concepts
2. Chapter 1: Recap of Mathematical Notation and Terminology FREE CHAPTER 3. Chapter 2: Random Variables and Probability Distributions 4. Chapter 3: Matrices and Linear Algebra 5. Chapter 4: Loss Functions and Optimization 6. Chapter 5: Probabilistic Modeling 7. Part 2: Intermediate Concepts
8. Chapter 6: Time Series and Forecasting 9. Chapter 7: Hypothesis Testing 10. Chapter 8: Model Complexity 11. Chapter 9: Function Decomposition 12. Chapter 10: Network Analysis 13. Part 3: Selected Advanced Concepts
14. Chapter 11: Dynamical Systems 15. Chapter 12: Kernel Methods 16. Chapter 13: Information Theory 17. Chapter 14: Non-Parametric Bayesian Methods 18. Chapter 15: Random Matrices 19. Index 20. Other Books You May Enjoy

Linear algebra

In this section, we introduce notation to describe vectors and matrices, which are key mathematical objects that we will encounter again and again throughout this book.

Vectors

In many circumstances, we will want to represent a set of numbers together. For example, the numbers 7.3 and 1.2 might represent the values of two features that correspond to a data point in a training set. We often group these numbers together in brackets and write them as (7.3, 1.2) or [7.3, 1.2]. Because of the similarity to the way we write spatial coordinates, we tend to call a collection of numbers that are held together a vector. A vector can be two-dimensional, as in the example just given, or d-dimensional, meaning it contains d components, and so might look like <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mfenced separators="|"><mml:mrow><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfenced></mml:math>.

We can write a vector in two ways. We can write it as a row vector, going across the page, such as the following vector:

<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mfenced open="(" close=")"><mrow><msub><mi>x</mi><mn>1</mn></msub><mo>,</mo><msub><mi>x</mi><mn>2</mn></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mi>x</mi><mi>d</mi></msub></mrow></mfenced><mo>=</mo><mtext>a</mtext></mrow></mrow></math> d-dimensional row vector

Eq. 8

Alternatively, we can write it as a column vector going...

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15 Math Concepts Every Data Scientist Should Know
Published in: Aug 2024
Publisher: Packt
ISBN-13: 9781837634187
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