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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 FREE CHAPTER
2. Chapter 1: Recap of Mathematical Notation and Terminology 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

Dirichlet processes

GPs are not the only type of process used in non-parametric Bayesian methods, although they are possibly the most used. In this section, we will introduce another type of stochastic process, the DP. As with GPs, we will use DPs as priors for functions that we want to make inferences about.

Since the last section was a lengthy one with a lengthy code example, we will keep this section short and only give a high-level view of DPs.

How do DPs differ from GPs?

As you might have guessed, we use a DP as a prior on a function. However, GPs already did that for us, so how do DPs differ from GPs? When we used GPs in GPR, the GP provided a prior for a generic function, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>f</mml:mi></mml:math>. There were no restrictions on the type of function, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>f</mml:mi></mml:math>, could be. Sometimes, we will want to model a particular type of function. For example, we might need to build a model of a probability distribution. In this case, we use a DP to construct our prior.

Let’s make that more explicit. I...

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