You're reading from Causal Inference and Discovery in Python

Product type Book

Published in May 2023

Publisher Packt

ISBN-13 9781804612989

Pages 456 pages

Edition 1st Edition

Languages

Concepts

Data Science

Author (1):

Aleksander Molak

Table of Contents (21) Chapters

Preface

1. Part 1: Causality – an Introduction

2. Chapter 1: Causality – Hey, We Have Machine Learning, So Why Even Bother?

3. Chapter 2: Judea Pearl and the Ladder of Causation

4. Chapter 3: Regression, Observations, and Interventions

5. Chapter 4: Graphical Models

6. Chapter 5: Forks, Chains, and Immoralities

7. Part 2: Causal Inference

8. Chapter 6: Nodes, Edges, and Statistical (In)dependence

9. Chapter 7: The Four-Step Process of Causal Inference

10. Chapter 8: Causal Models – Assumptions and Challenges

11. Chapter 9: Causal Inference and Machine Learning – from Matching to Meta-Learners

12. Chapter 10: Causal Inference and Machine Learning – Advanced Estimators, Experiments, Evaluations, and More

13. Chapter 11: Causal Inference and Machine Learning – Deep Learning, NLP, and Beyond

14. Part 3: Causal Discovery

15. Chapter 12: Can I Have a Causal Graph, Please?

16. Chapter 13: Causal Discovery and Machine Learning – from Assumptions to Applications

17. Chapter 14: Causal Discovery and Machine Learning – Advanced Deep Learning and Beyond

18. Chapter 15: Epilogue

19. Index

20. Other Books You May Enjoy

Graphs and distributions and how to map between them

In this section, we will focus on the mappings between the statistical and graphical properties of a system.

To be more precise, we’ll be interested in understanding how to translate between graphical and statistical independencies. In a perfect world, we’d like to be able to do it in both directions: from graph independence to statistical independence and the other way around.

It turns out that this is possible under certain assumptions.

The key concept in this chapter is one of independence. Let’s start by reviewing what it means.

How to talk about independence

Generally speaking, we say that two variables, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>X</mml:mi></mml:math> and , are independent when our knowledge about does not change our knowledge about (and vice versa). In terms of probability distributions, we can express it in the following way:

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math" display="block"><mml:mi>P</mml:mi><mml:mfenced separators="|"><mml:mrow><mml:mi>X</mml:mi></mml:mrow></mml:mfenced><mml:mo>=</mml:mo><mml:mi>P</mml:mi><mml:mo>(</mml:mo><mml:mi>X</mml:mi><mml:mo>|</mml:mo><mml:mi>Y</mml:mi><mml:mo>)</mml:mo></mml:math>

In other words: the marginal probability of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>Y</mml:mi></mml:math> is the same as the conditional probability of given...