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

Are there other criteria out there? Let’s do-calculus!

In the real world, not all causal graphs will have a structure that allows the use of the back-door or front-door criteria. Does this mean that we cannot do anything about them?

Fortunately, no. Back-door and front-door criteria are special cases of a more general framework called do-calculus (Pearl, 2009). Moreover, do-calculus has been proven to be complete (Shpitser and Pearl, 2006), meaning that if there is an identifiable causal effect in a given DAG, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>G</mml:mi></mml:math> , it can be found using the rules of do-calculus.

What are these rules?

The three rules of do-calculus

Before we can answer the question, we need to define some new helpful notation.

Given a DAG <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>G</mml:mi></mml:math> , we can say that is a modification of , where we removed all the incoming edges to the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi>X</mi></mrow></mrow></math> . We will call <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:msub><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:munder underaccent="false"><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mo>_</mml:mo></mml:munder></mml:mrow></mml:msub></mml:math> a modification of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>G</mml:mi></mml:math> , where we removed all the outgoing edges from the node .

For example, will denote a DAG, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>G</mml:mi></mml:math> , where we removed all the incoming edges to the...