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

Exchangeability

In this section, we’ll introduce the exchangeability assumption (also known as the ignorability assumption) and discuss its relation to confounding.

Exchangeable subjects

The main idea behind exchangeability is the following: the treated subjects, had they been untreated, would have experienced the same average outcome as the untreated did (being actually untreated) and vice versa (Hernán & Robins, 2020).

Formally speaking, exchangeability is usually defined as:

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mrow><mrow><mfenced open="{" close="}"><mrow><msup><mi>Y</mi><mn>0</mn></msup><mo>,</mo><msup><mi>Y</mi><mn>1</mn></msup></mrow></mfenced><mo>⫫</mo><mi mathvariant="normal">T</mi><mo>|</mo><mi mathvariant="normal">Z</mi></mrow></mrow></mrow></math>

In the preceding formula, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:msup><mml:mrow><mml:mi>Y</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup></mml:math> and are counterfactual outcomes under and respectively, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>Z</mml:mi></mml:math> is a vector of control variables. If you’re getting a feeling of confusion or even circularity when thinking about this definition, you’re most likely not alone. According to Pearl (2009), many people see this definition as difficult to understand.