You're reading from Causal Inference and Discovery in Python Unlock the secrets of modern causal machine learning with DoWhy, EconML, PyTorch and more

Product type Paperback

Published in May 2023

Publisher Packt

ISBN-13 9781804612989

Length 466 pages

Edition 1st Edition

Languages

Python

Tools

PyTorch

Concepts

Data Science

Author (1):

Aleksander Molak

View More author details

Table of Contents (22) Chapters

Preface

1. Part 1: Causality – an Introduction

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

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. Chapter 16: Unlock Your Book’s Exclusive Benefits

How to unlock these benefits in three easy steps

20. Index

21. Other Books You May Enjoy

Positivity

In this short section, we’re going to learn about the positivity assumption, sometimes also called overlap or common support.

First, let’s think about why this assumption is called positivity. It has to do with (strictly) positive probabilities – in other words, probabilities greater than zero.

What needs to have a probability greater than zero?

The answer to that is the probability of your treatment given all relevant control variables (the variables that are necessary to identify the effect – let’s call them <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> ). Formally:

The preceding formula must hold for all values of <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> that are present in the population of interest (Hernán & Robins, 2020) and for all values of treatment <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>T</mml:mi></mml:math> .

Let’s imagine a simple example. In our dataset, we have 30 subjects described by one continuous feature <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> . Each subject either received or did not receive a binary treatment <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>T</mi></mrow></math> , and each subject has some continuous outcome <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> . Additionally...