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 456 pages

Edition 1st Edition

Languages

Python

Tools

PyTorch

Concepts

Data Science

Author (1):

Aleksander Molak

View More author details

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? 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. Index

20. Other Books You May Enjoy

Starting simple – observational data and linear regression

In previous chapters, we discussed the concept of association. In this section, we’ll quantify associations between variables using a regression model. We’ll see the geometrical interpretation of this model and demonstrate that regression can be performed in an arbitrary direction. For the sake of simplicity, we’ll focus our attention on linear cases. Let’s start!

Linear regression

Linear regression is a basic data-fitting algorithm that can be used to predict the expected value of a dependent (target) variable, <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> , given values of some predictor(s), . Formally, this is written as <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mover><mi>Y</mi><mo stretchy="true">ˆ</mo></mover><mrow><mi>X</mi><mo>=</mo><mi>x</mi></mrow></msub><mo>=</mo><mi>E</mi><mfenced open="[" close="]"><mrow><mi>Y</mi><mo>|</mo><mi>X</mi><mo>=</mo><mi>x</mi></mrow></mfenced></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:msub><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>Y</mml:mi></mml:mrow><mml:mo>^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>X</mml:mi><mml:mo>=</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:math> is the predicted value 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> given that takes the value(s) . is the expected value operator. Note that can be multidimensional. In such cases, is usually represented as a matrix, X, with shape <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>N</mml:mi><mml:mo>×</mml:mo><mml:mi>D</mml:mi></mml:math> , where is the number of observations and is the dimensionality of (the number of...