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You're reading from  Causal Inference and Discovery in Python

Product typeBook
Published inMay 2023
PublisherPackt
ISBN-139781804612989
Edition1st Edition
Concepts
Data Science
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Author (1)
Aleksander Molak
Aleksander Molak
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Aleksander Molak

Aleksander Molak is a Machine Learning Researcher and Consultant who gained experience working with Fortune 100, Fortune 500, and Inc. 5000 companies across Europe, the USA, and Israel, designing and building large-scale machine learning systems. On a mission to democratize causality for businesses and machine learning practitioners, Aleksander is a prolific writer, creator, and international speaker. As a co-founder of Lespire, an innovative provider of AI and machine learning training for corporate teams, Aleksander is committed to empowering businesses to harness the full potential of cutting-edge technologies that allow them to stay ahead of the curve.
Read more about Aleksander Molak

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The back-door criterion

The back-door criterion is most likely the best-known technique to find causal estimands given a graph. And the best part is that you already know it!

In this section, we’re going to learn how the back-door criterion works. We’ll study its logic and learn about its limitations. This knowledge will allow us to find good causal estimands in a broad class of cases. Let’s start!

What is the back-door criterion?

The back-door criterion aims at blocking spurious paths between our treatment and outcome nodes. At the same time, we want to make sure that we leave all directed paths unaltered and are careful not to create new spurious paths.

Formally speaking, a set of variables, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi mathvariant="script">Z</mml:mi></mml:math>, satisfies the back-door criterion, given a graph <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>, and a pair of variables, if no node in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi mathvariant="script">Z</mml:mi></mml:math> is a descendant of <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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi mathvariant="script">Z</mml:mi></mml:math> blocks all the paths between <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 <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> that contain an arrow into <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> (Pearl, Glymour, and Jewell, 2016).

In the preceding definition, <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:mo>→</mml:mo><mml:mo>…</mml:mo><mml:mo>→</mml:mo><mml:mi>Y</mml:mi></mml:math> means that...

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Causal Inference and Discovery in Python
Published in: May 2023Publisher: PacktISBN-13: 9781804612989
© 2023 Packt Publishing Limited All Rights Reserved

Author (1)

author image
Aleksander Molak

Aleksander Molak is a Machine Learning Researcher and Consultant who gained experience working with Fortune 100, Fortune 500, and Inc. 5000 companies across Europe, the USA, and Israel, designing and building large-scale machine learning systems. On a mission to democratize causality for businesses and machine learning practitioners, Aleksander is a prolific writer, creator, and international speaker. As a co-founder of Lespire, an innovative provider of AI and machine learning training for corporate teams, Aleksander is committed to empowering businesses to harness the full potential of cutting-edge technologies that allow them to stay ahead of the curve.
Read more about Aleksander Molak

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