Skip navigation
Hardcover | $45.00 X | £37.95 | 288 pp. | 7 x 9 in | 15 color illus., 36 b&w illus. | November 2017 | ISBN: 9780262037310
eBook | $45.00 X | December 2017 | ISBN: 9780262344289
Mouseover for Online Attention Data
Open Access IconThis is an open access title

Essential Info

Elements of Causal Inference

Foundations and Learning Algorithms


The mathematization of causality is a relatively recent development, and has become increasingly important in data science and machine learning. This book offers a self-contained and concise introduction to causal models and how to learn them from data.

After explaining the need for causal models and discussing some of the principles underlying causal inference, the book teaches readers how to use causal models: how to compute intervention distributions, how to infer causal models from observational and interventional data, and how causal ideas could be exploited for classical machine learning problems. All of these topics are discussed first in terms of two variables and then in the more general multivariate case. The bivariate case turns out to be a particularly hard problem for causal learning because there are no conditional independences as used by classical methods for solving multivariate cases. The authors consider analyzing statistical asymmetries between cause and effect to be highly instructive, and they report on their decade of intensive research into this problem.

The book is accessible to readers with a background in machine learning or statistics, and can be used in graduate courses or as a reference for researchers. The text includes code snippets that can be copied and pasted, exercises, and an appendix with a summary of the most important technical concepts.

About the Authors

Jonas Peters is Associate Professor of Statistics at the University of Copenhagen.

Dominik Janzing is a Senior Research Scientist at the Max Planck Institute for Intelligent Systems in Tübingen, Germany.

Bernhard Schölkopf is Director at the Max Planck Institute for Intelligent Systems in Tübingen, Germany. He is coauthor of Learning with Kernels (2002) and is a coeditor of Advances in Kernel Methods: Support Vector Learning (1998), Advances in Large-Margin Classifiers (2000), and Kernel Methods in Computational Biology (2004), all published by the MIT Press.


Elements of Causal Inference is an important contribution to the growing literature on causal analysis. This lucid monograph elegantly weaves together statistics, machine learning, and causality to provide a holistic picture of how we and machines can use data to understand the world.”
David Blei, Professor of Computer Science and Statistics, Columbia University

“Causal inference is a well-established field in statistics, but it is still relatively underdeveloped within machine learning. This is partly due to the lack of good learning resources before Elements of Causal Inference came along. This book is high-quality work that breaks through, firmly establishing a connection between causal inference and general machine learning.”
Ricardo Silva, Senior Lecturer, University College London; Turing Fellow, Alan Turing Institute