Causal Artificial Intelligence

A Roadmap for Building Causally Intelligent Systems

Elias Bareinboim

Draft version (Apr/19): link

This textbook offers a comprehensive treatment of the principles, algorithms, and tools necessary for building causally intelligent systems. It bridges probability theory, causal inference, machine learning, and decision-making under uncertainty, providing a unified roadmap for addressing fundamental challenges in modern AI, including safety, generalization, robustness, and explainability.

Teaching & Slides (coming soon)

Lecture 1 Introduction

Ch. 1

Logistics; Motivation; Machine Learning.
Pearl's Causal Hierarchy.

Lecture 2 Structural Causal Models

Ch. 2

Structural Causal Models; Causal Diagrams.
Extra: CHT notes

Lecture 3 Identification of Causal Effects - Basics

Ch. 4, Sec. 4.1, 4.2 (< 4.2.1)

Intuition and Definition of Causal Effects.
The Truncated Factorization Product.
The Identification Problem

Lecture 4 The Problem of Confounding and the Back-door Criterion

Sec. 4.2.1

Identifiable and non-identifiable effects. Confounding Bias.
The Backdoor Criterion. Inverse probability Weighting/Propensity Score.

Lecture 5 The Algorithmic Back-door Criterion

Sec. 4.2.2-4.2.3

The Conditional Backdoor Criterion.
Adjustment-Backdoor Criterion. Poly-time delay Backdoor.

Lecture 6 The Interventional Calculus

Sec. 4.2.5, 4.2.6, 4.3

The Generalized Truncated Product.
The Front-door Case.
The interventional calculus (do-calculus).

Lecture 7 Causal Operators (L2) and Algorithmic Identification

Sec. 4.4

C-factors. C-Operators and Data Structure.
Systematic ID.

Lecture 8 Counterfactuals Foundations

Ch. 5, Sec. 5.1, 5.2

Counterfactual's definition. Motivation. Hinton's paradox.
Counterfactual Quantities & the Structural Basis Theorem

Lecture 9 The Counterfactual Calculus

Sec. 5.3

Counterfactual Contraints.
Counterfactual Calculus.

Lecture 10 Causal Operators (L3) and Algorithmic Identification

Sec. 5.4

Ctf-factors and operators. Consistent ctf-factors. Systematic ID.

Lecture 11 Partial Identification

Ch. 5, Sec. 5.5

Bounding interventional distributions (bow graph and IV model).
Causal offline-to-online Learning (COOL).

Lecture 12 The Sigma Calculus

Ch. 4, Sec. 4.6

Soft interventions. Sigma-Calculus.

Lecture 13 Fairness I

Ch. 6, Sec. 6.1-6.3

Theory of Decomposing Variations; Fundamental Problem of Causal Fairness; Explainability Plane.
TV-family; Using contrastive measures in practice; Structure of the TV-family; Towards the Fairness Map.

Lecture 14 Fairness II

Sec. 6.4.1

Causal Interactions. Bias quantification (Task 1).

Lecture 15 Fairness III

Sec. 6.4.1-6.4.3

Fair Predictions (Task 2). Fair Decision-Making (Task 3).

Lecture 16 Decision-Making I

Ch. 7-8

Causal Decision Model. Comparison w/ MDPs. Causal RL Tasks.
Off-police Learning. Online Learning. Causal identification.

Lecture 17 Decision-Making II

Sec. 9.1, 9.2, 9.5

Causal-offline-to-online Learning (COOL).
Causal Imitation Learning.
Causally-aligned Curriculum Learning.

Lecture 18 Decision-Making III

Sec. 9.3, 9.4, 9.6

Where to intervene.
Counterfactual Decision-Making.
Causal Game Theory.

Lecture 19 Generalizability I

Ch. 10, Sec. 11.1-11.2

Transportability Foundations; Direct Transportability; the Score TR algorithm.
Transportable Representations; Causal Mechanistic Stability & invariance learning; Overview of the DG literature.

Lecture 20 Generalizability II

Ch. 11.3, 11.4.

Partial Transportability & Adaptation.

Lecture 21 Generalizability III

Ch. 12

Interventional & Counterfactual Transportability.

Lecture 22 Generative I

Ch. 13

Neural Causal Models. Structural Constraints.
Causal Generative Modeling. Practical Implementation.

Lecture 23 Generative II

Ch. 14

Modeling and ACMs. Impossibility results.
Ctf-consistent estimators. Experimental results.

Lecture 24 Generative III

Ch. 15

PCH's Abstraction. Inferences across Abstractions. Representation Learning.

Lecture 25 Learning I

Ch. 16

Observational Equivalence Class.
Interventional Equivalence Class.

Lecture 26 Learning II

Ch. 17

Multi-domain Structural Learning.

Lecture 27 Learning III

Ch. 18

Causal Representation Learning.

Lecture 28 Parametric Identification

Ch. 19

Foundations of Linear SCMs. Causal Regression.
Instrumental Variables. Instrumental Sets. Decompositions.
Monotonic Identification. LATE.

Lecture 29 Causal Estimation

Ch. 20

Double Robutness.

Lecture 30 A Hierarchy of Graphical Models

Ch. 21

Other Inferential Systems.

Structure & Audience

Audience:
Graduate students, researchers, and advanced undergraduates in computer science, statistics, artificial intelligence, and related fields. A basic background in probability, statistics, and machine learning is recommended, though key concepts are introduced from first principles.

Book Structure:

Part	Key Concepts and Highlights
I. Foundations	Causal graphs, Structural Causal Models (SCMs), Pearl’s Causal Hierarchy (PCH)
II. Causal Reasoning & Understanding	Interventions, Counterfactual reasoning, Fairness analysis
III. Causal Decision-Making	Causal reinforcement learning (CRL), Counterfactual decision-making, Causal game theory
IV. Causal Generalizations	Transportability, Domain adaptation, Generalization of counterfactuals
V. Causal Generative Modeling	Neural causal models, Structural constraints, Causal generative modeling
VI. Causal Learning	Multi-domain structural learning, Causal representation learning
VII. Advanced Topics	Parametric identification, Causal estimation, Hierarchies of graphical models

Usage:
The book supports multiple curricular pathways depending on course goals:

Year-long Curriculum:
- Semester 1: Foundations of Causal AI — Chapters 1–7 provide a complete foundation suitable for a one-semester graduate-level course.
- Semester 2: Causal AI Research Topics — Chapters 8–18 explore advanced areas such as decision-making, fairness, generalization, generative modeling, and causal learning.

Streamlined and Modular Tracks:
- Rapid Foundations Track: Focus on Parts I–II to cover core principles quickly, enabling faster transition to advanced topics.
- Topical Focus Tracks:
   • Causal Decision-Making and Reinforcement Learning (Parts III–IV)
   • Causal Generalization and Robustness (Part IV)
   • Causal Generative Modeling and Representation Learning (Parts V–VI)

Errata

An initial list of errata will be posted here shortly here. Thank you for your patience and interest in improving the material.

About the Author

Elias Bareinboim is an Associate Professor of Computer Science at Columbia University and the founding director of the Causal Artificial Intelligence Lab.

His research focuses on causal and counterfactual inference, and their role in building more general, robust, and explainable AI systems. He is a leading advocate for the causal approach to AI, pioneering solutions to challenges such as decision-making, fairness, and generalization under uncertainty.

Bareinboim serves as the Editor-in-Chief of the Journal of Causal Inference and has received multiple awards, including the NSF CAREER Award, the DARPA Young Faculty Award, the ONR Young Investigator Award, and recognition as one of IEEE's "AI's 10 to Watch." For more information, visit his group homepage.

Contact & FAQ

For questions, feedback, or to report errata related to Causal Artificial Intelligence, please feel free to contact us.

Contact: book@causalai.net

Frequently Asked Questions

Will lecture slides be available for all chapters?
Yes, slides are being progressively posted in the Teaching & Slides section. Please check back for updates.

Will a final version of the textbook be published?
Yes, a finalized edition is planned. Updates will be shared through this website as they become available.

Can I use the slides and materials for teaching?
Yes — you are welcome to use the slides and materials for educational purposes with appropriate attribution.