The Mathematics of Causal Inference, with Reflections on Machine Learning and the Logic of Science
summary
Argues that causal questions require structural models, not just distributions, and gives concrete tools: structural equations, graphs and do-calculus with three complete transformation rules to convert mixed “see” and “do” queries into estimable formulas. Shows specific procedures for transportability and recoverability (when experimenting in one environment and applying results to another, or when data are missing), proves decidability boundaries, and demonstrates formulas for examples (smoking→cancer, sprinkler, warmup→injury) and algorithms that either produce unbiased estimators or show impossibility.
AI-written summary · about
chapters (38)
- 0:00Intro
- 7:11OUTLINE 1. The causal revolution - from statistics to counterfactuals from Babylon to Athens 2. The fundamental laws of causal inference
- 10:02TURING ON MACHINE LEARNING AND EVOLUTION
- 15:06COUNTERFACTUALS AND OUR SENSE OF JUSTICE
- 17:01WHY PHYSICS IS COUNTERFACTUAL Scientific Equations (eg. Hooke's Law) are non-algebraic
- 20:09WHAT KIND OF QUESTIONS SHOULD THE ROBOT ANSWER?
- 21:25TRADITIONAL STATISTICAL INFERENCE PARADIGM
- 22:15FROM STATISTICAL TO CAUSAL ANALYSIS 1. THE DIFFERENCES
- 24:10THE STRUCTURAL MODEL PARADIGM
- 25:24WHAT KIND OF QUESTIONS SHOULD THE ORACLE ANSWER?
- 28:55STRUCTURAL CAUSAL MODELS: THE WORLD AS A COLLECTION OF SPRINGS
- 30:43COUNTERFACTUALS ARE EMBARRASSINGLY SIMPLE
- 32:53THE TWO FUNDAMENTAL LAWS OF CAUSAL INFERENCE
- 34:10THE LAW OF CONDITIONAL INDEPENDENCE
- 35:10D-SEPARATION: NATURE'S LANGUAGE FOR COMMUNICATING ITS STRUCTURE
- 36:34SEEING VS. DOING
- 37:38THE LOGIC OF CAUSAL ANALYSIS
- 37:52THE MACHINERY OF CAUSAL CALCULUS
- 38:35DERIVATION IN CAUSAL CALCULUS
- 41:13EFFECT OF WARM-UP ON INJURY (After Shrier & Platt, 2008)
- 44:04MATHEMATICALLY SOLVED PROBLEMS
- 45:33TRANSPORTABILITY OF KNOWLEDGE ACROSS DOMAINS (with E. Bareinboim)
- 47:09MOVING FROM THE LAB TO THE REAL WORLD
- 47:49MOTIVATION WHAT CAN EXPERIMENTS IN LA TELL ABOUT NYC?
- 48:49TRANSPORT FORMULAS DEPEND ON THE STORY
- 49:55GOAL: ALGORITHM TO DETERMINE IF AN EFFECT IS TRANSPORTABLE
- 50:25TRANSPORTABILITY REDUCED TO CALCULUS
- 51:30META-SYNTHESIS AT WORK
- 52:22MISSING DATA: A SEEMINGLY STATISTICAL PROBLEM (Mohan, Pearl & Tian 2012)
- 53:19WHAT CAN CAUSAL THEORY DO FOR MISSING DATA?
- 54:35GOAL: ESTIMATE P(X,Y,Z)
- 55:39NAIVE ESTIMATE OF P(X,Y,Z)
- 57:03SMART ESTIMATE OF P(X,Y,Z)
- 57:45RECOVERABILITY FROM MISSING DATA
- 58:09RECOVERABILITY IN MARKOVIAN MODELS
- 58:19DECIDING RECOVERABILITY
- 58:55AN IMPOSSIBILITY THEOREM FOR MISSING DATA
- 59:23A STRONGER IMPOSSIBILITY THEOREM
related talks
01h 06mThe New Science of Cause and Effect
45mCausality and Statistics, a Love Not So Impossible After All
29m🧠🧹 Causality - Mental Hygiene for Data Science
43mA Practical Guide to Causality in Python (For The Perplexed)
01h 06mIntroduction to Causal Graphical Models: Graphs, d-separation, do-calculus
06mCausal Machine Learning – What’s in it for Data Scientists?
31mA Gentle Introduction To Causal Inference
11mCausal Inference For Socio-Economic & Engineering Systems