Source Summary: Pearl 2000 — Causality
Full title: Causality: Models, Reasoning, and Inference
Authors: Judea Pearl
Affiliation: UCLA (Computer Science and Statistics)
Venue: Cambridge University Press, 2000 (2nd ed. 2009)
PDF: papers/pearl-2000-causality-models-reasoning-and-inference.pdf
Note: Book; PDF is the 2nd edition (2009). Content from the book itself.
Contributions
- Do-calculus — a complete formal language for reasoning about interventions: P(Y | do(X=x)) distinguishes “X causes Y” from “X is correlated with Y.”
- Causal DAG / Structural Causal Model (SCM) — a graphical representation of causal structure; nodes = variables, edges = direct causal influence, exogenous noise = structural equations.
- The Ladder of Causation — three levels of causal reasoning: association (seeing), intervention (doing), counterfactual (imagining); clarifies what statistical models can and cannot answer.
- Identification theorem — conditions under which causal effects can be computed from observational data (when you can’t randomize).
- Unification of causal frameworks — connects potential outcomes (Rubin), structural equations (Wright, Simon), and graphical models into one coherent theory.
The Ladder of Causation
Pearl’s central framework: three levels of cognitive/computational ability:
| Rung | Query type | Example | Required |
|---|---|---|---|
| 1. Association | P(Y | X) | “People who take aspirin have fewer headaches” | Statistical model |
| 2. Intervention | P(Y | do(X)) | “If I give aspirin to this patient, will their headache go away?” | Causal model |
| 3. Counterfactual | P(Yₓ | X’, Y’) | “Would this patient’s headache have gone away had they taken aspirin, given that they didn’t?” | SCM + twin network |
Pure statistical models (including neural networks) operate only on Rung 1. They can model correlations, not causes. A rung-1 system can’t answer “what happens if I intervene?” — no matter how much data it has.
Structural Causal Models
An SCM consists of:
- Endogenous variables X₁, …, Xₙ (the variables of interest)
- Exogenous variables U₁, …, Uₙ (unobserved noise)
- Structural equations: Xᵢ = fᵢ(PAᵢ, Uᵢ) where PAᵢ are the direct causes of Xᵢ
A causal DAG (Directed Acyclic Graph) encodes the structure: an edge X → Y means X is a direct cause of Y, with all other causes held constant.
Example (Simpson’s Paradox resolution):
Drug → Recovery
Drug ← Gender → Recovery
If we observe that drug-takers recover less often overall (because gender confounds both drug-taking and recovery), should we prescribe the drug? The causal DAG makes this answerable: do(Drug=1) removes the Gender → Drug edge, leaving only the direct effect.
Do-Calculus
The do-operator P(Y | do(X=x)) represents the distribution of Y when we intervene to set X=x, as opposed to merely observing X=x.
Three rules (Pearl’s do-calculus) allow systematic reduction of interventional queries to observational quantities:
- Insertion/deletion of observations
- Action/observation exchange
- Insertion/deletion of actions
Completeness theorem: if a causal effect is identifiable from observational data, do-calculus will find it.
Why This Matters for AI
Neural networks are fundamentally rung-1 systems: they learn P(output | input) from data. This gives them:
- ✓ Strong predictions on the training distribution
- ✗ Inability to answer “what happens if I intervene?”
- ✗ Inability to explain why a prediction was made (correlation ≠ cause)
- ✗ Poor generalization under distribution shift (the data distribution changes when you act)
A system that can reason about causes — rung 2–3 — can:
- Plan: “which action will produce the best outcome?”
- Generalize: “how will this intervention behave in a new context?”
- Explain: “why did this outcome occur?”
This is the theoretical case for why world models (which model causal structure) are necessary for intelligence beyond statistical interpolation.
Key References
- Wright 1921 — path analysis (origin of causal graphs in statistics)
- Rubin 1974 — potential outcomes framework (alternative causal formalism unified here)
- Spirtes, Glymour & Scheines 1993 — constraint-based causal discovery algorithms