Do Calculus

"The do-operator marks the difference between watching a system and changing it."

Overview

Do-calculus gives graph-based rules for transforming interventional causal queries into estimable observational expressions when assumptions permit identification.

Causal inference is the part of the curriculum that separates observing from doing. It asks which assumptions allow a learner to move from associations in data to claims about interventions, alternatives, and mechanisms.

This section is written in LaTeX Markdown. Inline mathematics uses $...$, and display equations use `

`. The notes emphasize graph assumptions, intervention notation, counterfactual semantics, and the estimand-estimator split.

Prerequisites

• Structural Causal Models
• Conditional Probability
• Graph Algorithms
• Hypothesis Testing

Companion Notebooks

Learning Objectives

After completing this section, you will be able to:

• Define SCMs, structural assignments, and intervention distributions
• Distinguish conditioning from intervention using the do-operator
• Apply d-separation to simple causal graphs
• State backdoor and frontdoor adjustment formulas
• Separate causal estimands from statistical estimators
• Compute ATE, ATT, and simple counterfactual quantities
• Explain abduction, action, and prediction in SCM counterfactuals
• Describe constraint-based and score-based causal discovery
• Identify assumptions behind causal discovery algorithms
• Connect causal inference to robust ML, fairness, recommendation, and LLM agents

Study Flow

1. Read the pages in order and pause after each page to restate the main definition or theorem.
2. Run theory.ipynb when you want to check the formulas numerically.
3. Use exercises.ipynb after the reading path, not before it.
4. Return to this overview page when you need the chapter-level navigation.

Runnable Companions

• Theory notebook
• Exercises notebook