Causal Inference

A personal study project exploring the foundations of causal inference — working through the theory and implementing key concepts in Python.

The focus is on understanding and comparing the two dominant frameworks:

• Pearl's causal hierarchy — DAGs, do-calculus, structural causal models (SCMs)
• Rubin's potential outcomes framework — counterfactuals, average treatment effects, propensity scores

These two traditions ask the same question differently. Understanding both — and where they agree and diverge — is the goal.

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Structure

notebooks/
  01_dags_and_do_calculus.ipynb        # Pearl framework: DAGs, d-separation, interventions
  02_potential_outcomes.ipynb          # Rubin framework: ATE, ATT, propensity scores
  03_frameworks_comparison.ipynb       # Same problem, two frameworks — where do they meet?
  04_backdoor_frontdoor_criteria.ipynb # Identification strategies
  05_instrumental_variables.ipynb      # IV estimation

notes/
  pearl_vs_rubin.md                    # Conceptual comparison of the two frameworks
  key_concepts.md                      # Running glossary of terms and notation

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Key concepts covered

Pearl — Structural Causal Models

• Directed Acyclic Graphs (DAGs) and causal structure
• d-separation and conditional independence
• The do-operator: P(Y | do(X)) vs P(Y | X)
• Backdoor criterion, frontdoor criterion
• Counterfactuals from SCMs

Rubin — Potential Outcomes

• The fundamental problem of causal inference
• Average Treatment Effect (ATE) and Average Treatment Effect on the Treated (ATT)
• Propensity score matching and inverse probability weighting
• Ignorability and overlap assumptions

Where they meet Both frameworks ultimately formalize the same intuition — that causation is not correlation, and that identifying causal effects requires assumptions beyond the data. The structural and potential outcomes approaches are mathematically equivalent in many settings, but the language and tooling differ significantly.

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Libraries used

DoWhy · CausalPy · NetworkX · NumPy · pandas · matplotlib · statsmodels

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Motivation

Coming from a background in statistical modelling and applied ML (survival analysis, regression pipelines, Bayesian inference), causal inference is the natural next step — moving from predicting outcomes to understanding what drives them. This matters especially in domains like pharma and media where interventions, not just predictions, are the end goal.

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Work in progress — updated as I work through the material.