Causality and Machine Learning

Day 3: Estimation and causal inference

This day focuses on the transition from identification formulas to estimators. The goal is to understand how causal estimands can be estimated from observed data using outcome regression, inverse probability weighting, doubly robust estimators, and flexible machine-learning nuisance estimation.

This session is given by Johan de Aguas.

Learning objectives

By the end of this session, students should be able to:

• Define the average treatment effect under standard causal assumptions.
• Implement plug-in estimators.
• Implement AIPW estimators.
• Explain how doubly robust estimators combine outcome and treatment models.
• Use cross-fitting to reduce overfitting bias when nuisance functions are estimated flexibly.

Schedule and notebooks

Time	Topic	Format
10:05–10:45	Introduction, formalisms and causal effects	Lecture
10:45–11:00	Common causal estimands	Marimo lab
11:00–11:15	The causal roadmap, identification	Lecture
11:15–11:45	Estimation: parametric and ML plug-in	Lecture
11:45–12:00	Estimation: parametric and ML plug-in	Marimo lab
12:00–13:00	Lunch
13:05–13:45	AIPW and double robustness	Lecture
13:45–14:15	State-of-the-art and NN architectures	Lecture
14:15–14:30	AIPW	Marimo lab
14:30–15:00	Influence function, DML (and TMLE*)	Lecture
15:00–15:30	AIPW, DML (and TMLE*)	Marimo lab
15:30–16:00	Heterogeneous treatment effect
16:00–16:30	Heterogeneous treatment effect	Marimo lab

Computational setup

Students should have a working Python 3.11 or 3.12 environment. We will use the following libraries:

python -m venv .venv
source .venv/bin/activate
pip install numpy pandas scipy scikit-learn matplotlib statsmodels jupyterlab marimo pgmpy

Advanced readings

• Robins, J. M., Rotnitzky, A., & Zhao, L. P. (1994). Estimation of regression coefficients when some regressors are not always observed. Journal of the American Statistical Association, 89(427), 846–866. doi:10.1080/01621459.1994.10476818
• van der Laan, M. J., & Rubin, D. (2006). Targeted maximum likelihood learning. The International Journal of Biostatistics, 2(1), Article 11. doi:10.2202/1557-4679.1043
• Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W., & Robins, J. (2018). Double/debiased machine learning for treatment and structural parameters. The Econometrics Journal, 21(1), C1–C68. doi:10.1111/ectj.12097

Tutorials, online books and resources

• Applied causal inference
• Causal inference for the brave and true
• Causal inference and machine learning
• Machine learning-based causal inference
• Applied causal inference powered by ML and AI
• Awesome causal inference 1
• Awesome causal inference 2
• Awesome causality
• An illustrated guide to TMLE
• TMLE for binary outcome
• Theory behind TMLE (CrossValidated)
• EconML and CausalML
• The basics of double/debiased machine learning