# External Validity: From Do-Calculus to Transportability Across Populations

arXiv: https://arxiv.org/abs/1503.01603 · HTML: https://mlsanity.com/paper/1503.01603/

## Key facts

- Cited by 75 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Mar 2015.

## Built on by (most cited first, 30 of 75)

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- [Causal de Finetti: On the Identification of Invariant Causal Structure in Exchangeable Data](https://mlsanity.com/paper/2203.15756/) (2022)
- [From Statistical to Causal Learning](https://mlsanity.com/paper/2204.00607/) (2022)
- [Transporting Causal Mechanisms for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2107.11055/) (2021)
- [A Review of Generalizability and Transportability](https://mlsanity.com/paper/2102.11904/) (2021)
- [Active Bayesian Causal Inference](https://mlsanity.com/paper/2206.02063/) (2022)
- [Out-of-distribution Prediction with Invariant Risk Minimization: The Limitation and An Effective Fix](https://mlsanity.com/paper/2101.07732/) (2021)
- [Causal Inference Through the Structural Causal Marginal Problem](https://mlsanity.com/paper/2202.01300/) (2022)
- [Neural Causal Abstractions](https://mlsanity.com/paper/2401.02602/) (2024)
- [Image-based Treatment Effect Heterogeneity](https://mlsanity.com/paper/2206.06417/) (2022)
- [Causal Multi-Agent Reinforcement Learning: Review and Open Problems](https://mlsanity.com/paper/2111.06721/) (2021)
- [Deconfounded Visual Grounding](https://mlsanity.com/paper/2112.15324/) (2021)
- [A Tree-based Model Averaging Approach for Personalized Treatment Effect Estimation from Heterogeneous Data Sources](https://mlsanity.com/paper/2103.06261/) (2021)
- [Generative Causal Representation Learning for Out-of-Distribution Motion Forecasting](https://mlsanity.com/paper/2302.08635/) (2023)
- [Multiply Robust Federated Estimation of Targeted Average Treatment Effects](https://mlsanity.com/paper/2309.12600/) (2023)
- [Falsification before Extrapolation in Causal Effect Estimation](https://mlsanity.com/paper/2209.13708/) (2022)
- [Falsification of Internal and External Validity in Observational Studies via Conditional Moment Restrictions](https://mlsanity.com/paper/2301.13133/) (2023)
- [Offline Minimax Soft-Q-learning Under Realizability and Partial Coverage](https://mlsanity.com/paper/2302.02392/) (2023)
- [C2P: Featuring Large Language Models with Causal Reasoning](https://mlsanity.com/paper/2407.18069/) (2024)
- [Interpreting Low-level Vision Models with Causal Effect Maps](https://mlsanity.com/paper/2407.19789/) (2024)
- [Causality is Key for Interpretability Claims to Generalise](https://mlsanity.com/paper/2602.16698/) (2026)
- [Causal inference in drug discovery and development](https://mlsanity.com/paper/2209.14664/) (2022)
- [Who Are We Missing? A Principled Approach to Characterizing the Underrepresented Population](https://mlsanity.com/paper/2401.14512/) (2024)
- [Counterfactual Identifiability via Dynamic Optimal Transport](https://mlsanity.com/paper/2510.08294/) (2025)
- [Sequential Kernel Embedding for Mediated and Time-Varying Dose Response Curves](https://mlsanity.com/paper/2111.03950/) (2021)

## Abstract (arXiv)

The generalizability of empirical findings to new environments, settings or populations, often called "external validity," is essential in most scientific explorations. This paper treats a particular problem of generalizability, called "transportability," defined as a license to transfer causal effects learned in experimental studies to a new population, in which only observational studies can be conducted. We introduce a formal representation called "selection diagrams" for expressing knowledge about differences and commonalities between populations of interest and, using this representation, we reduce questions of transportability to symbolic derivations in the do-calculus. This reduction yields graph-based procedures for deciding, prior to observing any data, whether causal effects in the target population can be inferred from experimental findings in the study population. When the answer is affirmative, the procedures identify what experimental and observational findings need be obtained from the two populations, and how they can be combined to ensure bias-free transport.