Research map / Probabilistic and scientific modeling / Causal discovery
Do Finetti: On Causal Effects for Exchangeable Data
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Extends causal effect identification and estimation from i.i.d. data to exchangeable ICM generative processes via a generalized truncated factorization, a causal Pólya urn model, and a Do-Finetti algorithm for joint graph discovery and effect estimation from multi-environment data.
Problem
Causal effect estimation is typically formulated for i.i.d. data via SCMs and do-calculus, which does not extend to exchangeable, non-i.i.d. generative processes such as those arising in multi-environment data.
Approach
Defines interventions in ICM generative processes as assigning delta distributions to the sampling densities of intervened variables, derives a truncated factorization formula for exchangeable data under independent causal mechanisms, and shows that conditional interventional effects depend on other observations, unlike i.i.d. data.
Key results
- Do-Finetti achieves near-zero causal effect estimation MSE and correct DAG identification in bivariate synthetic experiments aggregated over 100 runs, while i.i.d. methods fail.
- Even i.i.d. with the true DAG never reaches the analytic solution under exchangeable data, per the reported experiments.
- The paper proves a truncated factorization theorem for ICM generative processes and shows conditional interventional effects depend on other observations, unlike i.i.d. data.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Do-Finetti instead of the i.i.d. algorithm | Causal effect estimation on synthetic multi-environment ICM data · Synthetic bivariate ICM data | MSE | Helped |
| Use the i.i.d. algorithm with the true DAG instead of Do-Finetti | Causal effect estimation on synthetic multi-environment ICM data · Synthetic bivariate ICM data | MSE | Hurt |
| Use Do-Finetti for simultaneous DAG identification and causal effect estimation | Synthetic multi-environment ICM data · Synthetic bivariate ICM data | DAG identification accuracy | Helped |
Surprising findings
- Under exchangeable ICM processes, conditioning on other observations (e.g., a collider) changes the interventional effect, a property absent in i.i.d. data.
- Even with the true DAG and infinite data, the i.i.d. truncated factorization never reaches the correct causal effect under exchangeable data.
Limitations
- Experiments are limited to small synthetic bivariate settings and a proof-of-concept algorithm.
- Algorithm is not designed for scale; the paper states much is left to do on scalable algorithms.
- Counterfactual queries in exchangeable contexts are not addressed.
Experimental setup
Datasets: synthetic data from causal Pólya urn model
Benchmarks: synthetic bivariate X->Y exchangeable data
Metrics: mean squared error vs analytic post-interventional solution DAG identification accuracy
Baselines: PC algorithm i.i.d. truncated factorization i.i.d. with true DAG do-Finetti with true DAG
Builds on: causal de Finetti theorems truncated factorization Causal-de-Finetti algorithm Pólya urn model PC algorithm
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