Do Finetti: On Causal Effects for Exchangeable Data

TL;DR

This paper develops a new framework for estimating causal effects in exchangeable data, extending traditional methods beyond i.i.d. assumptions to multi-environment settings.

Contribution

It introduces a generalized causal inference framework for exchangeable data, including a truncated factorization formula and an algorithm for causal discovery and effect estimation.

Findings

Introduces a truncated factorization formula for exchangeable data.

Develops a causal Pólya urn model to illustrate intervention effects.

Proposes an algorithm for simultaneous causal discovery and effect estimation.

Abstract

We study causal effect estimation in a setting where the data are not i.i.d. (independent and identically distributed). We focus on exchangeable data satisfying an assumption of independent causal mechanisms. Traditional causal effect estimation frameworks, e.g., relying on structural causal models and do-calculus, are typically limited to i.i.d. data and do not extend to more general exchangeable generative processes, which naturally arise in multi-environment data. To address this gap, we develop a generalized framework for exchangeable data and introduce a truncated factorization formula that facilitates both the identification and estimation of causal effects in our setting. To illustrate potential applications, we introduce a causal P\'olya urn model and demonstrate how intervention propagates effects in exchangeable data settings. Finally, we develop an algorithm that performs simultaneous causal discovery and effect estimation given multi-environment data.