Do Finetti: On Causal Effects for Exchangeable Data

Siyuan Guo, Chi Zhang, Karthika Mohan, Ferenc Huszár, Bernhard Schölkopf

Keywords: Causality; Exchangeability

TL;DR: Causal effect in exchangeable data that adhere to the independent causal mechanism principle

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 Pólya 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.

Primary Area: Causal inference

Submission Number: 14776