On the Recoverability of Causal Relations from Temporally Aggregated I.I.D. Data

TL;DR

This paper investigates how temporal aggregation affects causal discovery in I.I.D. data, revealing conditions under which causal relations can still be recovered despite aggregation distortions.

Contribution

It introduces formal notions of functional and conditional independence consistency, providing conditions for reliable causal discovery from aggregated data.

Findings

Aggregation can distort causal discovery, especially in nonlinear cases.

Partial linearity or prior knowledge can enable recovery of causal relations.

Theoretical and experimental evidence shows when causal discovery remains valid.

Abstract

We consider the effect of temporal aggregation on instantaneous (non-temporal) causal discovery in general setting. This is motivated by the observation that the true causal time lag is often considerably shorter than the observational interval. This discrepancy leads to high aggregation, causing time-delay causality to vanish and instantaneous dependence to manifest. Although we expect such instantaneous dependence has consistency with the true causal relation in certain sense to make the discovery results meaningful, it remains unclear what type of consistency we need and when will such consistency be satisfied. We proposed functional consistency and conditional independence consistency in formal way correspond functional causal model-based methods and conditional independence-based methods respectively and provide the conditions under which these consistencies will hold. We show theoretically and experimentally that causal discovery results may be seriously distorted by aggregation especially in complete nonlinear case and we also find causal relationship still recoverable from aggregated data if we have partial linearity or appropriate prior. Our findings suggest community should take a cautious and meticulous approach when interpreting causal discovery results from such data and show why and when aggregation will distort the performance of causal discovery methods.