Extension of eCITs to dependent samples

Extend embedded conditional independence tests to dependent observations, and establish their validity when speech-summary observations exhibit dependence through recurring speakers, shared topics, temporal structure, or other departures from the independent and identically distributed sampling assumption.

Background

The theoretical transfer results and the asymptotic validity of the projected covariance measure rely on independent and identically distributed observations. In the German Parliament application, however, speakers recur across speeches, topics are shared, observations are related across time, and protected attributes may remain constant within speaker.

Such dependence can make the PCM anti-conservative and may contribute to the large observed test statistics. The paper therefore leaves unresolved whether and how eCIT validity can be maintained under realistic dependence structures in speech data.

References

Lemmas~\ref{lem:lift} and \ref{lem:lifting-mean} and the asymptotic validity of the PCM all rely on the i.i.d.\ assumption, and positive dependence between observations can make the PCM anti-conservative. We can therefore not exclude that this dependence contributes to the observed magnitude of the statistics; extending the eCITs to dependent samples is left for future work.

— Embedded Conditional Independence Tests for Large Language Model Generated Text with an Application to German Parliament Speeches  (2609.00946 - Simnacher et al., 1 Sep 2026) in Section 4.2, Subsection “Real-world case study”