Behavior of the PDS edge filter under unblocked latent forks

Investigate the behavior of the post-double-selection edge filter when genuinely unblocked local latent forks remain after conditioning on observed lags.

Background

The paper applies a post-double-selection (PDS) filter to candidate causal edges using controls selected from observed lagged variables. The filter is intended to remove candidate edges that do not survive adjustment for a sparse set of observed predictors, but it is not presented as a general identification method for latent confounding.

A local latent fork, in which an unobserved variable directly influences both the putative cause and effect, is not blocked by conditioning on observed lags. The paper therefore leaves unresolved how the PDS filter behaves when such genuinely unblocked latent forks are present.

References

In particular, a latent fork $H_t\to xc_t$, $H_t\to xe_t$ is not blocked by conditioning on observed lags. The filter's narrower role is to remove candidate edges that do not survive adjustment for a sparse set of observed predictors; behavior under genuinely unblocked local forks remains an empirical question.

— LUCID: Learning Under Confounding for Inference and Discovery in Time Series  (2609.31315 - Fesanghary, 25 Sep 2026) in Appendix, subsection “PDS edge filter” (Appendix~\ref{app:pds})