Conditioning-Depth Diagnostics for Hidden Memory in Temporal Causal Discovery

Abstract

Reliable causal discovery in timeseries requires conditioning sets that capture the system state. When predictive history is omitted, residual dependence can appear as direct causal links. We test state adequacy by measuring how inferred graphs change as conditioning depth increases while the reported causal lag stays fixed. Under an adequate finite-order Markov representation, graphs should stabilize once enough observed history is conditioned on; latent common drive, omitted lags, nonstationarity, and measurement dynamics can instead produce depth sensitivity. We formalize this idea with graph instability statistics and evaluate c-GC and c-GC*, the two learners whose depth parameter implements a matched fixed-horizon history intervention. PCMCI+ and JPCMCI+ are excluded from the primary comparison because adaptive parent selection makes nominal depth edge-specific. In paired simulations, a clean order-1 process was stable in every repeat, whereas an AR(1) latent common driver produced positive instability in all c-GC repeats and eight of ten c-GC* repeats. In calcium imaging recordings, connectivity drops at the first transition beyond the one-lag baseline and then levels off, but B=200 bootstrap calibration does not reject the fitted order-1 null. The workflow therefore flags hidden memory or observed-state inadequacy without identifying the generating mechanism or recovering a latent graph.