Estimation--Prediction Tradeoff in Causal Probabilistic Temporal Graphs

Abstract: Temporal link prediction is usually evaluated by predictive performance on unseen edges, but in probabilistic temporal graphs this criterion can conflate model error with irreducible uncertainty. We study this issue by characterising an inherent estimation--prediction tradeoff in binary logistic models where regimes that maximise Fisher information and improve parameter recoverability are also those with the highest entropy, making individual predictions intrinsically harder even under perfect parameter recovery. We propose a probabilistic causal framework for generating temporal graphs with transient edges and known ground-truth causal structure, allowing temporal link prediction to be evaluated jointly with causal parameter recovery. For the proposed binary logistic parametrisation, we derive the Cramér--Rao bound and validate the tradeoff between parameter estimation error and irreducible predictive loss. Our results show that predictive accuracy alone may not reflect whether a model has learned the underlying causal mechanism, motivating benchmarks that distinguish reducible model error from intrinsic process uncertainty.