Estimation--Prediction Tradeoff in Causal Probabilistic Temporal Graphs

2026-06-26

AI Summary

Traditional temporal link prediction evaluation struggles to disentangle model error from the irreducible uncertainty inherent in the generative process, thereby obscuring whether a model has genuinely learned the underlying causal mechanisms. This work proposes a probabilistic causal temporal graph generation framework featuring transient edges and known causal structure, enabling joint assessment of causal parameter recovery and link prediction performance through a binary logistic model. By deriving the Cramér–Rao bound and analyzing Fisher information, the study reveals an intrinsic trade-off between parameter identifiability and prediction difficulty: higher identifiability corresponds to higher entropy, rendering individual link prediction fundamentally more challenging. Experimental results corroborate this theoretical trade-off, demonstrating that predictive accuracy alone is insufficient to gauge a model’s capacity to capture the true causal dynamics.

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.

Problem

• temporal link prediction
• probabilistic temporal graphs
• estimation-prediction tradeoff
• causal mechanism
• irreducible uncertainty

Innovation

• causal temporal graphs
• estimation-prediction tradeoff
• probabilistic link prediction
• Fisher information
• Cramér–Rao bound