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About this paper
Yahya Aalaila, Gerrit Großmann, Sumantrak Mukherjee, Jonas Wahl, Sebastian Vollmer
The authors combine a state-space model with a structural causal model to estimate hidden states and disturbances from noisy observations, then simulate trajectories after changing an initial state. In Lorenz simulations, generated counterfactuals diverged from a deterministic reference around step 500 with true parameters, 300 with a point estimate, and 10 with posterior parameter uncertainty. These results concern simulated settings.
Key insights
- Chaotic dynamics inherently limit counterfactual reliability: Even with perfect knowledge of true system parameters, small initial perturbations in chaotic systems lead to rapid and substantial divergence of counterfactual trajectories.
- Parameter uncertainty significantly exacerbates this unreliability: Slight inaccuracies in estimated parameters or sampling from their posterior distribution cause counterfactual trajectories to diverge earlier and more dramatically than due to chaos alone.
- Accurate factual state estimation does not guarantee robust counterfactuals: The ability to precisely track an observed system's hidden states does not translate to reliable counterfactual predictions in chaotic environments when hypothetical changes are introduced.
Summary by alphaXiv.
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