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Jointly learn dynamics and noise to robustly estimate CE from data

Develop data-driven methods that jointly infer the state-transition function and noise covariance to robustly estimate SVD-based and EI-based causal emergence from observations when governing equations are unknown, especially under high noise or limited data, mitigating errors from misestimated interdimensional correlations.

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Background

When the true dynamics are unknown, the paper uses neural networks to approximate both the transition mapping and covariance under a multivariate Gaussian assumption. The authors warn that this can be unreliable under high noise or limited data because parameter estimation errors and correlation misestimation can bias CE.

They call for representational methods that simultaneously capture both dynamics and noise structure to improve CE reliability in data-driven settings.

References

While our approach has made progress, several challenges remain unresolved. The third issue is that both SVD-based and EI-based CE quantification methods require training an NN to infer dynamics when the governing equations are unknown. However, NN-based approaches are data-dependent and prone to parameter estimation errors, particularly in capturing interdimensional correlations. In our case, a multivariate Gaussian model approximates both the dynamical function and covariance. Yet, under high noise or limited data, the learned dynamics may deviate from the true system, leading to unreliable CE estimates. For systems with unknown models, it is crucial to develop representations that jointly approximate both the underlying dynamics and noise structure.

— SVD-based Causal Emergence for Gaussian Iterative Systems (2502.08261 - Liu et al., 12 Feb 2025) in Discussion and conclusion