Emergent phenomena -- onset of epileptic seizures, sudden customer churn, or pandemic outbreaks -- often arise from hidden causal interactions in complex systems. We propose a machine learning method for their early detection that addresses a core challenge: unveiling and harnessing a system's latent causal structure despite the data-generating process being unknown and partially observed. The method learns an optimal feature representation from a one-parameter family of estimators -- powers of the empirical covariance or precision matrix -- offering a principled way to tune in to the underlying structure driving the emergence of critical events. A supervised learning module then classifies the learned representation. We prove structural consistency of the family and demonstrate the empirical soundness of our approach on seizure detection and churn prediction, attaining competitive results in both. Beyond prediction, and toward explainability, we ascertain that the optimal covariance power exhibits evidence of good identifiability while capturing structural signatures, thus reconciling predictive performance with interpretable statistical structure.

翻译：涌现现象——如癫痫发作、突发性客户流失或疫情爆发——通常源于复杂系统中隐藏的因果交互作用。本文提出一种用于早期检测此类现象的机器学习方法，其核心挑战在于：在数据生成过程未知且部分可观测的情况下，揭示并利用系统的潜在因果结构。该方法通过从单参数估计器族——经验协方差矩阵或精度矩阵的幂次——中学习最优特征表示，为调整至驱动关键事件涌现的底层结构提供了理论依据。随后，监督学习模块对习得的表示进行分类。我们证明了该估计器族的结构一致性，并在癫痫发作检测与客户流失预测任务中验证了方法的实证有效性，均取得具有竞争力的结果。除预测功能外，为提升可解释性，我们证实最优协方差幂次在捕捉结构特征的同时展现出良好的可辨识性证据，从而实现了预测性能与可解释统计结构的统一。