Towards Identifiability of Hierarchical Temporal Causal Representation Learning

• URL: http://arxiv.org/abs/2510.18310v1
• Date: Tue, 21 Oct 2025 05:40:17 GMT
• Title: Towards Identifiability of Hierarchical Temporal Causal Representation Learning
• Authors: Zijian Li, Minghao Fu, Junxian Huang, Yifan Shen, Ruichu Cai, Yuewen Sun, Guangyi Chen, Kun Zhang,
• Abstract summary: We propose a Causally Hierarchical Latent Dynamic (CHiLD) identification framework.<n>We exploit the natural sparsity of the hierarchical structure among latent variables to identify latent variables within each layer.<n>This model incorporates a contextual encoder to reconstruct multi-layer latent variables and normalize flow-based hierarchical prior networks.
• Score: 37.974090366909586
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Modeling hierarchical latent dynamics behind time series data is critical for capturing temporal dependencies across multiple levels of abstraction in real-world tasks. However, existing temporal causal representation learning methods fail to capture such dynamics, as they fail to recover the joint distribution of hierarchical latent variables from \textit{single-timestep observed variables}. Interestingly, we find that the joint distribution of hierarchical latent variables can be uniquely determined using three conditionally independent observations. Building on this insight, we propose a Causally Hierarchical Latent Dynamic (CHiLD) identification framework. Our approach first employs temporal contextual observed variables to identify the joint distribution of multi-layer latent variables. Sequentially, we exploit the natural sparsity of the hierarchical structure among latent variables to identify latent variables within each layer. Guided by the theoretical results, we develop a time series generative model grounded in variational inference. This model incorporates a contextual encoder to reconstruct multi-layer latent variables and normalize flow-based hierarchical prior networks to impose the independent noise condition of hierarchical latent dynamics. Empirical evaluations on both synthetic and real-world datasets validate our theoretical claims and demonstrate the effectiveness of CHiLD in modeling hierarchical latent dynamics.

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