标题： 面向分层时间因果表征学习的可辨识性 显示英文标题

标题： Towards Identifiability of Hierarchical Temporal Causal Representation Learning

摘要： 建模时间序列数据背后的分层潜在动态对于捕捉现实任务中多层抽象的时序依赖关系至关重要。 然而，现有的时间因果表示学习方法无法捕捉这种动态，因为它们无法从\textit{单时间步观测变量}中恢复分层潜在变量的联合分布。 有趣的是，我们发现可以通过三个条件独立的观察来唯一确定分层潜在变量的联合分布。 基于这一见解，我们提出了一种因果分层潜在动态（CHiLD）识别框架。 我们的方法首先利用时间上下文观测变量来识别多层潜在变量的联合分布。 随后，我们利用潜在变量之间的分层结构的自然稀疏性来识别每一层中的潜在变量。 在理论结果的指导下，我们开发了一个基于变分推断的时间序列生成模型。 该模型结合了一个上下文编码器来重建多层潜在变量，并使用基于归一化流的分层先验网络来施加分层潜在动态的独立噪声条件。 在合成和真实世界数据集上的实证评估验证了我们的理论主张，并展示了CHiLD在建模分层潜在动态方面的有效性。 显示英文摘要

摘要： 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.