Temporally causal representation learning aims to identify the latent causal process from time series observations, but most methods require the assumption that the latent causal processes do not have instantaneous relations. Although some recent methods achieve identifiability in the instantaneous causality case, they require either interventions on the latent variables or grouping of the observations, which are in general difficult to obtain in real-world scenarios. To fill this gap, we propose an \textbf{ID}entification framework for instantane\textbf{O}us \textbf{L}atent dynamics (\textbf{IDOL}) by imposing a sparse influence constraint that the latent causal processes have sparse time-delayed and instantaneous relations. Specifically, we establish identifiability results of the latent causal process based on sufficient variability and the sparse influence constraint by employing contextual information of time series data. Based on these theories, we incorporate a temporally variational inference architecture to estimate the latent variables and a gradient-based sparsity regularization to identify the latent causal process. Experimental results on simulation datasets illustrate that our method can identify the latent causal process. Furthermore, evaluations on multiple human motion forecasting benchmarks with instantaneous dependencies indicate the effectiveness of our method in real-world settings.

翻译：时序因果表示学习旨在从时间序列观测中识别潜在的因果过程，但大多数方法需要假设潜在因果过程不存在瞬时关系。尽管最近的一些方法在瞬时因果性情况下实现了可识别性，但它们要么需要对潜在变量进行干预，要么需要对观测进行分组，而这在现实场景中通常难以获得。为填补这一空白，我们提出了一种通过施加稀疏影响约束（即潜在因果过程具有稀疏的时间延迟和瞬时关系）来识别瞬时潜在动态的框架（IDOL）。具体而言，我们基于时间序列数据的上下文信息，利用充分变异性和稀疏影响约束，建立了潜在因果过程的可识别性结果。基于这些理论，我们结合了时序变分推理架构来估计潜在变量，并采用基于梯度的稀疏正则化方法来识别潜在因果过程。在模拟数据集上的实验结果表明，我们的方法能够识别潜在因果过程。此外，在多个具有瞬时依赖性的人体运动预测基准上的评估证明了我们的方法在现实场景中的有效性。