🤖 AI Summary
Existing time-series causal representation learning methods typically neglect instantaneous causal relationships, while emerging approaches accommodating such dependencies rely on latent-variable interventions or grouped observational data—conditions rarely satisfied in practice. To address this, we propose IDOL, the first framework enabling unique identification of latent causal processes with instantaneous dependencies without requiring interventions or data grouping. Theoretically, IDOL introduces sparse influence constraints—unifying delayed and instantaneous causal modeling—and temporal context variability, establishing strong identifiability guarantees. Methodologically, it integrates temporal variational inference with gradient-driven sparse regularization to jointly estimate latent variables and the causal graph. Experiments demonstrate that IDOL achieves exact structural recovery on synthetic benchmarks and significantly improves long-horizon prediction accuracy and causal interpretability across multiple human motion forecasting datasets.
📝 Abstract
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 extbf{ID}entification framework for instantane extbf{O}us extbf{L}atent dynamics ( extbf{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.