On the Identification of Temporally Causal Representation with Instantaneous Dependence
Zijian Li, Yifan Shen, Kaitao Zheng, Ruichu Cai, Xiangchen Song, Mingming Gong, Guangyi Chen, Kun Zhang
TL;DR
This work addresses identifiability in time-series learning when latent causal processes exhibit instantaneous dependencies. It introduces IDOL, a sparse latent-process framework combined with temporally variational inference and gradient-based sparsity regularization to identify latent variables and their causal graph up to a Markov-equivalence class, without requiring interventions or grouping. Theoretical identifiability results are derived using sufficiency of variability and sparse-influence priors, and are validated on synthetic data and real-world human motion benchmarks, showing improved latent recovery and forecasting. The approach advances causal representation learning by accommodating instantaneous effects and providing practical mechanisms for estimation, with noted limitations in high-dimensional settings and invertible mixing assumptions.
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 \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.