On the Identification of Temporally Causal Representation with Instantaneous Dependence

TL;DR

This paper introduces IDOL, a novel framework for identifying latent causal processes in time series with instantaneous and delayed dependencies, using sparsity constraints and variational inference.

Contribution

The paper proposes a new identifiability framework for instantaneous causal latent dynamics that does not require interventions or grouping, leveraging sparsity and variability.

Findings

Successfully identifies latent causal processes in simulations.

Effective in real-world human motion forecasting with instantaneous dependencies.

Outperforms existing methods in causal discovery accuracy.

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.