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On the Identification of Temporal Causal Representation with Instantaneous Dependence
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Proposes IDOL, which identifies temporally causal latent processes with instantaneous dependencies under a sparse latent process assumption (no interventions or observation grouping), using a variational inference architecture with an L1 gradient-based sparsity penalty.
Problem
Identifying latent causal processes from time series when latent variables have instantaneous (same-timestep) dependencies, without requiring interventions on latents or grouping of observations.
Approach
Replace intervention or grouping assumptions with a sparse latent process assumption (sparse time-delayed and instantaneous influences), exploiting contextual information from neighboring timestamps to identify latent variables up to a Markov equivalence class and, under extra conditions, the causal graph; implemented via a temporal VAE with normalizing-flow prior networks and L1 penalties on the
Key results
- On simulation datasets, IDOL achieves the highest MCC on A, B, C, E, F (e.g., 0.9645 on A, 0.9747 on F) versus TDRL, G-CaRL, and iCITRIS; TDRL is best on D (0.9796 vs 0.9766).
- On human motion forecasting, IDOL achieves the best MSE/MAE on most tasks, reportedly outperforming the strongest baseline by 4%-34%, with a Wilcoxon signed-rank test at p<0.05.
- On dense dataset E, IDOL's MCC drops to 0.7869, which the authors take as the boundary of the theory when the sparsity assumption is violated.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use IDOL instead of the strongest reported baseline | latent-variable identification · Simulations A, B, C, E, and F | MCC: A: 0.9416 -> 0.9645; B: 0.8727 -> 0.9142; C: 0.9001 -> 0.9801; E: 0.7228 -> 0.7869; F: 0.6678 -> 0.9747 | Helped |
| Use IDOL instead of TDRL on the no-instantaneous-effects simulation | latent-variable identification · Simulation D | MCC: 0.9796 -> 0.9766 | Hurt |
| Use IDOL instead of the strongest listed baseline | human motion forecasting · HumanEva Jog, predict length 125 | MSE: 0.1598 -> 0.1516 | Helped |
| Use IDOL instead of the strongest listed baseline | human motion forecasting · HumanEva Walking, predict length 50 | MSE: 0.1245 -> 0.1183 | Helped |
| Use IDOL instead of TDRL | human motion forecasting · Human SittingDown, predict length 375 | MSE: 0.0301 -> 0.0290 | Helped |
| Use IDOL instead of the strongest listed baseline | human motion forecasting · Human CatchThrow, predict length 75 | MSE: 0.0136 -> 0.0175 | Hurt |
| Use IDOL instead of the strongest listed baseline | human motion forecasting · Human CatchThrow, predict length 75 | MAE: 0.0686 -> 0.0844 | Hurt |
| Apply IDOL to dense latent-process data that violates sparsity assumption A3 | latent-variable identification · Simulation E | MCC: 0.7869 | Mixed |
Surprising findings
- On the no-instantaneous-effect dataset D, the TDRL baseline slightly outperforms IDOL (0.9796 vs 0.9766).
Limitations
- Not designed for high-dimensional time series, since modeling complex dependencies under sparsity constraints is challenging.
- Relies on an invertible mixing function, which may not hold in real-world scenarios.
- Performance degrades on dense latent processes that violate the sparsity assumption (dataset E).
Experimental setup
Datasets: Synthetic datasets A-F Human3.6M HumanEva-I
Benchmarks: Synthetic datasets A-F (MCC) Human3.6M HumanEva-I
Metrics: MCC MSE MAE
Baselines: beta-VAE FactorVAE TDRL iVAE TCL PCL SlowVAE iCITRIS G-CaRL Autoformer TimesNet MICN
Builds on: TDRL iCITRIS G-CaRL iVAE
Closest papers by meaning
- Towards Identifiability of Hierarchical Temporal Causal Representation Learning (NeurIPS 2025 · similarity 0.92)
- Identifiable Latent Polynomial Causal Models through the Lens of Change (ICLR 2024 · similarity 0.90)
- A Sparsity Principle for Partially Observable Causal Representation Learning (ICML 2024 · similarity 0.90)
- Causal Temporal Representation Learning with Nonstationary Sparse Transition (NeurIPS 2024 · similarity 0.90)
- Disentangling Continuous-Time Latent Dynamics: Identifiability of Latent SDEs via Diffusion Shifts (NeurIPS 2026 · similarity 0.90)
- CaRiNG: Learning Temporal Causal Representation under Non-Invertible Generation Process (ICML 2024 · similarity 0.89)
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