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Causal Temporal Representation Learning with Nonstationary Sparse Transition
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Proposes CtrlNS, a VAE-based framework that identifies nonstationary domain variables and time-delayed latent causal dynamics without observed domain indices or Markov priors, using a sparse transition constraint.
Problem
Causal temporal representation learning for nonstationary time series when domain variables are unobserved and no Markov prior on domains is available.
Approach
Identifies unobserved domain indices via transition-complexity (sparsity) minimization over transition functions, assuming transitions differ across domains in their causal support; then learns latent variables with conditional independence constraints, jointly optimized in a VAE with a gated set of transition networks (hard Gumbel-Softmax).
Key results
- On synthetic data, CtrlNS reaches 96.74 MCC for latent recovery and 98.21% accuracy for domain indices, versus 47.27 MCC and 34.94% accuracy for NCTRL.
- On Hollywood Extended action segmentation, CtrlNS reports 52.9 MoF, 32.7 IoU and 52.4 IoD, improving over ATBA (47.7, 28.5, 44.9).
- On CrossTask, CtrlNS reports 54.0 MoF versus 50.6 for ATBA, with IoU matched at 15.7 and IoD slightly lower (23.6 vs 24.6).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add sparse transition complexity regularization (ablation) | CtrlNS · Hollywood | MoF: 50.5 -> 52.9 | Helped |
| add sparse transition complexity regularization (ablation) | CtrlNS · Hollywood | IoU: 31.5 -> 32.7 | Helped |
| add sparse transition complexity regularization (ablation) | CtrlNS · Hollywood | IoD: 51.5 -> 52.4 | Helped |
| add the sparse transition module (ablation) | ATBA · Hollywood | MoF: 47.7 -> 52.9 | Helped |
| add the sparse transition module (ablation) | ATBA · Hollywood | IoU: 28.5 -> 32.7 | Helped |
| add the sparse transition module (ablation) | ATBA · Hollywood | IoD: 44.9 -> 52.4 | Helped |
| use CtrlNS instead of ATBA | Hollywood action segmentation · Hollywood | MoF: 47.7 -> 52.9 | Helped |
| use CtrlNS instead of ATBA | Hollywood action segmentation · Hollywood | IoU: 28.5 -> 32.7 | Helped |
| use CtrlNS instead of ATBA | Hollywood action segmentation · Hollywood | IoD: 44.9 -> 52.4 | Helped |
| use CtrlNS instead of ATBA | CrossTask action segmentation · CrossTask | MoF: 50.6 -> 54.0 | Helped |
| use CtrlNS instead of ATBA | CrossTask action segmentation · CrossTask | IoU: 15.7 -> 15.7 | No clear effect |
| use CtrlNS instead of ATBA | CrossTask action segmentation · CrossTask | IoD: 24.6 -> 23.6 | Hurt |
Surprising findings
- Baselines that ignore domain information (e.g., i-VAE, BetaVAE) can outperform NCTRL and TDRL, which use incorrect Markov assumptions on domain variables.
- Markov-based HMM methods underperform on real-world action segmentation, supporting the claim that Markov domain priors are limiting.
Limitations
- Identifiability theory relies on assumptions (mechanism variability, weak diverse lossy transitions, sparsity) that may be hard to verify in practice.
- Real-world evaluation is limited to action segmentation, and IoD on CrossTask is slightly below ATBA.
- Assumes parents restricted to the previous time step in the main analysis; higher-order delays are deferred to appendix.
Experimental setup
Datasets: Hollywood Extended CrossTask synthetic nonstationary time series
Benchmarks: Hollywood Extended CrossTask synthetic nonstationary causal temporal data
Metrics: MCC clustering accuracy MoF IoU IoD
Baselines: BetaVAE i-VAE TCL SlowVAE PCL TDRL HMNLICA NCTRL HMM+RNN CDFL TASL MuCon
Builds on: TDRL NCTRL HMNLICA ATBA i-VAE
Closest papers by meaning
- CaRiNG: Learning Temporal Causal Representation under Non-Invertible Generation Process (ICML 2024 · similarity 0.90)
- On the Identification of Temporal Causal Representation with Instantaneous Dependence (ICLR 2025 · similarity 0.90)
- Causal Representation Learning Made Identifiable by Grouping of Observational Variables (ICML 2024 · similarity 0.89)
- Learning Linear Causal Representations from General Environments: Identifiability and Intrinsic Ambiguity (NeurIPS 2024 · similarity 0.89)
- Towards Identifiability of Hierarchical Temporal Causal Representation Learning (NeurIPS 2025 · similarity 0.89)
- A Sparsity Principle for Partially Observable Causal Representation Learning (ICML 2024 · similarity 0.88)
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