Research map / Probabilistic and scientific modeling / Causal discovery
Towards Identifiability of Hierarchical Temporal Causal Representation Learning
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes CHiLD, a theoretically grounded identification framework and VAE-based generative model for time series with hierarchical latent dynamics, using temporal contextual observations and sparsity of hierarchical structure.
Problem
Existing temporal causal representation learning methods assume a single latent layer and cannot identify hierarchical latent dynamics from single-timestep observations, so they cannot recover the joint distribution of multi-layer latent variables.
Approach
Shows that the joint distribution of hierarchical latent variables is identifiable using 2L+1 adjacent (temporal contextual) observations via spectral decomposition of conditionally independent observations; then uses the natural sparsity of hierarchical structure (cross-derivative zeros) to identify each layer's latents. Implements this as a contextual TCN encoder, step-wise decoder, and normaliz
Key results
- On synthetic datasets A-G, CHiLD achieves the highest MCC on A, C, D, E, F, G (e.g., 0.901 on A vs 0.842 for IDOL), with B tied-level with TDRL.
- On real-world generation, CHiLD achieves the best Context-FID on Weather (0.507), WeatherBench (0.078), CESM2 (0.018), and most human motion datasets versus KoVAE, Diffusion-TS, TimeGAN, IDOL, cwVAE, TimeVAE.
- Theory shows that 2L+1 adjacent observations are the minimal information needed for block-wise identifiability of the joint multi-layer latent distribution.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use CHiLD instead of the strongest baseline | Real-world time-series generation · Weather, WeatherBench, CESM2, Throwcatch, Discussion, Purchases, WalkDog | Context-FID: Weather: 2.131(0.637) -> 0.507(0.042); WeatherBench: 0.171(0.032) -> 0.078(0.017); CESM2: 0.108(0.029) -> 0.018(0.003); | Helped |
| Use CHiLD instead of the strongest baseline | Real-world time-series generation · Box and Gestures | Context-FID: Box: 0.056(0.009) -> 0.092(0.011); Gestures: 0.018(0.004) -> 0.032(0.004) | Hurt |
| Use CHiLD instead of the strongest baseline | Real-world time-series generation · Weather, WeatherBench, CESM2, Gestures, Throwcatch, Discussion, Purchases, WalkDog | Correlational Score: Weather: 0.584(0.013) -> 0.165(0.004); WeatherBench: 20.384(0.082) -> 5.190(0.016); CESM2: 6.469(0.022) -> 1.250(0.009); | Helped |
| Use CHiLD instead of the strongest baseline | Real-world time-series generation · Box | Correlational Score: 0.812(0.026) -> 1.599(0.021) | Hurt |
| Use CHiLD rather than the strongest baseline | Synthetic latent representation learning · Synthetic datasets A, C, D, E | MCC: A: 0.842(0.033) -> 0.901(0.043); C: 0.801(0.031) -> 0.835(0.012); D: 0.788(0.082) -> 0.841(0.016); E: 0.741(0.043) -> 0. | Helped |
| Use CHiLD rather than the strongest baseline | Synthetic latent representation learning · Synthetic datasets B, F, G | MCC: B: 0.942(0.076) -> 0.941(0.037); F: 0.723(0.024) -> 0.808(0.002); G: 0.611(0.005) -> 0.774(0.007) | Mixed |
Surprising findings
- Dataset B (single-layer) results show CHiLD, IDOL and CaRiNG perform comparably, with TDRL slightly best, suggesting no advantage without hierarchical dynamics.
Limitations
- Component-wise identifiability relies on layer-wise conditional independence and sufficient variability assumptions.
- Performance drops on high-dimensional, many-layer synthetic datasets (F, G) though it still beats baselines.
- Theoretical assumptions (bounded, continuous densities, injective operators) may be strong in practice.
Experimental setup
Datasets: Stock ETTh1 fMRI MuJoCo Human3.6M HumanEva-I Weather WeatherBench CESM2 synthetic datasets A-G
Benchmarks: Stock ETTh1 fMRI MuJoCo Human3.6M HumanEva-I Weather WeatherBench CESM2
Metrics: MCC Context-FID Correlational Score
Baselines: beta-VAE FactorVAE TDRL iVAE TCL PCL SlowVAE CaRiNG IDOL cwVAE KoVAE TimeVAE
Builds on: IDOL CaRiNG iVAE TCL TDRL
Closest papers by meaning
- On the Identification of Temporal Causal Representation with Instantaneous Dependence (ICLR 2025 · similarity 0.92)
- CaRiNG: Learning Temporal Causal Representation under Non-Invertible Generation Process (ICML 2024 · similarity 0.90)
- Identifiable Latent Polynomial Causal Models through the Lens of Change (ICLR 2024 · similarity 0.89)
- Learning Linear Causal Representations from General Environments: Identifiability and Intrinsic Ambiguity (NeurIPS 2024 · similarity 0.89)
- Causal Temporal Representation Learning with Nonstationary Sparse Transition (NeurIPS 2024 · similarity 0.89)
- Differentiable Causal Discovery for Latent Hierarchical Causal Models (ICLR 2025 · similarity 0.89)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.