Towards Identifiability of Hierarchical Temporal Causal Representation Learning

2025/10/21 by Zijian Li, Minghao Fu, Li, Zijian +13 · 1 citation
Computer Science · Neuroscience · #Embodied and Extended Cognition #FOS: Computer and information sciences #Generative Adversarial Networks and Image Synthesis #Machine Learning (cs.LG) #Machine Learning in Healthcare #Methodology (stat.ME)

paper · pdf · doi:10.48550/arxiv.2510.18310

openalex publication_date 2025/10/21 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

Modeling hierarchical latent dynamics behind time series data is critical for capturing temporal dependencies across multiple levels of abstraction in real-world tasks. However, existing temporal causal representation learning methods fail to capture such dynamics, as they fail to recover the joint distribution of hierarchical latent variables from single-timestep observed variables. Interestingly, we find that the joint distribution of hierarchical latent variables can be uniquely determined using three conditionally independent observations. Building on this insight, we propose a Causally Hierarchical Latent Dynamic (CHiLD) identification framework. Our approach first employs temporal contextual observed variables to identify the joint distribution of multi-layer latent variables. Sequentially, we exploit the natural sparsity of the hierarchical structure among latent variables to identify latent variables within each layer. Guided by the theoretical results, we develop a time series generative model grounded in variational inference. This model incorporates a contextual encoder to reconstruct multi-layer latent variables and normalize flow-based hierarchical prior networks to impose the independent noise condition of hierarchical latent dynamics. Empirical evaluations on both synthetic and real-world datasets validate our theoretical claims and demonstrate the effectiveness of CHiLD in modeling hierarchical latent dynamics.

Citations

• Synergy Between Sufficient Changes and Sparse Mixing Procedure for Disentangled Representation Learning
• Learning General Causal Structures with Hidden Dynamic Process for Climate Analysis
• On the Identification of Temporally Causal Representation with Instantaneous Dependence
• Diffusion-TS: Interpretable Diffusion for General Time Series Generation
• Causal Representation Learning from Multiple Distributions: A General Setting
• CaRiNG: Learning Temporal Causal Representation under Non-Invertible Generation Process
• Identifying Semantic Component for Robust Molecular Property Prediction
• Generalizing Nonlinear ICA Beyond Structural Sparsity
• Causal Representation Learning Made Identifiable by Grouping of Observational Variables
• Subspace Identification for Multi-Source Domain Adaptation
• Generative Modeling of Regular and Irregular Time Series Data via Koopman VAEs
• Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecasting
• Causal Recurrent Variational Autoencoder for Medical Time Series Generation
• Temporally Disentangled Representation Learning
• HyperTime: Implicit Neural Representation for Time Series
• On the Identifiability of Nonlinear ICA: Sparsity and Beyond
• Causal Representation Learning for Instantaneous and Temporal Effects in Interactive Systems
• Deep Generative model with Hierarchical Latent Factors for Time Series Anomaly Detection
• Towards Generating Real-World Time Series Data
• TimeVAE: A Variational Auto-Encoder for Multivariate Time Series Generation
• Learning Temporally Causal Latent Processes from General Temporal Data
• Generative Adversarial Networks
• PSA-GAN: Progressive Self Attention GANs for Synthetic Time Series
• Disentangling Identifiable Features from Noisy Data with Structured Nonlinear ICA
• Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style
• Clockwork Variational Autoencoders
• Towards Nonlinear Disentanglement in Natural Data with Temporal Sparse Coding
• Conditional GAN for timeseries generation
• Hidden Markov Nonlinear ICA: Unsupervised Learning from Nonstationary Time Series
• Denoising Diffusion Probabilistic Models
• Normalizing Flows for Probabilistic Modeling and Inference
• Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning
• Disentangling by Factorising
• Real-valued (Medical) Time Series Generation with Recurrent Conditional GANs
• C-RNN-GAN: Continuous recurrent neural networks with adversarial training
• Temporal Convolutional Networks for Action Segmentation and Detection
• Temporal Convolutional Networks: A Unified Approach to Action Segmentation
• Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA
• A Recurrent Latent Variable Model for Sequential Data
• Variational Inference with Normalizing Flows
• Structured Stochastic Variational Inference
• Instrumental Variable Estimation of Nonparametric Models
• Independent component analysis: algorithms and applications
• Causal Representation Learning from Multimodal Biomedical Observations

Cited by

• PersonaX: Multimodal Datasets with LLM-Inferred Behavior Traits
• Geometric Causal Models

Related

• Differentiable Causal Discovery For Latent Hierarchical Causal Models
• Learning Temporally Causal Latent Processes from General Temporal Data
• Identification of Nonlinear Latent Hierarchical Models
• On the Identification of Temporally Causal Representation with Instantaneous Dependence
• Time Series Domain Adaptation via Latent Invariant Causal Mechanism