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Learning General Causal Structures with Hidden Dynamic Process for Climate Analysis

Minghao Fu, Biwei Huang, Zijian Li, Yujia Zheng, Ignavier Ng, Guangyi Chen, Yingyao Hu, Kun Zhang

TL;DR

The paper tackles learning general causal structures in climate time series with latent dynamic drivers. It introduces CaDRe, a nonparametric framework that jointly uncovers latent dynamics and causal relations among observed variables by linking SEMs and nonlinear ICA, and enforcing identifiability through context, flow-based priors, and Jacobian-based structure learning. The estimation method integrates a time-series VAE with two encoders and a decoder, guided by ELBO and sparsity/DAG penalties to recover latent causal graphs. Experiments on synthetic and real climate data demonstrate identifiability of latent space and causal graphs, competitive forecasting accuracy, and interpretable graphs that align with domain knowledge, enabling scientific discovery and climate insight.

Abstract

Understanding climate dynamics requires going beyond correlations in observational data to uncover their underlying causal process. Latent drivers, such as atmospheric processes, play a critical role in temporal dynamics, while direct causal influences also exist among geographically proximate observed variables. Traditional Causal Representation Learning (CRL) typically focuses on latent factors but overlooks such observable-to-observable causal relations, limiting its applicability to climate analysis. In this paper, we introduce a unified framework that jointly uncovers (i) causal relations among observed variables and (ii) latent driving forces together with their interactions. We establish conditions under which both the hidden dynamic processes and the causal structure among observed variables are simultaneously identifiable from time-series data. Remarkably, our guarantees hold even in the nonparametric setting, leveraging contextual information to recover latent variables and causal relations. Building on these insights, we propose CaDRe (Causal Discovery and Representation learning), a time-series generative model with structural constraints that integrates CRL and causal discovery. Experiments on synthetic datasets validate our theoretical results. On real-world climate datasets, CaDRe not only delivers competitive forecasting accuracy but also recovers visualized causal graphs aligned with domain expertise, thereby offering interpretable insights into climate systems.

Learning General Causal Structures with Hidden Dynamic Process for Climate Analysis

TL;DR

The paper tackles learning general causal structures in climate time series with latent dynamic drivers. It introduces CaDRe, a nonparametric framework that jointly uncovers latent dynamics and causal relations among observed variables by linking SEMs and nonlinear ICA, and enforcing identifiability through context, flow-based priors, and Jacobian-based structure learning. The estimation method integrates a time-series VAE with two encoders and a decoder, guided by ELBO and sparsity/DAG penalties to recover latent causal graphs. Experiments on synthetic and real climate data demonstrate identifiability of latent space and causal graphs, competitive forecasting accuracy, and interpretable graphs that align with domain knowledge, enabling scientific discovery and climate insight.

Abstract

Understanding climate dynamics requires going beyond correlations in observational data to uncover their underlying causal process. Latent drivers, such as atmospheric processes, play a critical role in temporal dynamics, while direct causal influences also exist among geographically proximate observed variables. Traditional Causal Representation Learning (CRL) typically focuses on latent factors but overlooks such observable-to-observable causal relations, limiting its applicability to climate analysis. In this paper, we introduce a unified framework that jointly uncovers (i) causal relations among observed variables and (ii) latent driving forces together with their interactions. We establish conditions under which both the hidden dynamic processes and the causal structure among observed variables are simultaneously identifiable from time-series data. Remarkably, our guarantees hold even in the nonparametric setting, leveraging contextual information to recover latent variables and causal relations. Building on these insights, we propose CaDRe (Causal Discovery and Representation learning), a time-series generative model with structural constraints that integrates CRL and causal discovery. Experiments on synthetic datasets validate our theoretical results. On real-world climate datasets, CaDRe not only delivers competitive forecasting accuracy but also recovers visualized causal graphs aligned with domain expertise, thereby offering interpretable insights into climate systems.
Paper Structure (76 sections, 11 theorems, 55 equations, 10 figures, 16 tables)

This paper contains 76 sections, 11 theorems, 55 equations, 10 figures, 16 tables.

Table of Contents

  1. Introduction
  2. Problem Setup
  3. Identification Theory
  4. Latent Space Recovery and Latent Variables Identification
  5. Nonparametric Causal Discovery with Hidden Dynamic Process
  6. Estimation Methodology
  7. Overall Architecture.
  8. Structure Learning.
  9. Experiment
  10. On Synthetic Climate Data
  11. On Real-World Climate Data
  12. Baselines.
  13. Scientific Discovery using the Estimated Causal Graphs.
  14. Quantitative Results on CD.
  15. Physical Interpretability of Latent Space.
  16. ...and 61 more sections

Key Result

Lemma 1

(Injective DAG Operator) Under Assumption con:faith dag, $L_{\mathbf{x}_t \mid \mathbf{s}_t}$ is injective for all $t \in \mathcal{T}$.

Figures (10)

  • Figure 1: From climate system to causal graph. $\mathbf{x}_t$ represent observed data and $\mathbf{z}_t$ denotes unobserved variables behind $\mathbf{x}_t$, $\epsilon^z_t$ denotes the stochasticity in latent causal process, and $s_t$ denotes the noise variable varying with $\mathbf{z}_t$, e.g., human activities chen1995effects.
  • Figure 2: Equivalent SEM and ICA. The gray line in SEM denotes the influence $x_{t,2} \rightarrow x_{t,1}$ through the observation causal relation, which is equivalently represented as an indirect effect (the orange line): $s_{t,2} \dashrightarrow x_{t,1}$ in ICA, which can be decomposed into $s_{t,2} \rightarrow x_{t,2}$ and $x_{t,2} \rightarrow x_{t,1}$.
  • Figure 3: The estimation procedure of CaDRe. The model framework includes two encoders: z-encoder for extracting latent variables $\mathbf{z}_t$, and s-encoder for extracting nonstationary noise $\mathbf{s}_t$. A decoder reconstructs $\mathbf{x}_t$ from them. Additionally, prior networks estimate the prior distribution using a normalizing flow, focusing on learning the causal structures based on the Jacobian matrix. $\mathcal{L}_s$ imposes a sparsity constraint and $\mathcal{L}_d$ enforces the DAG structure on Jacobian matrix. $\mathcal{D}_{KL}$ enforces independence of the estimated noise by minimizing its KL divergence w.r.t. $\mathcal{N}(0, \mathbf{I})$. In summary, this method learns independent noise to inversely infer the causal structures.
  • Figure 4: Comparison with Constraint-Based CD. We report the mean/standard deviation for all experiments. Top: Results with $d_x = 6$, $d_z = 3$, varying $n = \{ 200, 1000, 5000, 10000, 20000\}$. Bottom: Results with the sample size $n = 10000$ while selecting $d_x = \{3,6,8,10\}$.
  • Figure 5: Estimated latent variables, latent causal process, and causal graph over the observed climate grids from CESM2, together with the wind field from rasp2020weatherbench, where longer red arrows indicate stronger winds. We also draw the overall wind trend in each map to show the consistency.
  • ...and 5 more figures

Theorems & Definitions (24)

  • Lemma 1
  • Theorem 1
  • Lemma 2
  • Theorem 2
  • Corollary 2.1
  • Corollary 2.2
  • Theorem 3
  • Definition 1
  • proof
  • Example 1
  • ...and 14 more