Title: Learning General Causal Structures with Hidden Dynamic Process for Climate Analysis
Venue: NeurIPS 2025
Accepted: no
Keywords: Climate Analysis; Causal Discovery; Causal Representation Learning
Abstract: The heart of climate analysis is a rational effort to understand the causes behind the purely observational data. Latent driving forces, such as atmospheric processes, play a critical role in temporal dynamics, and the task of inferring such latent forces is often a problem of Causal Representation Learning (CRL). Moreover, geographically nearby regions may directly interact with each other, and such direct causal relations among the observed data are often not modeled in traditional CRL, making the problem more challenging. 
In this paper, we propose a unified framework that can uncover not only the latent driving forces, but also the causal relations among the observed variables. 
We establish conditions under which the hidden dynamic process and the relations among the observed variables are simultaneously identifiable from time-series data. Even without parametric assumptions on the causal relations, we provide identifiability guarantees for recovering latent variables and the relations among the observed variables via contextual information. 
Guided by these insights, we propose a framework for nonparametric Causal Discovery and Representation learning (CaDRe), based on a time-series generative model with structural constraints. Synthetic data validates our theoretical claims. On real-world climate datasets, CaDRe achieves competitive forecasting performance and offers the visualized causal graphs consistent with domain knowledge, which is expected to improve our understanding of the climate systems.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis work establishes a refined connection between SEM (Structural Equation Model) with non-linear ICA (Independent Component Analysis), and applies it in climate analysis applications. Specifically, it extends ICA-based causality discovery to nonparametric settings with the presence of latent confounders. It proves an equivalence between SEM and non-linear ICA in this setting so that it is possible to learn an ICA instead of SEM. The training objective consists of ELBO and two penalty terms. Experiments on both synthetic and real-world climate datasets demonstrate the performance of proposed CaDRe and validate the theoretical design.\n\nSTRENGTHS AND WEAKNESSES:\nThis work is solid in general, with some (probably minor) issue before granting an acceptance. On the strengths, the proof of the existence of equivalent ICA to SEM is not trivial, and this work manages to make the formulations and proofs simple in presentation. Additionally, the performance of the proposed CaDRe could be validated on real-world datasets in the climate domain. The discovered of causailties also coincident with climate knowledge.\n\nHowever, there are some weaknesses of this paper, from which the current manuscript can be improved.\n\nW1. The proposed method could generalize to domains beyond climate data, wherever there could be latent variables, it seems CaDRe can be used. There are many time series data in other domains which could also serve as the testbed. Please correct me if there are some specific constraints that CaDRe can only be used on climate data.\n\nW2. On synthetic data, the comparison are mainly with causal learning models, yet the comparison with time series models are not convincing, as the compared models PCMCI and LPCMCI are methods up to year 2020. Comparison of more recent time series models are needed.\n\nW3. On real-world data, the experiment is conducted on only one dataset CESM2, whose statistics and scale is uncertain from the main page.\n\nW3. It is not very clear how the latent variables (z) are interpreted for climate analysis. Specifically, there should be details of how visualization is conducted.\n\nW4. The advantage of learning non-linear ICA instead of SEM should also be discussed and verified. In other words, this word should emphasize why bother to prove the existence of equivalent ICA and try to build it, instead of just training an SEM. \n\nW5. Efficiency is not considered in this manuscript. The training/inference time is not reported for any method.\n\nQUESTIONS:\nPlease refer to the weaknesses.\n\nLIMITATIONS:\nThis is a pure ML research work without potential negative social impact.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper handles causal discovery over observational variables while identifying the latent variables. The authors assume a generative model grounded in climate analysis intuitions where an observed variable is causally affected not only by its lagged or instantaneous counterparts but also by some of the latent variables. The authors also assume that some of the latents $z_t$ are not necessarily causal parents but may modulate the causal mechanism behind observed variables $x_t$ through a random term $s_t$. The authors demonstrate a pointwise identification of latent variables and an “edge-by-edge” identification over the causal graph over observed variables. Experiments show improvement in structure recovery w.r.t. baselines.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths\n- The authors made commendable efforts in clearly communicating their works, although some parts might have been better written.  \n- The theoretical part has discussed the main important aspects of the problem.  \n- The model proposed was compared against a very fair number of baselines in both causal discovery and time series forecasting.  \n- I took note of the quality of the appendix complementing the main paper (although some elements should have been stated in the core paper for better clarity—see below).  \n\n## Weaknesses\n- For “$s_{t,i} = g_{si}(z_t, \\epsilon_{x_{t,i}})$” in Eq. 1, authors mentioned “noise conditioned on $z_t$”; however, it should not be considered “noise,” since it depends on $z_t$. $s_t$ plays the role of an endogenous mediator.  \n- “$s_{t}$ is said to be ‘designed to capture inherent climatic variability, such as perturbations introduced by human activities on CO₂’”: I think further attention should be paid to explaining the idea behind $s_t$. I am not an expert in climate analysis, but it is unclear how $s_t$, being—for example—interpreted as perturbations induced by human activity on CO₂, could be “driven” by latent causes like solar radiation as said in the text.  \n- The authors mention causal representation learning, and in Table 1 the model CADRe claims to recover a “latent causal graph.” However, there is no discussion of the identification of the causal graphs between the latent variables (lagged and instantaneous edges). Unless mistaken, there is no clear discussion of how such a graph is identified or learned—only pointwise identifiability of latents in Thm 1. This should be clarified, plus I think it should be clarified that identifying $\\mathrm{pa}_\\ell(x_{i,t})$, although concerning latent variables, is not a classical task of CRL.  \n- “We denote $J_d(\\hat z_{t+1})$ as the Jacobian matrix of the function $r$,” the notation is confusing: the Jacobian of $r$ should better be denoted $J_r$, but $r$ in line 235 has two arguments $(\\hat z_{t+1}, \\hat z_t)$. Can you please clarify the notations and enhance the presentation quality of the paragraph “Prior Estimation of $z_t$ and $s_t$”?\n\n\n## Notation and Typo issues\n\n- “the stochasticility” should be “stochasticity.”  \n- Bad notation to use $M$ for a functional in “A4 (Differentiability:)” (line 137).  \n- “As depicted in Eq. (A19),” in line 151, the equation is missing (I know it is in the separate appendix, but its omission disrupts the flow).  \n- Line 139: “where $h$ is differentiable.” should read “where $h_z$ is differentiable.”  \n-  Paragraph “Prior Estimation of $z_t$ and $s_t$.” is poorly written and difficult to read.  \n- Line 242: “we using” should be “we are using.”  \n-  Line 257: “$D(A)$” overlaps with $D$ used earlier for KL divergence.  \n-  Equations 10–11: Please specify the summands in $\\Sigma$; it is very unclear.  \n- Line 267: Metric names should be at least mentioned, and definitions could be deferred to the appendix.\n\nQUESTIONS:\n- Theorem 3 (lines 202–203): Definition 5 is missing from the paper (present only in the appendix), making the theorem statement on the identification of observational causal graph unclear. Moreover, the definition in the appendix refers to $s_t$, creating confusion because $s_t$ are the stochastic mediators. The authors did not claim such identifying $s_t$ in the main text. Looking at the proof, Definition 5 appears to be an intermediate step near the end of observational causal graph identification. Can you please clarify the result related to Def 5 and how it relates to identifying the observed causal graph?  \n- In Table 2: Can you further elaborate on the meaning of “the best-converged result per seed is selected to avoid local minima”?  \n- In Figure 5, “$d_x = 6$ and $d_z = 3$” are very low dimensions; How do the exact metrics reported in Figure 5 evolve as a function of $d_x$, including other baselines?  \n- Figure 6: “CaDRe matches observational causal graphs to physical wind patterns.” What about other baselines that could provide the same instantaneous causal graph? How do they qualitatively match the physical wind patterns?\n\nLIMITATIONS:\n* Authors did not discuss how the developed approach may or may not generalize to other domains beyond climate analysis.\n* The distributional assumptions like A2 and A3 are very strong.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces CaDRe, which aims to uncover the latent driving forces and causal relations among the observed variables in climate analysis. They provided a detailed theoretical analysis and demonstrated the effectiveness of the proposed method using synthetic and real-world experiments.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n\n1. This paper provides novel methods and insights for the application of causal discovery in the field of climate analysis, and achieves solid results.\n\n2. This paper provides a detailed theoretical analysis of the proposed causal discovery framework.\n\n**Weaknesses**\n\n1. This paper uses an MLP to map observed variables into a latent space for causal discovery. However, the paper does not explain whether the latent space has a clear physical meaning and whether it has a consistent meaning across different datasets.\n\n2. Although the authors mention discussions about higher-order Markov structures in the article, there does not seem to be much experimental verification.\n\nQUESTIONS:\n1. The author maps observed variables to latent variables, and the dimension between variables changes from $d_x$ to $d_z$. It is expected that latent variables can represent variables with clear meanings, such as pressure and precipitation, but is this representation consistent? Is the physical meaning of latent variables fixed and clear across different datasets?\n\n2. We can understand that due to the rapid changes in the climate system, the time lagged effects between variables may not need to be set to a particularly high order, but using only 1 lag is not sufficient. We can provide some experimental results under high-order conditions.\n\n3. The experimental results in Table 2 show that when $d_x$ becomes larger, the effect of the fixed 3-dimensional latent variables $d_z$ becomes worse. However, we noticed that when $d_x$ is 100, $d_z$ is also 3, but its index results are significantly better. How should we understand this?\n\nLIMITATIONS:\nyes.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper, introduces a novel framework called CaDRe (Causal Discovery and Representation Learning). Its primary goal is to uncover complex causal structures within climate systems from purely observational time-series data. A core innovation of CaDRe lies in its unification of Causal Representation Learning (CRL) and Causal Discovery (CD), establishing rigorous identifiability conditions for both latent processes and observed causal graphs, even without strong parametric assumptions. The framework leverages a novel theoretical connection between Structural Equation Models (SEM) and Nonlinear Independent Component Analysis (ICA) to achieve this. Methodologically, CaDRe is instantiated as a state-space Variational Autoencoder (VAE) that incorporates flow-based priors and gradient-based structural penalties to ensure the identifiability and sparsity of the learned causal graphs.\nEmpirical validation, through synthetic data experiments, confirms its theoretical claims, demonstrating CaDRe's ability to recover latent representations and causal structures. On real-world climate datasets (CESM2 sea surface temperature), CaDRe achieves competitive forecasting performance and visualizes causal graphs consistent with domain knowledge, such as wind circulation patterns and land-sea interactions, even revealing structural patterns that may inspire new hypotheses in climate science.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n- the paper explicitly identifies the need for a \"unified framework\". By simultaneously addressing both latent variable discovery (CRL) and observed variable causal discovery (CD), CaDRe tackles a more complete and realistic problem than methods that focus on only one aspect or assume simpler data-generating processes.\n- The paper provides rigorous identifiability proofs in a nonparametric setting , which is crucial for the complex and often unknown functional forms in climate systems.The assumptions are clearly stated and discussed, indicating a deep theoretical understanding.\n- Beyond competitive forecasting performance , CaDRe's ability to generate \"visualized causal graphs consistent with domain knowledge\" is a major strength for scientific applications.\nWeaknesses:\n- The method exhibits performance degradation as the data dimensionality increases. This implies that as the number of variables in climate models grows, or when analyzing at finer scales where more interconnected factors need to be considered, CaDRe's efficiency and accuracy might be impacted. This could limit its direct applicability in handling extremely complex and high-dimensional climate datasets.\n\nQUESTIONS:\n- How robust is CaDRe when some of the conditions in Assumptions A1-A5 are partially violated in real-world data? Are there ways to quantify the degree of these violations and assess their impact on the results?\n- How can the \"physical interpretability\" of the latent variables $$z_t$$ and noise terms $$s_t$$ be quantified or evaluated beyond consistency with domain knowledge? Are there more rigorous metrics?\n\nLIMITATIONS:\n- Performance Degradation with Dimensionality: The method shows reduced performance as d increases, though partitioning variables via geographical priors is suggested as a solution.\n- Reliance on Observational Data: The framework assumes access to time-series data, but climate observations are often sparse or noisy, which may impact identifiability in practice.", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 2, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nCausal discovery and representation learning are important approaches to better understand, for instance, Earth's climate or generally (spatio-)temporal data. The work builds a theory of when causal links are identifiable from such purely observational data while considering causal dependencies within and between both the observed and latent factors. The novel framework CaDRe is then composed of standard machine learning components and can uncover such causal graphs. Empirical findings on synthetic and real-world Earth data confirm the model's effectiveness.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths:**\n- The paper is of high quality and written clearly.\n- The problem being tackled is important. It is a significant contribution.\n- The provided identification theory on latent variables is a substantial contribution, although in large parts deferred to the appendix. I did not check it in detail.\n- The construction of the CD method is convincing and not more complex than necessary.\n- The empirical findings support the methods' effectiveness.\n- I am not sufficiently familiar with the field of CD/CRL to judge the overall novelty of the method nor the completeness of CD/CRL baselines.\n\n**Opportunities for improvement (weaknesses):**\n- The time-series forecasting baselines in Sec. 5.2 are not the latest (see, e.g., TimeMixer, xLSTM-Mixer, Chimera, or pretrained models such as Timer-XL). However, this does not substantially weaken the findings.\n- While the key contributions are theoretical and on the modeling side (i.e., not the application), the core motivation for CaDRe was still climate science. However, only a single experiment on it is provided (CD in Sec. 5.2), which could be evaluated in more depth.\n- The results on CD on actual climate data (Sec. 5.2) are solely qualitative. They lack contextualization of how existing models would fare. Additionally, a quantitative measure of correctness would be helpful as an aggregate indicator. This would be helpful since it is very hard to even qualitatively judge the appropriateness of the learned graph. Adding colors to denote correct/incorrect edges could be one more opportunity to improve this directly. The caption of Fig. 6/description in the text is overall rather minimal. See also Q1 below.\n- No next steps (future work) are discussed.\n\nQUESTIONS:\n- Q1: What is the meaning of the arrow length in Fig. 6: The certainty of the edge existing in that orientation, or the strength of the influence?\n- Q2: What are the latent factors that have been identified by CaDRe? The goal of CD/CRL in climate sciences is to uncover hidden structure, so having a latent representation we can understand is key.\n\nLIMITATIONS:\nThe discussion of limitations is very minimal. Aspects that are not sufficiently explored are robustness to noise and, generally, the set of assumptions necessary to run the method.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 2, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-03"}