Causal Discovery

Follow this topic Ask about this topic

Causal discovery studies how to recover directed relationships among variables when experiments are limited or observational data alone are ambiguous. Methods include conditional-independence tests, score-based and ordering searches, functional models such as additive-noise and LiNGAM, and approaches that use interventions or changes across environments; time-series methods also model lagged effects and feedback. Latent confounding, missing data, nonstationarity, and measurement noise complicate recovery, so results often depend on assumptions and may identify only an equivalence class rather than one graph. Current work seeks methods that scale to large and diverse datasets while quantifying uncertainty and testing robustness, with a continuing challenge of translating benchmark performance into reliable real-world discoveries.

Latest papers

222 papers31 papers in the last four weeks, up 72% on the four weeks before. 0.2% of all new papers.

Mar 23, 2026

Causal Discovery in Action: Learning Chain-Reaction Mechanisms from Interventions

Causal discovery is challenging in general dynamical systems because, without strong structural assumptions, the underlying causal graph may not be identifiable even from interventional data. However, many real-world systems exhibit directional, cascade-like structure, in which components activate sequentially and upstream failures suppress downstream effects. We study causal discovery in such chain-reaction systems and show that the causal structure is uniquely identifiable from blocking interventions that prevent individual components from activating. We propose a minimal estimator with finite-sample guarantees, achieving exponential error decay and logarithmic sample complexity. Experiments on synthetic models and diverse chain-reaction environments demonstrate reliable recovery from a few interventions, while observational heuristics fail in regimes with delayed or overlapping causal effects.

Panayiotis Panayiotou, Özgür Şimşek

Department of Computer Science, University of Bath, UK

Causal Discovery Causal Identifiability Causal Intervention

Mar 23, 2026

On the Number of Conditional Independence Tests in Constraint-based Causal Discovery

Learning causal relations from observational data is a fundamental problem with wide-ranging applications across many fields. Constraint-based methods infer the underlying causal structure by performing conditional independence tests. However, existing algorithms such as the prominent PC algorithm need to perform a large number of independence tests, which in the worst case is exponential in the maximum degree of the causal graph. Despite extensive research, it remains unclear if there exist algorithms with better complexity without additional assumptions. Here, we establish an algorithm that achieves a better complexity of

p^{\mathcal{O}(s)}

tests, where

p

is the number of nodes in the graph and

s

denotes the maximum undirected clique size of the underlying essential graph. Complementing this result, we prove that any constraint-based algorithm must perform at least

2^{Ω(s)}

conditional independence tests, establishing that our proposed algorithm achieves exponent-optimality up to a logarithmic factor in terms of the number of conditional independence tests needed. Finally, we validate our theoretical findings through simulations, on semi-synthetic gene-expression data, and real-world data, demonstrating the efficiency of our algorithm compared to existing methods in terms of number of conditional independence tests needed.

Marc Franquesa Monés, Jiaqi Zhang, Caroline Uhler

Eric and Wendy Schmidt Center, Broad Institute of MIT and Harvard · Centre de Formació Interdisciplinària Superior, Universitat Politècnica de Catalunya · Laboratory for Information and Decision Systems, Massachusetts Institute of Technology

Constraint-Based Causal Discovery Causal Discovery Causal Structure Learning Conditional Independence Testing

Mar 21, 2026

A Knowledge-Informed Pretrained Model for Causal Discovery

Causal discovery has been widely studied, yet many existing methods rely on strong assumptions or fall into two extremes: either depending on costly interventional signals or partial ground truth as strong priors, or adopting purely data driven paradigms with limited guidance, which hinders practical deployment. Motivated by real-world scenarios where only coarse domain knowledge is available, we propose a knowledge-informed pretrained model for causal discovery that integrates weak prior knowledge as a principled middle ground. Our model adopts a dual source encoder-decoder architecture to process observational data in a knowledge-informed way. We design a diverse pretraining dataset and a curriculum learning strategy that smoothly adapts the model to varying prior strengths across mechanisms, graph densities, and variable scales. Extensive experiments on in-distribution, out-of distribution, and real-world datasets demonstrate consistent improvements over existing baselines, with strong robustness and practical applicability.

Wenbo Xu, Yue He, Yunhai Wang +4

Renmin University of China, China · Tsinghua University, China · Zhejiang University, China

Causal Discovery

Mar 21, 2026

Neural Autoregressive Flows for Markov Boundary Learning

Recovering Markov boundary -- the minimal set of variables that maximizes predictive performance for a response variable -- is crucial in many applications. While recent advances improve upon traditional constraint-based techniques by scoring local causal structures, they still rely on nonparametric estimators and heuristic searches, lacking theoretical guarantees for reliability. This paper investigates a framework for efficient Markov boundary discovery by integrating conditional entropy from information theory as a scoring criterion. We design a novel masked autoregressive network to capture complex dependencies. A parallelizable greedy search strategy in polynomial time is proposed, supported by analytical evidence. We also discuss how initializing a graph with learned Markov boundaries accelerates the convergence of causal discovery. Comprehensive evaluations on real-world and synthetic datasets demonstrate the scalability and superior performance of our method in both Markov boundary discovery and causal discovery tasks.

Khoa Nguyen, Bao Duong, Viet Huynh +1

Deakin Applied Artificial Intelligence Initiative, Geelong, Australia · Edith Cowan University, Perth, Australia

Causal Structure Learning Causal Discovery Bayesian Networks

Mar 21, 2026

RECLAIM: Cyclic Causal Discovery Amid Measurement Noise

Uncovering causal relationships is a fundamental problem across science and engineering. However, most existing causal discovery methods assume acyclicity and direct access to the system variables -- assumptions that fail to hold in many real-world settings. For instance, in genomics, cyclic regulatory networks are common, and measurements are often corrupted by instrumental noise. To address these challenges, we propose RECLAIM, a causal discovery framework that natively handles both cycles and measurement noise. RECLAIM learns the causal graph structure by maximizing the likelihood of the observed measurements via expectation-maximization (EM), using residual normalizing flows for tractable likelihood computation. We consider two measurement models: (i) Gaussian additive noise, and (ii) a linear measurement system with additive Gaussian noise. We provide theoretical consistency guarantees for both the settings. Experiments on synthetic data and real-world protein signaling datasets demonstrate the efficacy of the proposed method.

Muralikrishnna G. Sethuraman, Faramarz Fekri

School of Electrical and Computer Engineering, Georgia Institute of Technology

Causal Discovery

Mar 19, 2026

MARLIN: Multi-Agent Reinforcement Learning for Incremental DAG Discovery

Uncovering causal structures from observational data is crucial for understanding complex systems and making informed decisions. While reinforcement learning (RL) has shown promise in identifying these structures in the form of a directed acyclic graph (DAG), existing methods often lack efficiency, making them unsuitable for online applications. In this paper, we propose MARLIN, an efficient multi agent RL based approach for incremental DAG learning. MARLIN uses a DAG generation policy that maps a continuous real valued space to the DAG space as an intra batch strategy, then incorporates two RL agents state specific and state invariant to uncover causal relationships and integrates these agents into an incremental learning framework. Furthermore, the framework leverages a factored action space to enhance parallelization efficiency. Extensive experiments on synthetic and real datasets demonstrate that MARLIN outperforms state of the art methods in terms of both efficiency and effectiveness.

Dong Li, Zhengzhang Chen, Xujiang Zhao +5

Department of Computer Science, Baylor University · NEC Labs America · School of Computer and Cyber Sciences, Augusta University +2

Causal Discovery Causal Structure Learning Incremental Learning Multi-Agent Reinforcement Learning

Mar 18, 2026

Cohomological Obstructions to Global Counterfactuals: A Sheaf-Theoretic Foundation for Generative Causal Models

Current continuous generative models (e.g., Diffusion Models, Flow Matching) implicitly assume that locally consistent causal mechanisms naturally yield globally coherent counterfactuals. In this paper, we prove that this assumption fails fundamentally when the causal graph exhibits non-trivial homology (e.g., structural conflicts or hidden confounders). We formalize structural causal models as cellular sheaves over Wasserstein spaces, providing a strict algebraic topological definition of cohomological obstructions in measure spaces. To ensure computational tractability and avoid deterministic singularities (which we define as manifold tearing), we introduce entropic regularization and derive the Entropic Wasserstein Causal Sheaf Laplacian, a novel system of coupled non-linear Fokker-Planck equations. Crucially, we prove an entropic pullback lemma for the first variation of pushforward measures. By integrating this with the Implicit Function Theorem (IFT) on Sinkhorn optimality conditions, we establish a direct algorithmic bridge to automatic differentiation (VJP), achieving O(1)-memory reverse-mode gradients strictly independent of the iteration horizon. Empirically, our framework successfully leverages thermodynamic noise to navigate topological barriers ("entropic tunneling") in high-dimensional scRNA-seq counterfactuals. Finally, we invert this theoretical framework to introduce the Topological Causal Score, demonstrating that our Sheaf Laplacian acts as a highly sensitive algebraic detector for topology-aware causal discovery.

Rui Wu, Hong Xie, Yongjun Li

School of Management, University of Science and Technology of China · School of Computer Science and Engineering, University of Science and Technology of China

Causal Counterfactual Generation Causal Inference Structural Causal Models Causal Discovery

Mar 16, 2026

Evaluating Causal Discovery Algorithms for Path-Specific Fairness and Utility in Healthcare

Causal discovery in health data faces evaluation challenges when ground truth is unknown. We address this by collaborating with experts to construct proxy ground-truth graphs, establishing benchmarks for synthetic Alzheimer's disease and heart failure clinical records data. We evaluate the Peter-Clark, Greedy Equivalence Search, and Fast Causal Inference algorithms on structural recovery and path-specific fairness decomposition, going beyond composite fairness scores. On synthetic data, Peter-Clark achieved the best structural recovery. On heart failure data, Fast Causal Inference achieved the highest utility. For path-specific effects, ejection fraction contributed 3.37 percentage points to the indirect effect in the ground truth. These differences drove variations in the fairness-utility ratio across algorithms. Our results highlight the need for graph-aware fairness evaluation and fine-grained path-specific analysis when deploying causal discovery in clinical applications.

Nitish Nagesh, Elahe Khatibi, Thomas Hughes +3

University of California Irvine · University of Orl´eans, France

Causal Discovery Algorithmic Fairness Healthcare

Mar 12, 2026

HCP-DCNet: A Hierarchical Causal Primitive Dynamic Composition Network for Self-Improving Causal Understanding

The ability to understand and reason about cause and effect -- encompassing interventions, counterfactuals, and underlying mechanisms -- is a cornerstone of robust artificial intelligence. While deep learning excels at pattern recognition, it fundamentally lacks a model of causality, making systems brittle under distribution shifts and unable to answer ``what-if'' questions. This paper introduces the Hierarchical Causal Primitive Dynamic Composition Network (HCP-DCNet), a unified framework that bridges continuous physical dynamics with discrete symbolic causal inference. Departing from monolithic representations, HCP-DCNet decomposes causal scenes into reusable, typed causal primitives organized into four abstraction layers: physical, functional, event, and rule. A dual-channel routing network dynamically composes these primitives into task-specific, fully differentiable Causal Execution Graphs (CEGs). Crucially, the system employs a causal-intervention-driven meta-evolution strategy, enabling autonomous self-improvement through a constrained Markov decision process. We establish rigorous theoretical guarantees, including type-safe composition, routing convergence, and universal approximation of causal dynamics. Extensive experiments across simulated physical and social environments demonstrate that HCP-DCNet significantly outperforms state-of-the-art baselines in causal discovery, counterfactual reasoning, and compositional generalization. This work provides a principled, scalable, and interpretable architecture for building AI systems with human-like causal abstraction and continual self-refinement capabilities.

Ming Lei, Shufan Wu, Christophe Baehr

Shanghai JiaoTong University, Shanghai · M´et´eo France/CNRS, Universit´e de Toulouse, CNRM UMR 3589, Toulouse, France

Causal Reasoning Causal Abstraction Causal Representation Learning Causal Discovery Counterfactual Reasoning Self-Improving Agents

Mar 5, 2026

Learning Causal Structure of Time Series using Best Order Score Search

Causal structure learning from observational data is central to many scientific and policy domains, but the time series setting common to many disciplines poses several challenges due to temporal dependence. In this paper we focus on score-based causal discovery for multivariate time series and introduce TS-BOSS, a time series extension of the recently proposed Best Order Score Search (BOSS) (Andrews et al. 2023). TS-BOSS performs a permutation-based search over dynamic Bayesian network structures while leveraging grow-shrink trees to cache intermediate score computations, preserving the scalability and strong empirical performance of BOSS in the static setting. We provide theoretical guarantees establishing the soundness of TS-BOSS under suitable assumptions, and we present an intermediate result that extends classical subgraph minimality results for permutation-based methods to the dynamic (time series) setting. Our experiments on synthetic data show that TS-BOSS is especially effective in high auto-correlation regimes, where it consistently achieves higher adjacency recall at comparable precision than standard constraint-based methods. Overall, TS-BOSS offers a high-performing, scalable approach for time series causal discovery and our results provide a principled bridge for extending sparsity-based, permutation-driven causal learning theory to dynamic settings.

Irene Gema Castillo Mansilla, Urmi Ninad

University of Potsdam, Potsdam, Germany · Department of Computer Science, University of Potsdam, Potsdam, Germany

Time-Series Causal Discovery Bayesian Networks Score-Based Causal Discovery Causal Discovery Causal Structure Learning

Mar 5, 2026

Federated Causal Discovery Across Heterogeneous Datasets under Latent Confounding

Causal discovery across multiple datasets is often constrained by data privacy regulations and cross-site heterogeneity, limiting the use of conventional methods that require a single, centralized dataset. To address these challenges, we introduce fedCI, a federated conditional independence test that rigorously handles heterogeneous datasets with non-identical sets of variables, site-specific effects, and mixed variable types, including continuous, ordinal, binary, and categorical variables. At its core, fedCI uses a federated Iteratively Reweighted Least Squares (IRLS) procedure to estimate the parameters of generalized linear models underlying likelihood-ratio tests for conditional independence. Building on this, we develop fedCI-IOD, a federated extension of the Integration of Overlapping Datasets (IOD) algorithm, that replaces its meta-analysis strategy and enables, for the fist time, federated causal discovery under latent confounding across distributed and heterogeneous datasets. By aggregating evidence federatively, fedCI-IOD not only preserves privacy but also substantially enhances statistical power, achieving performance comparable to fully pooled analyses and mitigating artifacts from low local sample sizes. Our tools are publicly available as the fedCI Python package, a privacy-preserving R implementation of IOD, and a web application for the fedCI-IOD pipeline, providing versatile, user-friendly solutions for federated conditional independence testing and causal discovery.

Maximilian Hahn, Alina Zajak, Dominik Heider +1

University of Münster, Institute of Medical Informatics, Münster, Germany

Causal Discovery Causal Discovery with Latent Confounding Conditional Independence Testing Heterogeneous Federated Learning

Mar 5, 2026

Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learning

Causal discovery with latent variables is a fundamental task. Yet most existing methods rely on strong structural assumptions, such as enforcing specific indicator patterns for latents or restricting how they can interact with others. We argue that a core obstacle to a general, structural-assumption-free approach is the lack of an equivalence characterization: without knowing what can be identified, one generally cannot design methods for how to identify it. In this work, we aim to close this gap for linear non-Gaussian models. We establish the graphical criterion for when two graphs with arbitrary latent structure and cycles are distributionally equivalent, that is, they induce the same observed distribution set. Key to our approach is a new tool, edge rank constraints, which fills a missing piece in the toolbox for latent-variable causal discovery in even broader settings. We further provide a procedure to traverse the whole equivalence class and develop an algorithm to recover models from data up to such equivalence. To our knowledge, this is the first equivalence characterization with latent variables in any parametric setting without structural assumptions, and hence the first structural-assumption-free discovery method. Code and an interactive demo are available at https://equiv.cc.

Haoyue Dai, Immanuel Albrecht, Peter Spirtes +1

Carnegie Mellon University · FernUniversität in Hagen · MBZUAI

Causal Discovery Causal Discovery with Latent Confounding Causal Identifiability Structural Causal Models

Mar 4, 2026

Invariant Causal Routing for Governing Social Norms in Online Market Economies

Social norms are stable behavioral patterns that emerge endogenously within economic systems through repeated interactions among agents. In online market economies, such norms -- like fair exposure, sustained participation, and balanced reinvestment -- are critical for long-term stability. We aim to understand the causal mechanisms driving these emergent norms and to design principled interventions that can steer them toward desired outcomes. This is challenging because norms arise from countless micro-level interactions that aggregate into macro-level regularities, making causal attribution and policy transferability difficult. To address this, we propose Invariant Causal Routing (ICR), a causal governance framework that identifies policy-norm relations stable across heterogeneous environments. ICR integrates counterfactual reasoning with invariant causal discovery to separate genuine causal effects from spurious correlations and to construct interpretable, auditable policy rules that remain effective under distribution shift. In heterogeneous agent simulations calibrated with real data, ICR yields more stable norms, smaller generalization gaps, and more concise rules than correlation or coverage baselines, demonstrating that causal invariance offers a principled and interpretable foundation for governance.

Xiangning Yu, Qirui Mi, Xiao Xue +4

Tianjin University, Tianjin, China · Institute of Automation, Chinese Academy of Sciences, Beijing, China · Peking University, Beijing, China +1

Causal Intervention AI Agent Governance Emergent Behavior in Multi-Agent Systems Causal Discovery

Mar 4, 2026

Dictionary Based Pattern Entropy for Causal Direction Discovery

Discovering causal direction from temporal observational data is particularly challenging for symbolic sequences, where functional models and noise assumptions are often unavailable. We propose a novel \emph{Dictionary Based Pattern Entropy (

DPE

)} framework that infers both the direction of causation and the specific subpatterns driving changes in the effect variable. The framework integrates Algorithmic Information Theory (AIT) and Shannon Information Theory. Causation is interpreted as the emergence of compact, rule based patterns in the candidate cause that systematically constrain the effect.

DPE

constructs direction-specific dictionaries and quantifies their influence using entropy-based measures, enabling a principled link between deterministic pattern structure and stochastic variability. Causal direction is inferred via a minimum-uncertainty criterion, selecting the direction exhibiting stronger and more consistent pattern-driven organization. As summarized in Table 7,

DPE

consistently achieves reliable performance across diverse synthetic systems, including delayed bit-flip perturbations, AR(1) coupling, 1D skew-tent maps, and sparse processes, outperforming or matching competing AIT-based methods (

ETC_E

,

ETC_P

,

LZ_P

). In biological and ecological datasets, performance is competitive, while alternative methods show advantages in specific genomic settings. Overall, the results demonstrate that minimizing pattern level uncertainty yields a robust, interpretable, and broadly applicable framework for causal discovery.

Harikrishnan N B, Shubham Bhilare, Aditi Kathpalia +1

Department of Computer Science and Information Systems, BITS Pilani K K Birla Goa Campus, NH 17B, Bypass, Road, Zuarinagar, 403726, Goa, India · Department of Applied Mechanics and Biomedical Engineering, Indian Institute of Technology Madras, IIT P.O., Chennai 600036, India · Complex Systems Programme, National Institute of Advanced Studies, IISc Campus, Bengaluru, 560012, Karnataka, India

Time-Series Causal Discovery Causal Discovery

Mar 3, 2026

Scalable Contrastive Causal Discovery under Unknown Soft Interventions

Observational causal discovery is only identifiable up to the Markov equivalence class. While interventions can reduce this ambiguity, in practice interventions are often soft with multiple unknown targets. In many realistic scenarios, only a single intervention regime is observed. We propose a scalable causal discovery model for paired observational and interventional settings with shared underlying causal structure and unknown soft interventions. The model aggregates subset-level PDAGs and applies contrastive cross-regime orientation rules to construct a globally consistent maximal PDAG under Meek closure, enabling generalization to both in-distribution and out-of-distribution settings. Theoretically, we prove that our model is sound with respect to a restricted

Ψ

equivalence class induced solely by the information available in the subset-restricted setting. We further show that the model asymptotically recovers the corresponding identifiable PDAG and can orient additional edges compared to non-contrastive subset-restricted methods. Experiments on synthetic data demonstrate improved causal structure recovery, generalization to unseen graphs with held-out causal mechanisms, and scalability to larger graphs, with ablations supporting the theoretical results.

Mingxuan Zhang, Khushi Desai, Sopho Kevlishvili +1

Department of Systems Biology, Columbia University · Irving Institute for Cancer Dynamics, Columbia University · Department of Computer Science, Columbia University +2

Causal Discovery Structural Causal Models Causal Identifiability Causal Intervention

Mar 3, 2026

I-CAM-UV: Integrating Causal Graphs over Non-Identical Variable Sets Using Causal Additive Models with Unobserved Variables

Causal discovery from observational data is a fundamental tool in various fields of science. While existing approaches are typically designed for a single dataset, we often need to handle multiple datasets with non-identical variable sets in practice. One straightforward approach is to estimate a causal graph from each dataset and construct a single causal graph by overlapping. However, this approach identifies limited causal relationships because unobserved variables in each dataset can be confounders, and some variable pairs may be unobserved in any dataset. To address this issue, we leverage Causal Additive Models with Unobserved Variables (CAM-UV) that provide causal graphs having information related to unobserved variables. We show that the ground truth causal graph has structural consistency with the information of CAM-UV on each dataset. As a result, we propose an approach named I-CAM-UV to integrate CAM-UV results by enumerating all consistent causal graphs. We also provide an efficient combinatorial search algorithm and demonstrate the usefulness of I-CAM-UV against existing methods.

Hirofumi Suzuki, Kentaro Kanamori, Takuya Takagi +3

Fujitsu Limited · Faculty of Data Science, Shiga University · RIKEN AIP +2

Causal Discovery Causal Discovery with Latent Confounding

Mar 3, 2026

Distributed Dynamic Invariant Causal Prediction in Environmental Time Series

The extraction of invariant causal relationships from time series data with environmental attributes is critical for robust decision-making in domains such as climate science and environmental monitoring. However, existing methods either emphasize dynamic causal analysis without leveraging environmental contexts or focus on static invariant causal inference, leaving a gap in distributed temporal settings. In this paper, we propose Distributed Dynamic Invariant Causal Prediction in Time-series (DisDy-ICPT), a novel framework that learns dynamic causal relationships over time while mitigating spatial confounding variables without requiring data communication. We theoretically prove that DisDy-ICPT recovers stable causal predictors within a bounded number of communication rounds under standard sampling assumptions. Empirical evaluations on synthetic benchmarks and environment-segmented real-world datasets show that DisDy-ICPT achieves superior predictive stability and accuracy compared to baseline methods A and B. Our approach offers promising applications in carbon monitoring and weather forecasting. Future work will extend DisDy-ICPT to online learning scenarios.

Ziruo Hao, Tao Yang, Xiaofeng Wu +1

Causal Inference Time-Series Causal Discovery Causal Discovery Causal Discovery with Latent Confounding

Mar 3, 2026

Causal Discovery Should Embrace the Wisdom of the Crowd

This paper argues for recognizing an emerging paradigm of causal learning by wisdom of the crowd. Recent developments in government, industry, and research point to the rise of decentralized and crowd-based approaches within causal modeling, where causal knowledge distributed across many contributors can be systematically elicited and integrated with causal learning workflows. In this paradigm, causal learning becomes a distributed decision-making problem: each participant contributes partial and potentially noisy knowledge, while collective contributions help construct a global causal structure. This direction is enabled by advances in crowdsourcing platforms, expert knowledge elicitation, aggregation techniques, and large language model (LLM)-augmented information acquisition. Its promise is increasingly visible in early research and emerging real-world practices. Building on this momentum, we outline a framework for crowd-based causal learning spanning elicitation, modeling, aggregation, and optimization. We further discuss the opportunities and challenges introduced by this paradigm and call for interdisciplinary collaboration across causal learning, collective intelligence, human-AI interaction, and decision science.

Ryan Feng Lin, Yuantao Wei, Huiling Liao +2

Department of Industrial and Systems Engineering, University of Washington, Seattle, WA 98195, USA · Department of Applied Mathematics, Illinois Institute of Technology · Department of Electrical & Computer Engineering, Texas A&M University

Causal Discovery Decentralized Learning

Mar 1, 2026

No More Maybe-Arrows: Resolving Causal Uncertainty by Breaking Symmetries

The recent works on causal discovery have followed a similar trend of learning partial ancestral graphs (PAGs) since observational data constrain the true causal directed acyclic graph (DAG) only up to a Markov equivalence class. This limits their application in the majority of downstream tasks, as uncertainty in causal relations remains unresolved. We propose a new refinement framework, CausalSAGE, for converting PAGs to DAGs while respecting the underlying causal relations. The framework expands discrete variables into state-level representations, constrains the search space using structural knowledge and soft priors, and applies a unified differentiable objective for joint optimization. The final DAG is obtained by aggregating the optimized structures and enforcing acyclicity when necessary. Our experimental evaluations show that the obtained DAGs preserve the underlying causal relations while also being efficient to obtain.

Tingrui Huang, Devendra Singh Dhami

Department of Mathematics and Computer Science, Eindhoven University of Technology

Causal Discovery Causal Structure Learning

Feb 27, 2026

Operationalizing Longitudinal Causal Discovery Under Real-World Workflow Constraints

Causal discovery has achieved substantial theoretical progress, yet its deployment in large-scale longitudinal systems remains limited. A key obstacle is that operational data are generated under institutional workflows whose induced partial orders are rarely formalized, enlarging the admissible graph space in ways inconsistent with the recording process. We characterize a workflow-induced constraint class for longitudinal causal discovery that restricts the admissible directed acyclic graph space through protocol-derived structural masks and timeline-aligned indexing. Rather than introducing a new optimization algorithm, we show that explicitly encoding workflow-consistent partial orders reduces structural ambiguity, especially in mixed discrete--continuous panels where within-time orientation is weakly identified. The framework combines workflow-derived admissible-edge constraints, measurement-aligned time indexing and block structure, bootstrap-based uncertainty quantification for lagged total effects, and a dynamic representation supporting intervention queries. In a nationwide annual health screening cohort in Japan with 107,261 individuals and 429,044 person-years, workflow-constrained longitudinal LiNGAM yields temporally consistent within-time substructures and interpretable lagged total effects with explicit uncertainty. Sensitivity analyses using alternative exposure and body-composition definitions preserve the main qualitative patterns. We argue that formalizing workflow-derived constraint classes improves structural interpretability without relying on domain-specific edge specification, providing a reproducible bridge between operational workflows and longitudinal causal discovery under standard identifiability assumptions.

Tadahisa Okuda, Shohei Shimizu, Thong Pham +2

Kyoto University Graduate School of Medicine, Kyoto, Japan · SANKEN, The University of Osaka, Osaka, Japan · Faculty of Data Science, Shiga University, Shiga, Japan +3

Causal Discovery Causal Structure Learning Time-Series Causal Discovery Structural Causal Models

Feb 27, 2026

Moment Matters: Mean and Variance Causal Graph Discovery from Heteroscedastic Observational Data

Heteroscedasticity -- where the variance of a variable changes with other variables -- is pervasive in real data, and elucidating why it arises from the perspective of statistical moments is crucial in scientific knowledge discovery and decision-making. However, standard causal discovery does not reveal which causes act on the mean versus the variance, as it returns a single moment-agnostic graph, limiting interpretability and downstream intervention design. We propose a Bayesian, moment-driven causal discovery framework that infers separate mean and variance causal graphs from observational heteroscedastic data. We first derive the identification results by establishing sufficient conditions under which these two graphs are separately identifiable. Building on this theory, we develop a variational inference method that learns a posterior distribution over both graphs, enabling principled uncertainty quantification of structural features (e.g., edges, paths, and subgraphs). To address the challenges of parameter optimization in heteroscedastic models with two graph structures, we take a curvature-aware optimization approach and develop a prior incorporation technique that leverages domain knowledge on node orderings, improving sample efficiency. Experiments on synthetic, semi-synthetic, and real data show that our approach accurately recovers mean and variance structures and outperforms state-of-the-art baselines.

Yoichi Chikahara

Communication Science Laboratories, NTT, Inc., Kyoto, Japan

Causal Discovery Causal Identifiability

Feb 24, 2026

Causal Direction from Convergence Time: Faster Training in the True Causal Direction

We introduce Causal Computational Asymmetry (CCA), a principle for causal direction identification based on optimization dynamics in which one neural network is trained to predict

Y

from

X

and another to predict

X

from

Y

, and the direction that converges faster is inferred to be causal. Under the additive noise model

Y = f(X) + \varepsilon

with

\varepsilon \perp X

and

f

nonlinear and injective, we establish a formal asymmetry: in the reverse direction, residuals remain statistically dependent on the input regardless of approximation quality, inducing a strictly higher irreducible loss floor and non-separable gradient noise in the optimization dynamics, so that the reverse model requires strictly more gradient steps in expectation to reach any fixed loss threshold; consequently, the forward (causal) direction converges in fewer expected optimization steps. CCA operates in optimization-time space, distinguishing it from methods such as RESIT, IGCI, and SkewScore that rely on statistical independence or distributional asymmetries, and proper z-scoring of both variables is required for valid comparison of convergence rates. On synthetic benchmarks, CCA achieves 26/30 correct causal identifications across six neural architectures, including 30/30 on sine and exponential data-generating processes. We further embed CCA into a broader framework termed Causal Compression Learning (CCL), which integrates graph structure learning, causal information compression, and policy optimization, with all theoretical guarantees formally proved and empirically validated on synthetic datasets.

Abdulrahman Tamim

Independent Researcher

Causal Discovery

Feb 23, 2026

DMCD: Semantic-Statistical Framework for Causal Discovery

We present DMCD (DataMap Causal Discovery), a two-phase causal discovery framework that integrates LLM-based semantic drafting from variable metadata with statistical validation on observational data. In Phase I, a large language model proposes a sparse draft DAG, serving as a semantically informed prior over the space of possible causal structures. In Phase II, this draft is audited and refined via conditional independence testing, with detected discrepancies guiding targeted edge revisions. We evaluate our approach on three metadata-rich real-world benchmarks spanning industrial engineering, environmental monitoring, and IT systems analysis. Across these datasets, DMCD achieves competitive or leading performance against diverse causal discovery baselines, with particularly large gains in recall and F1 score. Probing and ablation experiments suggest that these improvements arise from semantic reasoning over metadata rather than memorization of benchmark graphs. Overall, our results demonstrate that combining semantic priors with principled statistical verification yields a high-performing and practically effective approach to causal structure learning.

Samarth KaPatel, Sofia Nikiforova, Giacinto Paolo Saggese +1

Causify AI

Causal Discovery Causal Structure Learning

Feb 23, 2026

Rethinking Chronological Causal Discovery with Signal Processing

Causal discovery problems use a set of observations to deduce causality between variables in the real world, typically to answer questions about biological or physical systems. These observations are often recorded at regular time intervals, determined by a user or a machine, depending on the experiment design. There is generally no guarantee that the timing of these recordings matches the timing of the underlying biological or physical events. In this paper, we examine the sensitivity of causal discovery methods to this potential mismatch. We consider empirical and theoretical evidence to understand how causal discovery performance is impacted by changes of sampling rate and window length. We demonstrate that both classical and recent causal discovery methods exhibit sensitivity to these hyperparameters, and we discuss how ideas from signal processing may help us understand these phenomena.

Kurt Butler, Damian Machlanski, Panagiotis Dimitrakopoulos +1

School of Engineering, The University of Edinburgh, Edinburgh, UK · Causality in Healthcare AI Hub (CHAI), UK

Causal Discovery Time-Series Causal Discovery

Feb 22, 2026

VCDF: A Validated Consensus-Driven Framework for Time Series Causal Discovery

Time series causal discovery is essential for understanding dynamic systems, yet many existing methods remain sensitive to noise, non-stationarity, and sampling variability. We propose the Validated Consensus-Driven Framework (VCDF), a simple and method-agnostic layer that improves robustness by evaluating the stability of causal relations across blocked temporal subsets. VCDF requires no modification to base algorithms and can be applied to methods such as VAR-LiNGAM and PCMCI. Experiments on synthetic datasets show that VCDF improves VAR-LiNGAM by approximately 0.08-0.12 in both window and summary F1 scores across diverse data characteristics, with gains most pronounced for moderate-to-long sequences. The framework also benefits from longer sequences, yielding up to 0.18 absolute improvement on time series of length 1000 and above. Evaluations on simulated fMRI data and IT-monitoring scenarios further demonstrate enhanced stability and structural accuracy under realistic noise conditions. VCDF provides an effective reliability layer for time series causal discovery without altering underlying modeling assumptions.

Gene Yu, Ce Guo, Wayne Luk

Department of Computing, Imperial College London, London, United Kingdom

Time-Series Causal Discovery Causal Discovery

Feb 18, 2026

Leveraging Large Language Models for Causal Discovery: a Constraint-based, Argumentation-driven Approach

Causal discovery seeks to uncover causal relations from data, typically represented as causal graphs, and is essential for predicting the effects of interventions. While expert knowledge is required to construct principled causal graphs, many statistical methods have been proposed to leverage observational data with varying formal guarantees. Causal Assumption-based Argumentation (ABA) is a framework that uses symbolic reasoning to ensure correspondence between input constraints and output graphs, while offering a principled way to combine data and expertise. We explore the use of large language models (LLMs) as imperfect experts for Causal ABA, eliciting semantic structural priors from variable names and descriptions and integrating them with conditional-independence evidence. Experiments on standard benchmarks and semantically grounded synthetic graphs demonstrate state-of-the-art performance, and we additionally introduce an evaluation protocol to mitigate memorisation bias when assessing LLMs for causal discovery.

Zihao Li, Fabrizio Russo

Department of Computing, Imperial College London, UK

Causal Discovery Causal Structure Learning Constraint-Based Causal Discovery

Feb 17, 2026

Sparse Additive Model Pruning for Order-Based Causal Structure Learning

Causal structure learning, also known as causal discovery, aims to estimate causal relationships between variables as a form of a causal directed acyclic graph (DAG) from observational data. One of the major frameworks is the order-based approach that first estimates a topological order of the underlying DAG and then prunes spurious edges from the fully-connected DAG induced by the estimated topological order. Previous studies often focus on the former ordering step because it can dramatically reduce the search space of DAGs. In practice, the latter pruning step is equally crucial for ensuring both computational efficiency and estimation accuracy. Most existing methods employ a pruning technique based on generalized additive models and hypothesis testing, commonly known as CAM-pruning. However, this approach can be a computational bottleneck as it requires repeatedly fitting additive models for all variables. Furthermore, it may harm estimation quality due to multiple testing. To address these issues, we introduce a new pruning method based on sparse additive models, which enables direct pruning of redundant edges without relying on hypothesis testing. We propose an efficient algorithm for learning sparse additive models by combining the randomized tree embedding technique with group-wise sparse regression. Experimental results on both synthetic and real datasets demonstrated that our method is significantly faster than existing pruning methods while maintaining comparable or superior accuracy.

Kentaro Kanamori, Hirofumi Suzuki, Takuya Takagi

Artificial Intelligence Laboratory, Fujitsu Limited

Causal Structure Learning Causal Discovery

Feb 16, 2026

Use What You Know: Causal Foundation Models with Partial Graphs

Estimating causal quantities traditionally relies on bespoke estimators tailored to specific assumptions. Recently proposed Causal Foundation Models (CFMs) promise a more unified approach by amortising causal discovery and inference in a single step. However, in their current state, they do not allow for the incorporation of any domain knowledge, which can lead to suboptimal predictions. We bridge this gap by introducing methods to condition CFMs on causal information, such as the causal graph or more readily available ancestral information. When access to complete causal graph information is too strict a requirement, our approach also effectively leverages partial causal information. We systematically evaluate conditioning strategies and find that injecting learnable biases into the attention mechanism, together with a graph-convolutional encoder, is a highly effective method to utilise full and partial causal information. Our experiments show that this conditioning allows a general-purpose CFM to match the performance of specialised models trained on specific causal structures. Overall, our approach addresses a central hurdle on the path towards all-in-one causal foundation models: the capability to answer causal queries in a data-driven manner while effectively leveraging any amount of domain expertise.

Arik Reuter, Anish Dhir, Cristiana Diaconu +6

University of Cambridge, Cambridge, United Kingdom · Max Planck Institute for Intelligent Systems, Tübingen, Germany · Gatsby Computational Neuroscience Unit, University College London +5

Causal Foundation Models Causal Discovery Causal Inference

Feb 13, 2026

Uncertainty Quantification in Federated Granger Causality Learning

Granger causality identifies predictive dependencies in multivariate time series. In distributed settings where parties cannot share data, federated causal learning enables joint analysis. Most federated causal methods assume that clients observe the same features and infer causal relationships as point estimates, with little formal uncertainty quantification. These assumptions do not hold in many industrial systems, where clients observe different features, and the objective is to estimate cross-client dependencies (edges). These dependencies must be estimated indirectly through repeated client-server iterations. Uncertainty from client data and model parameters propagates through this process, making point estimates alone insufficient for assessing cross-client edges. This paper characterizes this uncertainty propagation and uses edge-specific variances to distinguish genuine cross-client dependencies from spurious estimated edges. We consider aleatoric uncertainty from client data variability and epistemic uncertainty from model parameters. We derive closed-form variance recursions and steady-state variances for the client-server iterations. We prove that the propagated contribution of the initial model-parameter uncertainty vanishes asymptotically. These variances enable statistically principled selection of cross-client edges. Synthetic experiments show that our approach improves cross-client edge recovery over competing baselines. On real-world industrial datasets, it achieves high root-cause identification accuracy while yielding interpretable dependency structures.

Ayush Mohanty, Nazal Mohamed, Nagi Gebraeel

Georgia Institute of Technology Atlanta, GA 30332

Time-Series Causal Discovery Causal Discovery Federated Graph Learning

Feb 9, 2026

CauScale: Neural Causal Discovery at Scale

Causal discovery is essential for advancing data-driven fields such as scientific AI and data analysis, yet existing approaches face significant time- and space-efficiency bottlenecks when scaling to large graphs. To address this challenge, we present CauScale, a neural architecture designed for efficient causal discovery that scales inference to graphs with up to 1000 nodes. CauScale improves time efficiency via a reduction unit that compresses data embeddings and improves space efficiency by adopting tied attention weights to avoid maintaining axis-specific attention maps. To keep high causal discovery accuracy, CauScale adopts a two-stream design: a data stream extracts relational evidence from high-dimensional observations, while a graph stream integrates statistical graph priors and preserves key structural signals. CauScale successfully scales to 500-node graphs during training, where prior work fails due to space limitations. Across testing data with varying graph scales and causal mechanisms, CauScale achieves 99.6% mAP on in-distribution data and 84.4% on out-of-distribution data, while delivering 4-13,000 times inference speedups over prior methods. Our project page is at https://github.com/OpenCausaLab/CauScale.

Bo Peng, Sirui Chen, Jiaguo Tian +2

Shanghai Jiao Tong University · Shanghai Artificial Intelligence Laboratory · Shanghai Innovation Institute +1

Efficient Neural Network Inference Causal Discovery