Causal Discovery

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Overview

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.

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

May 6, 2026

Order-based Rehearsal Learning

When a machine learning (ML) model forecasts an undesired event, one often seeks a decision to avoid it, known as the avoiding undesired future (AUF) problem. Many rehearsal learning methods have been proposed for AUF, but they rely on an underlying graph structure; learning such a graph from observational data is challenging and can incur substantial estimation error. In this work, we demonstrate that the order structure can be sufficient for AUF decision-making, and propose the first order-based rehearsal learning method. Although an order is less informative than a graph, it can be sufficient to identify the influence of decisions from observational data, suggesting that learning the entire graph is not always necessary. To learn the order, we develop an information-theoretic method that imposes no restrictions on the form of structural functions or the type of noise distributions. For AUF decision-making, we construct an order-based sampler to approximate the influence of decisions and, combined with a surrogate objective for maximizing the post-decision success probability, reduce the AUF task to a differentiable optimization problem. Experiments show that our order learning method outperforms existing methods, and that our AUF approach not only surpasses methods relying on learned graphs or learned orders, but also matches or even exceeds oracle baselines that are given the true graph.

Yu-Xuan Tao, Tian-Zuo Wang, Zhi-Hua Zhou

National Key Laboratory for Novel Software Technology, Nanjing University, China · School of Artifcial Intelligence, Nanjing University, China

Causal DiscoveryCausal Structure Learning
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May 6, 2026

When Does Gene Regulatory Network Inference Break? A Controlled Diagnostic Study of Causal and Correlational Methods on Single-Cell Data

Despite theoretical advantages, causal methods for Gene Regulatory Network (GRN) inference from single-cell RNA-seq data consistently fail to match or outperform correlation-based baselines in many realistic benchmarks, a persistent puzzle which casts doubt on the value of causality for this task. We argue that existing benchmarks are insufficiently controlled to answer this question because they evaluate on real or semi-real data where multiple pathologies co-occur, confounding failure modes, and obscuring the specific conditions under which different inference methods excel or fail. To address this gap, we introduce a controlled diagnostic framework that isolates seven biologically motivated pathologies (dropout, latent confounders, cell-type mixing, feedback loops, network density, sample size, and pseudotime drift) and measure how six representative methods spanning three inference paradigms degrade as each pathology intensifies. Across 6,120 controlled experiments, we find that causal methods genuinely dominate in clean and structurally favorable regimes, but specific pathologies (notably dropout and latent confounders) selectively neutralize their advantages. We further introduce an error-type decomposition that reveals methods with similar aggregate accuracy commit qualitatively different errors. To probe whether single-pathology effects persist when multiple stressors co-occur, we perform an interaction sweep over the three most impactful pathologies and find that their joint effects are sub-additive, while also exposing density-conditional cross-overs invisible to single-dial analysis. Our findings offer a nuanced understanding of when and why different methods succeed or fail for GRN inference, providing actionable insights for method development and practical guidance for practitioners.

Miguel Fernandez-de-Retana, Ruben Sanchez-Corcuera, Unai Zulaika +2

Faculty of Engineering University of Deusto Bilbao, Spain

Causal DiscoveryGene Regulatory Network InferenceSpurious Correlation RobustnessGenomicsSingle-Cell RNA Sequencing
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May 6, 2026

PAIR-CI: Calibrated Conditional Independence Testing for Causal Discovery with Incomplete Data

The standard constraint-based paradigm for causal discovery with incomplete data -- impute first, test second -- is frequently miscalibrated: any consistent conditional independence (CI) test rejects a true null with probability approaching 1 when imputation error induces spurious conditional dependence. We introduce PAIR-CI, a nonparametric CI test that restores calibration by integrating multiple imputation directly into the inferential procedure via a paired permutation design. PAIR-CI compares cross-validated models that include and exclude the candidate variable while receiving the same imputed conditioning set, forcing imputation error to cancel in their loss difference rather than contaminate the test statistic. A provably consistent variance estimator jointly accounts for uncertainty arising from cross-validation and multiple imputation -- to our knowledge, the first formal unification of these two inferential frameworks. In simulations, existing imputation-based CI tests exhibit false positive rates of 28--45% when data are missing not at random (MNAR), whereas PAIR-CI averages below the nominal 5% level across data-generating processes and missingness mechanisms. These gains are largest in nonlinear settings and grow with causal graph size: when integrated into the PC algorithm, PAIR-CI reduces structural Hamming distance by 8% on 10-variable nonlinear graphs, 15% on 30-variable equivalents, and up to 44% on the 56-variable HAILFINDER network, with stable performance in all settings.

Thomas S. Robinson, Ranjit Lall

Department of Methodology London School of Economics and Political Science London, UK · Department of Politics and International Relations University of OxfordMay Oxford, UK

Permutation TestingIncomplete Data ImputationCausal DiscoveryCausal InferenceConditional Independence Testing
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May 6, 2026

Causal discovery under mean independence and linearity

Causal discovery methods such as LiNGAM identify causal structure from observational data by assuming mutually independent disturbances. This assumption is fragile: shared volatility, common scale effects, or other forms of dependence can cause the methods to recover the wrong causal order, even with infinite data. We introduce the Linear Mean-Independent Acyclic Model (LiMIAM), which replaces full independence with weaker one-sided mean-independence restrictions on the disturbances. Under finite-order consequences of these restrictions, source nodes are generically identifiable, and hence a compatible causal order can be recovered recursively. Our proof is constructive and leads to DirectLiMIAM, a sequential residual-based algorithm for causal discovery under dependent noise. In simulations with mean-independent but dependent disturbances, DirectLiMIAM outperforms LiNGAM methods. A large-scale empirical application to the oil market highlights the implausibility of the independence assumption and the ability of DirectLiMIAM to recover a realistic causal ordering, from policy to production and from prices to inflation.

Geert Mesters, Alvaro Ribot, Anna Seigal +1

Structural Causal ModelsCausal DiscoveryCausal Identifiability
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May 5, 2026

Partial Effective Information Decomposition for Synergistic Causality

Causality is a central topic in scientific inquiry, yet for complex systems, the identification and analysis of synergistic causation remain a challenging and fundamental problem. In the context of causal relations among multivariate variables, a decomposition framework grounded in interventionist causation is still lacking. To address this gap, this paper proposes Partial Effective Information Decomposition (PEID), a framework that decomposes the influence of multiple source variables on a target variable under maximum-entropy interventions into unique and synergistic information, thereby providing a unified and computable characterization of synergistic causal relations. Theoretically, in the three-variable case, the proposed framework is compatible with the major axioms of Partial Information Decomposition (PID). Empirically, under maximum-entropy interventions, correlations among input variables are removed, causing redundancy to vanish and thereby enabling PEID to compute synergistic relations. Furthermore, based on this framework, it is possible to define causal graphs containing hyperedges as well as downward causation, thus offering a unified toolkit for analyzing cross-scale and multivariate causal mechanisms in complex systems. Finally, applying the framework to a machine-learning-based air quality forecasting task on KnowAir-V2, we demonstrate that PEID can extract interpretable inter-station causal structures from a learned dynamical model. These results suggest that PEID provides a general interventionist information-theoretic tool for analyzing multivariate and synergistic causal mechanisms in complex systems.

Mingzhe Yang, Shuo Wang, Jiang Zhang

School of Systems Science Beijing Normal University

Causal DiscoveryCausal Intervention
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May 4, 2026

TCD-Arena: Assessing Robustness of Time Series Causal Discovery Methods Against Assumption Violations

Causal Discovery (CD) is a powerful framework for scientific inquiry. Yet, its practical adoption is hindered by a reliance on strong, often unverifiable assumptions and a lack of robust performance assessment. To address these limitations and advance empirical CD evaluation, we present TCD-Arena, a modularized, highly customizable, and extendable testing kit to assess the robustness of time series CD algorithms against stepwise more severe assumption violations. For demonstration, we conduct an extensive empirical study comprising around 30 million individual CD attempts and reveal nuanced robustness profiles for 33 distinct assumption violations. Further, we investigate CD ensembles and find that they have the potential to improve general robustness, which has implications for real-world applications. With this, we strive to ultimately facilitate the development of CD methods that are reliable for a diverse range of synthetic and potentially real-world data conditions.

Gideon Stein, Niklas Penzel, Tristan Piater +1

Computer Vision Group Jena Friedrich Schiller University Jena Jena, Thuringia, 07743, DE

Time-Series Causal DiscoveryCausal Discovery
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May 3, 2026

PRCD-MAP: Learning How Much to Trust Imperfect Priors in Causal Discovery

External priors of unknown reliability create a brittle trade-off in causal discovery: blind trust amplifies errors, blind rejection wastes signal. Real priors are also heterogeneously reliable -- physical laws are trustworthy, LLM-suggested edges are speculative -- yet existing methods either ignore priors or impose them through globally uniform trust. We propose PRCD-MAP, a soft prior-consumption layer that assigns per-edge trust to an imperfect prior and uses it to modulate a prior-aware ℓ1\ell_1 and prior-weighted ℓ2\ell_2 regularizer in a MAP objective. Trust is calibrated by empirical Bayes on a Laplace-approximated marginal likelihood and propagated along the prior graph by an MLP, so data-confirmed neighborhoods boost trust and contradictions suppress it. PRCD-MAP enjoys a population-level safety guarantee: it is ε\varepsilon-safe in expectation over the prior-generation distribution, with ε≤C⋅acc(1−acc)⋅d2/T\varepsilon\leq C\cdot\mathrm{acc}(1{-}\mathrm{acc})\cdot d^2/T at the parametric T−1T^{-1} rate and vanishing at the prior-quality endpoints. When the prior is uninformative, learned trust provably collapses to its floor and the method recovers a no-prior baseline. Empirically, on real CausalTime data PRCD-MAP exploits informative LLM priors (LLM-prior gain +0.067/+0.089+0.067/+0.089 AUROC on AQI/Medical over a no-prior PRCD-MAP backbone; combined backbone+prior lead +0.123/+0.043+0.123/+0.043 over PCMCI+), auto-attenuates on the anonymous-variable Traffic stress test, and retains a lead at d=300d{=}300; against BayesDAG, the closest soft-Bayesian baseline, PRCD-MAP wins on every CausalTime dataset under a matched W0W_0-only protocol. A four-way ablation isolates each component: EB calibration and MLP trust propagation jointly carry the plurality of the gain, with positive sign on every dataset. Extensions to nonlinear (NAM) and cross-sectional settings show the calibrated-trust principle is setting-agnostic.

Xihang Shan, Da Zhou

School of Mathematical Sciences Xiamen University Fujian, China

Time-Series Causal DiscoveryBayesian InferenceCausal Discovery
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May 1, 2026

M-CaStLe: Uncovering Local Causal Structures in Multivariate Space-Time Gridded Data

Causal graph discovery for space-time systems is challenging in high-dimensional gridded data, which often has many more grid cells than temporal observations per cell. The Causal Space-Time Stencil Learning (CaStLe) meta-algorithm was developed to address that niche under space-time locality and stationarity assumptions, but it is currently limited to univariate analyses. In this work, we present M-CaStLe. M-CaStLe generalizes the local embedding and parent-identification phases of CaStLe to jointly model local within-variable and cross-variable space-time causal structures in gridded data. Like CaStLe, by constraining candidate parents to a constant-size space-time neighborhood and pooling spatial replicates, M-CaStLe increases effective sample size to make discovery tractable in high-dimensional settings. We further decompose the resulting multivariate stencil graph into reaction and spatial graphs to aid interpretation in complex settings. We study M-CaStLe in four settings: a multivariate space-time vector autoregression benchmark with known ground truth, an advective-diffusive-reaction partial differential equation verification problem with derived physical reference structure, an atmospheric chemistry case study in a low-temporal-sample regime, and an El Niño Southern Oscillation study on reanalysis data, identifying phase-dependent ocean--atmosphere coupling. Across these settings, M-CaStLe more accurately recovers multivariate causal structure in controlled settings and identifies important physical dynamics in real-world case studies. Overall, M-CaStLe advances causal discovery for multivariate space-time systems while retaining interpretability at the grid level.

J. Jake Nichol, Michael Weylandt, G. Matthew Fricke +2

Scientific Machine Learning, Center for Computing Research Sandia National Laboratories · Zicklin School of Business Baruch College, CUNY · Department of Computer Science University of New Mexico +2

Time-Series Causal DiscoveryClimate ScienceCausal DiscoveryCausal Structure Learning
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Apr 29, 2026

Causal Learning with Neural Assemblies

Can Neural Assemblies -- groups of neurons that fire together and strengthen through co-activation -- learn the direction of causal influence between variables? While established as a computationally general substrate for classification, parsing, and planning, neural assemblies have not yet been shown to internalize causal directionality. We demonstrate that the inherent operations of neural assemblies -- projection, local plasticity control, and sparse winner selection -- are sufficient for directional learning. We introduce DIRECT (DIRectional Edge Coupling/Training), a mechanism that co-activates source and target assemblies under an adaptive gain schedule to internalize directed relations. Unlike backpropagation-based methods, DIRECT relies solely on local plasticity, making the resulting causal claims auditable at the mechanism level. Our findings are verified through a dual-readout validation strategy: (i) synaptic-strength asymmetry, measuring the emergent weight gap between forward and reverse links, and (ii) functional propagation overlap, quantifying the reliability of directional signal flow. Across multiple domains, the framework achieves perfect structural recovery under a supervised, known-structure setting. These results establish neural assemblies as an auditable bridge between biologically plausible dynamics and formal causal models, offering an "explainable by design" framework where causal claims are traceable to specific neural winners and synaptic asymmetries.

Evangelia Kopadi, Dimitris Kalles

Hellenic Open University Greece

Neural ProcessesCausal DiscoveryCausal Structure LearningBiologically Plausible LearningCausal InterpretabilityLocal Learning
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Apr 28, 2026

Optimization-Free Topological Sort for Causal Discovery via the Schur Complement of Score Jacobians

Continuous causal discovery typically couples representation learning with structural optimization via non-convex acyclicity penalties, which subjects solvers to local optima and restricts scalability in high-dimensional regimes. We propose a decoupled paradigm that shifts the causal discovery bottleneck from non-convex optimization to statistical score estimation. We introduce the Score-Schur Topological Sort (SSTS), an algorithm that extracts topological order directly from unconstrained generative models, bypassing constrained structure optimization. We establish that the causal hierarchy leaves a geometric signature within the score function: iterative graph marginalization is mathematically equivalent to computing the Schur complement of the Score-Jacobian Information Matrix (SJIM) under linear conditions. This translates the acyclicity constraint into an algebraic procedure with a dominant cost of O(d^3) operations. For non-linear systems, we formulate the expectation gap of Schur marginalization and introduce Block-SSTS to compress extraction depth, bounding structural error. Empirically, SSTS allows causal structural analysis on non-linear graphs up to d=1000. At this scale, our framework indicates that once the non-convex optimization bottleneck is mathematically bypassed, the structural fidelity of continuous causal discovery is bounded by the finite-sample estimation variance of the global score geometry. By reducing graph extraction to matrix operations, this work reframes scalable causal discovery from a constrained optimization problem to a statistical estimation challenge.

Rui Wu, Hong Xie

School of Computer Science and Engineering University of Science and Technology of China

Score-Based Causal DiscoveryCausal DiscoveryCausal Structure Learning
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Apr 27, 2026

Can Current Agents Close the Discovery-to-Application Gap? A Case Study in Minecraft

Discovering causal regularities and applying them to build functional systems--the discovery-to-application loop--is a hallmark of general intelligence, yet evaluating this capacity has been hindered by the vast complexity gap between scientific discovery and real-world engineering. We introduce SciCrafter, a Minecraft-based benchmark that operationalizes this loop through parameterized redstone circuit tasks. Agents must ignite lamps in specified patterns (e.g., simultaneously or in timed sequences); scaling target parameters substantially increases construction complexity and required knowledge, forcing genuine discovery rather than reliance on memorized solutions. Evaluating frontier models including GPT-5.2, Gemini-3-Pro, and Claude-Opus-4.5 under a general-purpose code agent scaffold, we find that all plateau at approximately 26% success rate. To diagnose these failures, we decompose the loop into four capacities--knowledge gap identification, experimental discovery, knowledge consolidation, and knowledge application--and design targeted interventions whose marginal contributions serve as proxies for corresponding gaps. Our analysis reveals that although the general knowledge application capability still remains as the biggest gap across all models, for frontier models the knowledge gap identification starts to become a major hurdle--indicating the bottleneck is shifting from solving problems right to raising the right problems for current AI. We release SciCrafter as a diagnostic probe for future research on AI systems that navigate the full discovery-to-application loop.

Zhou Ziheng, Huacong Tang, Jinyuan Zhang +9

University of California, Los Angeles · Peking University · Amazon

AI Agents for Scientific DiscoveryCircuit DiscoveryCausal DiscoveryAI Agent Benchmarks
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Apr 26, 2026

Causal Representation Learning from General Environments under Nonparametric Mixing

Causal representation learning aims to recover the latent causal variables and their causal relations, typically represented by directed acyclic graphs (DAGs), from low-level observations such as image pixels. A prevailing line of research exploits multiple environments, which assume how data distributions change, including single-node interventions, coupled interventions, or hard interventions, or parametric constraints on the mixing function or the latent causal model, such as linearity. Despite the novelty and elegance of the results, they are often violated in real problems. Accordingly, we formalize a set of desiderata for causal representation learning that applies to a broader class of environments, referred to as general environments. Interestingly, we show that one can fully recover the latent DAG and identify the latent variables up to minor indeterminacies under a nonparametric mixing function and nonlinear latent causal models, such as additive (Gaussian) noise models or heteroscedastic noise models, by properly leveraging sufficient change conditions on the causal mechanisms up to third-order derivatives. These represent, to our knowledge, the first results to fully recover the latent DAG from general environments under nonparametric mixing. Notably, our results match or improve upon many existing works, but require less restrictive assumptions about changing environments.

Ignavier Ng, Shaoan Xie, Xinshuai Dong +2

1Carnegie Mellon University · 2Mohamed bin Zayed University of Artificial Intelligence

Causal Representation LearningCausal DiscoveryCausal Structure LearningCausal Identifiability
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Apr 26, 2026

Causal Discovery as Dialectical Aggregation: A Quantitative Argumentation Framework

Constraint-based causal discovery is brittle in finite-sample regimes because erroneous conditional-independence (CI) decisions can cascade into substantial structural errors. We propose Quantitative Argumentation for Causal Discovery (QACD), a semantics-driven framework that represents CI outcomes as graded, defeasible arguments rather than irreversible constraints. QACD maps statistical test outcomes to argument strengths and aggregates conflicting evidence through connectivity-mediated witness propagation, producing a fixed-point acceptability labeling over candidate adjacencies. Experiments on standard benchmark Bayesian networks suggest that QACD improves structural coherence and interventional reliability in several noisy or inconsistent CI regimes, while remaining competitive with classical constraint-based, hybrid, and prior argumentation-based baselines.

Sheng Wei, Yulin Chen, Beishui Liao

The College of Computer Science and Technology, Zhejiang University · School of Philosophy, Zhejiang University · ZLAIRE, Zhejiang University +1

Causal DiscoveryComputational ArgumentationConstraint-Based Causal Discovery
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Apr 24, 2026

From Local to Cluster: A Unified Framework for Causal Discovery with Latent Variables

Latent variables pose a fundamental challenge to causal discovery and inference. Conventional local methods focus on direct neighbors but fail to provide macro level insights. Cluster level methods enable macro causal reasoning but either assume clusters are known a priori or require causal sufficiency. Moreover, directly applying single variable causal discovery methods to cluster level problems violates causal sufficiency and leads to incorrect results. To overcome these limitations, this paper proposes L2C (Local to Cluster Causal Abstraction), a unified framework that bridges local structure learning and cluster level causal discovery. Unlike prior work that requires a complete manual assignment of micro variables to clusters, L2C discovers the partition automatically from local causal patterns. Our solution leverages a cluster reduction theorem to reduce any cluster to at most three nodes without loss of causal information, applies local causal discovery to identify direct causes, effects, and V structures in the presence of latent variables, and performs macro level causal inference via cluster level calculus on the learned cluster graph. L2C does not assume causal sufficiency, as latent variables are handled through local discovery. Theoretical analysis shows that L2C ensures soundness, atomic completeness, and computational efficiency. Extensive experiments on synthetic and real world data demonstrate that L2C accurately recovers ground truth clusters and achieves superior macro causal effect identification compared to existing baselines.

Zongyu Li

Causal Effect EstimationCausal DiscoveryCausal AbstractionCausal Discovery with Latent Confounding
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Apr 21, 2026

Separable Pathways for Causal Reasoning: How Architectural Scaffolding Enables Hypothesis-Space Restructuring in LLM Agents

Causal discovery through experimentation and intervention is fundamental to robust problem solving. It requires not just updating beliefs within a fixed framework but revising the hypothesis space itself, a capacity current AI agents lack when evidence demands representations they have not previously constructed. We extend the blicket detector paradigm from developmental science to test this capacity in AI agents equipped with architectural scaffolding that targets hypothesis-space restructuring. Our compositional architecture has two discrete components: context graphs, which structure exploration as typed state machines, and dynamic behaviors, which monitor for evidence that the current hypothesis space is inadequate and expand it at runtime. Across 1,085 experimental trials, these components make orthogonal contributions: context graphs drive reasoning quality within the post-switch hypothesis space, accounting for 94% of the accuracy gain, while dynamic behaviors drive reasoning eligibility by detecting regime changes and preventing premature commitment to outdated hypotheses.

John Alderete, Sebastian Benthal, Connie Xu +1

Amigo AI · Simon Fraser University · International Computer Science Institute

Causal DiscoveryLLM AgentsCausal Interventions in Language ModelsLLM Reasoning
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Apr 20, 2026

Implicit Causal Graph Construction in Text via Chain Discovery

Causal graphs in text are typically populated by observable, predefined events. In contrast, we study implicit causal graph construction from text by treating each described cause-effect pair as the begin- and endpoint of an underlying latent causal graph and using large language models (LLMs) to infer intermediate causal events. We compare end-to-end graph construction with methods that frame the task as causal chain discovery. In the latter, graphs are built either by aggregating inferred chains or by progressively expanding partial chains through an iterative search process. We further explore Wisdom of the Crowd extensions that access causal knowledge from multiple LLMs in post-hoc aggregation and collaborative inference settings. We analyze trade-offs among these approaches and evaluate the validity of inferred causal relations using a manually curated database of 1,560 scientifically validated causal pairs. This database-based evaluation is proposed as reliable, resource-efficient, and transferable to settings where ground-truth graphs are unavailable.

Liesbeth Allein, Marie-Francine Moens

Department of Computer Science, KU Leuven, Belgium · Department of Electronics and Information Systems, Ghent University, Belgium

Causal DiscoveryCausal Reasoning in Language ModelsCausal Inference
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Apr 16, 2026

ClimateCause: Complex and Implicit Causal Structures in Climate Reports

Understanding climate change requires reasoning over complex causal networks. Yet, existing causal discovery datasets predominantly capture explicit, direct causal relations. We introduce ClimateCause, a manually expert-annotated dataset of higher-order causal structures from science-for-policy climate reports, including implicit and nested causality. Cause-effect expressions are normalized and disentangled into individual causal relations to facilitate graph construction, with unique annotations for cause-effect correlation, relation type, and spatiotemporal context. We further demonstrate ClimateCause's value for quantifying readability based on the semantic complexity of causal graphs underlying a statement. Finally, large language model benchmarking on correlation inference and causal chain reasoning highlights the latter as a key challenge.

Liesbeth Allein, Nataly Pineda-Castañeda, Andrea Rocci +1

Department of Computer Science, KU Leuven, Belgium · Institute of Argumentation, Linguistics, and Semiotics (IALS), Universit`a della Svizzera italiana, Switzerland

Relation ExtractionClimate ScienceCausal DiscoveryCausal Reasoning
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Apr 16, 2026

CAMO: An Agentic Framework for Automated Causal Discovery from Micro Behaviors to Macro Emergence in LLM Agent Simulations

LLM-empowered agent simulations are increasingly used to study social emergence, yet the micro-to-macro causal mechanisms behind macro outcomes often remain unclear. This is challenging because emergence arises from intertwined agent interactions and meso-level feedback and nonlinearity, making generative mechanisms hard to disentangle. To this end, we introduce CAMO, an automated Causal discovery framework from Micro behaviors to Macro Emergence in LLM agent simulations. CAMO converts mechanistic hypotheses into computable factors grounded in simulation records and learns a compact causal representation centered on an emergent target YY. CAMO outputs a computable Markov boundary and a minimal upstream explanatory subgraph, yielding interpretable causal chains and actionable intervention levers. It also uses simulator-internal counterfactual probing to orient ambiguous edges and revise hypotheses when evidence contradicts the current view. Experiments across four emergent settings demonstrate the promise of CAMO.

Xiangning Yu, Yuwei Guo, Yuqi Hou +2

College of Intelligence and Computing, Tianjin University, Tianjin, China · Tianjin Key Laboratory of Healthy Habitat and Smart Technology, Tianjin, China · Laboratory of Computation and Analytics of Complex Management Systems, Tianjin University, Tianjin, China

Causal DiscoveryCausal Structure LearningMulti-Agent SystemsLarge Language Model-Based Social SimulationEmergent Behavior in Multi-Agent Systems
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Apr 10, 2026

A novel hybrid approach for positive-valued DAG learning

Causal discovery from observational data remains a fundamental challenge in machine learning and statistics, particularly when variables represent inherently positive quantities such as gene expression levels, asset prices, company revenues, or population counts, which often follow multiplicative rather than additive dynamics. We propose the Hybrid Moment-Ratio Scoring (H-MRS) algorithm, a novel method for learning directed acyclic graphs (DAGs) from positive-valued data by combining moment-based scoring with log-scale regression. The key idea is that for positive-valued variables, the moment ratio E[Xj2]E[(E[Xj∣S])2]\frac{\mathbb{E}[X_j^2]}{\mathbb{E}[(\mathbb{E}[X_j \mid S])^2]} provides an effective criterion for causal ordering, where SS denotes candidate parent sets. H-MRS integrates log-scale Ridge regression for moment-ratio estimation with a greedy ordering procedure based on raw-scale moment ratios, followed by Elastic Net-based parent selection to recover the final DAG structure. Experiments on synthetic log-linear data demonstrate competitive precision and recall. The proposed method is computationally efficient and naturally respects positivity constraints, making it suitable for applications in genomics and economics. These results suggest that combining log-scale modeling with raw-scale moment ratios provides a practical framework for causal discovery in positive-valued domains.

Yao Zhao

Department of Statistics, Operations, and Data Science Fox School of Business, Temple University Philadelphia, PA, USA

Score-Based Causal DiscoveryCausal DiscoveryCausal Structure Learning
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Apr 8, 2026

iTAG: Inverse Design for Natural Text Generation with Accurate Causal Graph Annotations

A fundamental obstacle to causal discovery from text is the lack of causally annotated text data for use as ground truth, due to high annotation costs. This motivates an important task of generating text with causal graph annotations. Early template-based generation methods sacrifice text naturalness in exchange for high causal graph annotation accuracy. Recent Large Language Model (LLM)-dependent methods directly generate natural text from target graphs through LLMs, but do not guarantee causal graph annotation accuracy. Therefore, we propose iTAG, which performs real-world concept assignment to nodes before converting causal graphs into text in existing LLM-dependent methods. iTAG frames this process as an inverse problem with the causal graph as the target, iteratively examining and refining concept selection through Chain-of-Thought (CoT) reasoning so that the induced relations between concepts are as consistent as possible with the target causal relationships described by the causal graph. iTAG demonstrates both extremely high annotation accuracy and naturalness across extensive tests, and the results of testing text-based causal discovery algorithms with the generated data show high statistical correlation with real-world data. This suggests that iTAG-generated data can serve as a practical surrogate for scalable benchmarking of text-based causal discovery algorithms.

Wenshuo Wang, Boyu Cao, Nan Zhuang +1

School of Future Technology, South China University of Technology, Guangzhou, China · China Mobile GBA Innovation Institute, Guangzhou, China · Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China

Synthetic Data Generation for Language ModelsInverse DesignControllable Text GenerationCausal Discovery
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Apr 7, 2026

Bivariate Causal Discovery Using Rate-Distortion MDL: An Information Dimension Approach

Approaches to bivariate causal discovery based on the minimum description length (MDL) principle approximate the (uncomputable) Kolmogorov complexity of the models in each causal direction, selecting the one with the lower total complexity. The premise is that nature's mechanisms are simpler in their true causal order. Inherently, the description length (complexity) in each direction includes the description of the cause variable and that of the causal mechanism. In this work, we argue that current state-of-the-art MDL-based methods do not correctly address the problem of estimating the description length of the cause variable, effectively leaving the decision to the description length of the causal mechanism. Based on rate-distortion theory, we propose a new way to measure the description length of the cause, corresponding to the minimum rate required to achieve a distortion level representative of the underlying distribution. This distortion level is deduced using rules from histogram-based density estimation, while the rate is computed using the related concept of information dimension, based on an asymptotic approximation. Combining it with a traditional approach for the causal mechanism, we introduce a new bivariate causal discovery method, termed rate-distortion MDL (RDMDL). We show experimentally that RDMDL achieves competitive performance on the Tübingen dataset. All the code and experiments are publicly available at github.com/tiagobrogueira/Causal-Discovery-In-Exchangeable-Data.

Tiago Brogueira, Mário A. T. Figueiredo

Instituto de Telecomunicações, Instituto Superior Técnico, Universidade de Lisboa, Portugal

Causal DiscoveryMinimum Description Length
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Apr 6, 2026

Non-monotonic causal discovery with Kolmogorov-Arnold Fuzzy Cognitive Maps

Fuzzy Cognitive Maps constitute a neuro-symbolic paradigm for modeling complex dynamic systems, widely adopted for their inherent interpretability and recurrent inference capabilities. However, the standard FCM formulation, characterized by scalar synaptic weights and monotonic activation functions, is fundamentally constrained in modeling non-monotonic causal dependencies, thereby limiting its efficacy in systems governed by saturation effects or periodic dynamics. To overcome this topological restriction, this research proposes the Kolmogorov-Arnold Fuzzy Cognitive Map (KA-FCM), a novel architecture that redefines the causal transmission mechanism. Drawing upon the Kolmogorov-Arnold representation theorem, static scalar weights are replaced with learnable, univariate B-spline functions located on the model edges. This fundamental modification shifts the non-linearity from the nodes' aggregation phase directly to the causal influence phase. This modification allows for the modeling of arbitrary, non-monotonic causal relationships without increasing the graph density or introducing hidden layers. The proposed architecture is validated against both baselines (standard FCM trained with Particle Swarm Optimization) and universal black-box approximators (Multi-Layer Perceptron) across three distinct domains: non-monotonic inference (Yerkes-Dodson law), symbolic regression, and chaotic time-series forecasting. Experimental results demonstrate that KA-FCMs significantly outperform conventional architectures and achieve competitive accuracy relative to MLPs, while preserving graph- based interpretability and enabling the explicit extraction of mathematical laws from the learned edges.

Jose L. Salmeron

School of Engineering, CUNEF Universidad, Madrid, Spain

Fuzzy Cognitive MapsFuzzy LogicNonmonotonic ReasoningCausal DiscoveryKolmogorov-Arnold Networks
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Apr 3, 2026

SDVDiag: Using Context-Aware Causality Mining for the Diagnosis of Connected Vehicle Functions

Real-world implementations of connected vehicle functions are spreading steadily, yet operating these functions reliably remains challenging due to their distributed nature and the complexity of the underlying cloud, edge, and networking infrastructure. Quick diagnosis of problems and understanding the error chains that lead to failures is essential for reducing downtime. However, diagnosing these systems is still largely performed manually, as automated analysis techniques are predominantly data-driven and struggle with hidden relationships and the integration of context information. This paper addresses this gap by introducing a multimodal approach that integrates human feedback and system-specific information into the causal analysis process. Reinforcement Learning from Human Feedback is employed to continuously train a causality mining model while incorporating expert knowledge. Additional modules leverage distributed tracing data to prune false-positive causal links and enable the injection of domain-specific relationships to further refine the causal graph.Evaluation is performed using an automated valet parking application operated in a connected vehicle test field. Results demonstrate a significant increase in precision from 14% to 100% for the detection of causal edges and improved system interpretability compared to purely data-driven approaches, highlighting the potential for system operators in the connected vehicle domain.

Matthias Weiß, Falk Dettinger, Elias Detrois +2

Institute of Industrial Automation and Software Engineering (IAS), University of Stuttgart, Pfaffenwaldring 47, 70550 Stuttgart, Germany

Fault DiagnosisCausal Discovery
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Apr 2, 2026

Causal-Audit: A Framework for Risk Assessment of Assumption Violations in Time-Series Causal Discovery

Time-series causal discovery methods rely on assumptions such as stationarity, regular sampling, and bounded temporal dependence. When these assumptions are violated, structure learning can produce confident but misleading causal graphs without warning. We introduce Causal-Audit, a framework that formalizes assumption validation as calibrated risk assessment. The framework computes effect-size diagnostics across five assumption families (stationarity, irregularity, persistence, nonlinearity, and confounding proxies), aggregates them into four calibrated risk scores with uncertainty intervals, and applies an abstention-aware decision policy that recommends methods (e.g., PCMCI+, VAR-based Granger causality) only when evidence supports reliable inference. The semi-automatic diagnostic stage can also be used independently for structured assumption auditing in individual studies. Evaluation on a synthetic atlas of 500 data-generating processes (DGPs) spanning 10 violation families demonstrates well-calibrated risk scores (AUROC > 0.95), a 62% false positive reduction among recommended datasets, and 78% abstention on severe-violation cases. On 21 external evaluations from TimeGraph (18 categories) and CausalTime (3 domains), recommend-or-abstain decisions are consistent with benchmark specifications in all cases. An open-source implementation of our framework is available.

Marco Ruiz, Miguel Arana-Catania, David R. Ardila +1

Institute for Systems and Robotics, Instituto Superior Técnico, 1049-001 Lisbon, Portugal · Digital Scholarship at Oxford, University of Oxford, Oxford, OX1 3BG, United Kingdom · Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA

Time-Series Causal DiscoveryCausal DiscoverySelective Prediction
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Apr 2, 2026

Smoothing the Landscape: Causal Structure Learning via Diffusion Denoising Objectives

Understanding causal dependencies in observational data is critical for informing decision-making. These relationships are often modeled as Bayesian Networks (BNs) and Directed Acyclic Graphs (DAGs). Existing methods, such as NOTEARS and DAG-GNN, often face issues with scalability and stability in high-dimensional data, especially when there is a feature-sample imbalance. Here, we show that the denoising score matching objective of diffusion models could smooth the gradients for faster, more stable convergence. We also propose an adaptive k-hop acyclicity constraint that improves runtime over existing solutions that require matrix inversion. We name this framework Denoising Diffusion Causal Discovery (DDCD). Unlike generative diffusion models, DDCD utilizes the reverse denoising process to infer a parameterized causal structure rather than to generate data. We demonstrate the competitive performance of DDCDs on synthetic benchmarking data. We also show that our methods are practically useful by conducting qualitative analyses on two real-world examples. Code is available at this url: https://github.com/haozhu233/ddcd.

Hao Zhu, Di Zhou, Donna Slonim

Beth Israel Deaconess Medical Center Harvard Medical School Boston, MA, USA · Department of Computer Science Tufts University Medford, MA, USA

Causal DiscoveryCausal Structure LearningBayesian Network Structure Learning
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Mar 31, 2026

CausalPulse: An Industrial-Grade Neurosymbolic Multi-Agent Copilot for Causal Diagnostics in Smart Manufacturing

Modern manufacturing environments demand real-time, trustworthy, and interpretable root-cause insights to sustain productivity and quality. Traditional analytics pipelines often treat anomaly detection, causal inference, and root-cause analysis as isolated stages, limiting scalability and explainability. In this work, we present CausalPulse, an industry-grade multi-agent copilot that automates causal diagnostics in smart manufacturing. It unifies anomaly detection, causal discovery, and reasoning through a neurosymbolic architecture built on standardized agentic protocols. CausalPulse is being deployed in a Robert Bosch manufacturing plant, integrating seamlessly with existing monitoring workflows and supporting real-time operation at production scale. Evaluations on both public (Future Factories) and proprietary (Planar Sensor Element) datasets show high reliability, achieving overall success rates of 98.0% and 98.73%. Per-criterion success rates reached 98.75% for planning and tool use, 97.3% for self-reflection, and 99.2% for collaboration. Runtime experiments report end-to-end latency of 50-60s per diagnostic workflow with near-linear scalability (R^2=0.97), confirming real-time readiness. Comparison with existing industrial copilots highlights distinct advantages in modularity, extensibility, and deployment maturity. These results demonstrate how CausalPulse's modular, human-in-the-loop design enables reliable, interpretable, and production-ready automation for next-generation manufacturing.

Chathurangi Shyalika, Utkarshani Jaimini, Cory Henson +1

Artificial Intelligence Institute, University of South Carolina · Stride Lab, University of Michigan, Dearborn · Bosch Center for Artificial Intelligence, Pittsburgh

Smart ManufacturingRoot Cause AnalysisManufacturingIndustrial Anomaly DetectionNeuro-Symbolic ReasoningCausal Discovery+1
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Mar 27, 2026

Identification of Bivariate Causal Directionality Based on Anticipated Asymmetric Geometries

Identification of causal directionality in bivariate numerical data is a fundamental research problem with important practical implications. This paper presents two alternative methods to identify direction of causation by considering conditional distributions: (1) Anticipated Asymmetric Geometries (AAG) and (2) Monotonicity Index (MI). The AAG method compares the actual conditional distributions to anticipated ones along two variables. Different comparison metrics, such as Pearson correlation, cosine distance, Hellinger distance, Jaccard index, Jeffreys divergence, K-L divergence, K-S distance, MAE, MSE, mutual information, and Wasserstein distance have been evaluated. Anticipated distributions have been projected as normal based on dual response statistics: mean and standard deviation. The MI method compares the calculated monotonicity indexes of the gradients of conditional distributions along two axes and exhibits count of gradient sign changes. Both methods assume stochastic properties of the bivariate data and exploit anticipated unimodality of conditional distributions of the effect. The proposed methods are straightforward and include only a limited number of hyperparameters that affect the accuracy of the identification. For a given set of hyperparameters, both the AAG and MI methods provide a unique, deterministic solution. To address sensitivity to hyperparameters, tuning has been done by utilizing a full factorial Design of Experiment. It turns out that the AAG method outperforms MI, achieving top weighted accuracies of 82.7% with simple tuning and 84.4% with size-adaptive tuning, compared with 81.6% for GRCI or 82.0% for CAREFL-H on the 99 pairs of the Tubingen real-world cause-effect examples. To evaluate the decisiveness of the identification method, a decision tree was fitted on the input data's symmetrical bivariate statistics to detect misclassified cases.

Alex Glushkovsky

Causal Discovery
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Mar 26, 2026

Causal-INSIGHT: Probing Temporal Models to Extract Causal Structure

Understanding directed temporal interactions in multivariate time series is essential for interpreting complex dynamical systems and the predictive models trained on them. We present Causal-INSIGHT, a model-agnostic, post-hoc interpretation framework for extracting model-implied (predictor-dependent), directed, time-lagged influence structure from trained temporal predictors. Rather than inferring causal structure at the level of the data-generating process, Causal-INSIGHT analyzes how a fixed, pre-trained predictor responds to systematic, intervention-inspired input clamping applied at inference time. From these responses, we construct directed temporal influence signals that reflect the dependencies the predictor relies on for prediction, and introduce Qbic, a sparsity-aware graph selection criterion that balances predictive fidelity and structural complexity without requiring ground-truth graph labels. Experiments across synthetic, simulated, and realistic benchmarks show that Causal-INSIGHT generalizes across diverse backbone architectures, maintains competitive structural accuracy, and yields significant improvements in temporal delay localization when applied to existing predictors.

Benjamin Redden, Hui Wang, Shuyan Li

School of Electronics, Electrical Engineering and Computer Science, Queen’s University Belfast, Belfast, United Kingdom

Causal InterpretabilityCausal Discovery
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Mar 25, 2026

Enes Causal Discovery

Enes The proposed architecture is a mixture of experts, which allows for the model entities, such as the causal relationships, to be further parameterized. More specifically, an attempt is made to exploit a neural net as implementing neurons poses a great challenge for this dataset. To explain, a simple and fast Pearson coefficient linear model usually achieves good scores. An aggressive baseline that requires a really good model to overcome that is. Moreover, there are major limitations when it comes to causal discovery of observational data. Unlike the sachs one did not use interventions but only prior knowledge; the most prohibiting limitation is that of the data which is addressed. Thereafter, the method and the model are described and after that the results are presented.

Alexis Kafantaris

Causal Discovery
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Mar 24, 2026

Causal AI For AMS Circuit Design: Interpretable Parameter Effects Analysis

Analog-mixed-signal (AMS) circuits are highly non-linear and operate on continuous real-world signals, making them far more difficult to model with data-driven AI than digital blocks. To close the gap between structured design data (device dimensions, bias voltages, etc.) and real-world performance, we propose a causal-inference framework that first discovers a directed-acyclic graph (DAG) from SPICE simulation data and then quantifies parameter impact through Average Treatment Effect (ATE) estimation. The approach yields human-interpretable rankings of design knobs and explicit 'what-if' predictions, enabling designers to understand trade-offs in sizing and topology. We evaluate the pipeline on three operational-amplifier families (OTA, telescopic, and folded-cascode) implemented in TSMC 65nm and benchmark it against a baseline neural-network (NN) regressor. Across all circuits the causal model reproduces simulation-based ATEs with an average absolute error of less than 25%, whereas the neural network deviates by more than 80% and frequently predicts the wrong sign. These results demonstrate that causal AI provides both higher accuracy and explainability, paving the way for more efficient, trustworthy AMS design automation.

Mohyeu Hussain, David Koblah, Reiner Dizon-Paradis +1

University of Florida

Electronic Design AutomationCausal InterpretabilityCausal Effect EstimationCausal Discovery
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