Causal Discovery

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17 papers in the last four weeks, up 183% on the four weeks before. 0.2% of all new papers.

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Latest papers 148

Jun 22, 2026cs.AI

Causal Discovery in the Era of Agents

Recent attempts to combine large language models (LLMs) with causal discovery ask models to infer pairwise directions, propose graph structures, or inject language-model outputs as priors and constraints. These approaches promise faster analysis, but they also obscure whether a causal evidence is supported by data and assumptions or by textual associations, prompt artifacts and hallucinated mechanisms. We argue for a different role for agents in causal discovery. Agents should inspect data, retrieve context, explain method assumptions and clarify graph outputs, but they should not supply edges, orientations, priors, constraints or causal conclusions. We propose the principle that agents assist the workflow, while causal claims remain grounded in data, explicit assumptions, formal algorithms, diagnostics and user or domain-expert decisions. We instantiate this principle in causal-learn+, an online platform that coordinates data analysis, preprocessing, method recommendation, expert-knowledge incorporation, formal discovery and interpretation around the algorithmic ecosystem of causal-learn. A case study on Big Five personality data illustrates agent-assisted pipeline of causal discovery without turning language-model unreliability into causal evidence. The platform is available at causallearn.com.

Yujia Zheng, Vishal Verma, Mantej Gill +3

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

AI Agents for Scientific Discovery Causal Discovery

Jun 22, 2026cs.LG

One Ruler: A Same-Hands Re-Evaluation of Bivariate Causal Direction on Tuebingen, with a Parameter-Free Compression Baseline

Headline accuracies on the Tuebingen cause-effect pairs are routinely compared across papers even though each is measured under its authors' own protocol -- different pair subsets, weightings, model-selection, and decision rates. We argue this is the wrong comparison and run the right one: a same-hands re-evaluation in which every method is run by us on the identical 102 pairs, with one strict rule -- no tuning and a decision forced on every pair. As a clean reference point we introduce a deliberately minimal baseline: sorted-conditional compression, which feeds quantized, sorted, first-differenced data to an off-the-shelf compressor (bz2) and has zero fitted parameters. Under the common ruler the ranking differs sharply from the literature. Our baseline reaches 74.7% weighted accuracy (p = 3.7e-7); on the same 100 pairs that SLOPE is evaluated on it scores 76.0%, a 1.2-point gap below the authors' own forced-decision SLOPE (77.2%) that is well inside noise (McNemar p = 0.39). A faithful re-run of RECI lands at 70.7% -- inside the original authors' reported error bar, not the 77.5% often quoted (which we trace to a mis-copied cell). SLOPE's published 82.4% is a decided-subset figure: scoring the authors' own stored output only on the pairs its significance test chose to answer reproduces 81.7%. Under the common ruler the methods cluster in the low-to-mid 70s and the zero-parameter compressor ties the strongest of them. We document the mechanisms that inflate published figures (test-set model selection, significance-gated abstention) and contribute two further results: compression score magnitude is a model-free confounding flag (p = 2.8e-68), and a pre-registered falsification test fails in an instructive way that bounds the method's theoretical interpretation. Code, pre-registrations, and per-pair outputs are released.

Wietse Stienstra

State of the Art — Compression Lab

Causal Discovery Benchmark Validity Causal Inference

Jun 21, 2026cs.LG

A Survey on Federated Causal Discovery and Inference

Causal reasoning, which encompasses the discovery of causal structures and the inference of causal effects, is fundamental to data-driven decision making. In practice, data for reliable causal analysis are often distributed across institutions and cannot be centralized due to privacy regulations or communication constraints. Federated learning (FL) addresses this by enabling collaborative analysis without raw data sharing, giving rise to the rapidly growing field of federated causal discovery (FCD) and inference (FCI). However, the interdisciplinary nature of this field and the absence of a comprehensive survey present barriers to entry for researchers. This paper bridges that gap by providing a systematic review through multi-dimensional taxonomies. Grounded in the three core design decisions underlying any FCD solution, namely how structures are learned, how data are partitioned, and what structural knowledge each party obtains, we organize FCD along three axes: methodological paradigm, federation topology, and structural scope. We further examine key practical dimensions, including temporal dynamics, data heterogeneity, missing data, and non-identical variable sets. For FCI, we categorize methods by target estimand (average versus individualized/conditional treatment effects) and by estimation strategy, from classical weighting methods to modern deep generative architectures. Unlike prior works that treat FCD and FCI separately, we formalize their connection as complementary stages of a unified federated causal reasoning pipeline, where FCD supplies the structural knowledge required for valid effect estimation in FCI. Finally, we highlight their shared concerns regarding privacy, communication efficiency, theoretical guarantees, and application domains, and conclude by identifying open challenges for future research.

Xianjie Guo, Yuwei Wang, Guodu Xiang +4

School of Computer Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China · School of Computer Science and Information Engineering, Hefei University of Technology, Hefei 230601, China · College of Computing and Data Science, Nanyang Technological University, Singapore 639798 +1

Causal Effect Estimation Causal Discovery Causal Inference Federated Learning

Jun 19, 2026cs.LG

DCD-PFN: A Decoupling-Aware Foundation Model for Causal Discovery

Causal discovery is critical for understanding complex data-generating mechanisms, yet traditional algorithms often struggle with highly non-linear and noisy systems, or suffer from severe computational bottlenecks. Recent tabular foundation models based on Prior-Data Fitted Networks (PFNs) have demonstrated remarkable zero-shot inference capabilities, but their potential for explicit structural causal discovery remains underexplored. To bridge this gap, we propose DCD-PFN, a decoupling-aware foundation model for causal discovery. Instead of directly amortizing global graph reconstruction, DCD-PFN focuses on local causal discovery through a decoupling-based paradigm. Through pre-training on diverse synthetic Structural Causal Models (SCMs), the model learns sample-wise decoupling weights that enable Markov boundary (MB) identification. Furthermore, by leveraging parallelized local discovery, DCD-PFN efficiently reconstructs global causal graphs while remaining grounded in the theoretical foundations of decoupling-based causal discovery. Experiments demonstrate that our foundation model achieves robust zero-shot generalization.

Zhengkang Guan, Yikang Chen, Yi He +5

College of Computer Science and Technology Zhejiang University

Causal Foundation Models Structural Causal Models Causal Discovery Causal Structure Learning Prior-Data Fitted Networks

Jun 17, 2026cs.LG

Latent Confounded Causal Discovery via Lie Bracket Geometry

Recent work on Kan-Do-Calculus (KDC) has established that the boundary between passive observation and active intervention in causal inference is a category-theoretic bi-adjunction, with interventions modeled by left Kan extensions and conditioning by right Kan extensions. This paper introduces two causal discovery algorithms under latent confounding, building on the information-geometric and categorical consequences of KDC. In smooth statistical settings, Radon-Nikodym derivatives between observational and interventional measures induce local causal vector fields; failures of these fields to close under Lie brackets become computable Frobenius residuals, which we interpret as witnesses of failed visible integrability and possible latent or unmodeled structure. Our first algorithm, BRIDGE (Bracket Residuals for Interventional Discovery and Geometric Estimation), combines an interventional density or Radon-Nikodym-ratio engine with a geometric screen that proposes a high-recall family of admissible arrows, identifies non-closing visible pairs as latent-obstruction candidates, and passes the reduced family to downstream score-based or differentiable discovery routines. The second algorithmic contribution, Spectral Kan-Do Flow Matching (SKFM), learns amortized intervention fields and factors latent curvature spectrally, exposing the direct Lie-space endpoint toward which BRIDGE points. A detailed set of experiments show that both algorithms are capable of discovering causal models with latent confounders while collapsing the super-exponential space of possible DAGs by many orders of magnitude. This paper introduces a new paradigm in causal discovery, where latent structure is inferred directly from the geometry of intervention-induced flows.

Sridhar Mahadevan

Adobe Research and University of Massachusetts, Amherst

Causal Discovery Causal Intervention Causal Discovery with Latent Confounding

Jun 17, 2026cs.LG

Unsupervised Causal Abstractions Discovery

Causal abstractions formalize when a high-level structural causal model (SCM) captures the interventional behavior of a lower-level SCM. Existing applications of this notion largely follow a hypothesis-testing paradigm: an expert proposes a candidate high-level model and then evaluates if the low-level system implements it. We study the complementary problem of learning a high-level model directly from low-level measurements. Our contributions leverage hypotheses from low-rank causal discovery, and can be summarized as follows: (1) we show that observations generated by a low-rank graph induce latents that form a causal abstraction, (2) we provide identifiability results about these latents, and (3) we propose a practical objective to learn this high-level SCM.

Théo Saulus, Simon Lacoste-Julien, Dhanya Sridhar

Mila - Quebec AI Institute · Université de Montréal · Canada CIFAR AI Chair

Structural Causal Models Causal Discovery Causal Abstraction Causal Identifiability

Jun 17, 2026cs.LG

Identifying Structural Biases from Causal Mechanism Shifts

Causal discovery methods commonly assume that all data is independently and identically distributed (i.i.d.) and that there are no unmeasured variables affecting the system. In practice, these assumptions are often violated, leading to inaccurate inference. In this paper, we study how to identify hidden confounding and selection biases from causal mechanism shifts. In particular, we show that structural biases lead to dependent mechanism shifts. That is, by considering for which variables the mechanisms change given data from different environments, we can tell which variables are unbiased, which are subject to hidden confounding, and which are undergoing selection bias. We formalize this into an empirically testable criterion based on mutual information, and show under which conditions it identifies structural biases. To tell which nodes are subject to what kind of bias, we introduce the StruBI algorithm. Experiments on synthetic and real-world data show that StruBI works well in practice, accurately recovering affected variable sets and types of biases, outperforming the state-of-the-art by a wide margin.

Praharsh Nanavati, Jilles Vreeken, David Kaltenpoth

CISPA Helmholtz Center for Information Security

Structural Causal Models Causal Discovery Causal Inference Selection Bias Causal Discovery with Latent Confounding

Jun 16, 2026stat.ML

Tensor-based second-order causal discovery

Causal discovery seeks to uncover the causal dependencies among variables. For this purpose, we propose an algorithm called Tensor-based Second-order Causal Discovery (TSCD). Its input is a tensor obtained from the covariance matrices of observational and interventional data. Assuming the causal dependencies follow a linear structural equation model on a directed acyclic graph (DAG), TSCD outputs the DAG and the functions on its edges, requiring only that the noise variables are uncorrelated. We also implement a version of the approach for nonlinear models. Our focus on second-order statistics (via the covariance matrices) is motivated by their statistical and computational efficiency relative to higher-order moments, their identifiability relative to first-order statistics, and that they work regardless of whether the variables are Gaussian. We show that TSCD has identifiable causal order and parameters from a number of interventions that is logarithmic in the number of variables. Experiments show that TSCD is robust to noise, competitive with existing methods, and scales to hundreds of variables.

Nathan Ouyang, Kexin Wang, Anna Seigal

Structural Causal Models Causal Discovery

Jun 16, 2026stat.ML

Fast Nonparametric Conditional Independence Testing via Two-Stage Regression

Constraint-based causal discovery relies on repeated conditional independence tests, but fast nonparametric tests often sacrifice calibration, especially when variables depend on the conditioning set through nonlinear relationships. We introduce BLITZ (Broad-to-Local Independence Testing via residualiZation), a nonparametric conditional independence test designed to run well under a second while maintaining the accuracy needed for the thousands of queries performed by constraint-based causal discovery algorithms. BLITZ first removes broad smooth dependence on the conditioning set using low-order polynomial regression, then applies a small nonlinear feature map and residualizes those features with shallow tree regressions. The resulting statistic tests residual cross-covariance, with a moment-matched chi-square approximation to the null distribution. We show theoretically that the two-stage design reduces the effective complexity faced by the tree residualizers, allowing shallow trees to control residual conditional-mean bias while avoiding excessive overfitting. In simulations, BLITZ provides better null calibration than fast kernel, random-feature, and regression-based competitors while remaining among the fastest methods tested. In causal discovery experiments on synthetic graphs and flow-cytometry data, BLITZ yields more reliable endpoint orientations among retained adjacencies and competitive structural recovery. These results suggest that broad-to-local residualization is a practical route to calibrated, scalable nonparametric conditional independence testing for causal discovery.

Eric V. Strobl

Department of Biomedical Informatics, University of Pittsburgh, Pittsburgh, PA 15213, USA

Causal Discovery Causal Structure Learning Causal Inference Conditional Independence Testing Statistical Hypothesis Testing

Jun 16, 2026cs.LG

FoundCause: Causal Discovery with Latent Confounders from Observational Data

Causal discovery from observational data remains challenging due to the need to recover directed structure and latent confounding without interventions. We propose FoundCause, an amortized causal discovery model trained entirely on synthetic data that maps datasets directly to causal graphs in a single forward pass. By learning from large collections of simulated structural causal models, FoundCause captures transferable statistical patterns that generalize beyond individual datasets. The architecture incorporates several key inductive biases for causal discovery. It uses a permutation-invariant transformer encoder with alternating attention over samples and variables to jointly model cross-variable dependence and per-variable distributions. Pairwise statistical features derived from classical asymmetry measures are injected through statistics-conditioned attention, guiding the model toward known causal signals. A factorized decoder separates edge existence from direction, while a triangular refinement module enables reasoning over higher-order causal motifs such as chains and colliders. In addition, a dedicated confounder module based on learnable latent tokens explicitly models hidden common causes, and the model explicitly handles missing data via its masked input representation. To our knowledge, FoundCause is the first amortized causal discovery approach to explicitly model latent confounding. FoundCause outperforms 11 classical non-amortized methods (e.g., PC, GES, NOTEARS-style optimization) and 4 amortized causal discovery methods on 15 real-world datasets, achieving +9.6% improvement in

F_1

, +1.2% in AUROC, and an 18.9% reduction in structural Hamming distance relative to the strongest non-amortized methods, while performing inference in a single forward pass.

Patrick Blöbaum, Krishnakumar Balasubramanian, Shiva Prasad Kasiviswanathan

Amazon Web Services · Department of Statistics, University of California, Davis

Structural Causal Models Amortized Inference Causal Discovery Causal Discovery with Latent Confounding

Jun 15, 2026cs.LG

From Tokens to Policy: Causal and Interpretable Heterogeneous Treatment Effects Identification

Heterogeneous Treatment Effect (HTE) identification is essential to explain the impact of an intervention and optimize our policies accordingly. Existing approaches trade expressivity for interpretability, but, if some active heterogeneity drivers are unmeasured, methods at both ends of this spectrum allow for spurious HTE characterization with no causal reading. In this work, we focus on controlled experiments and argue that an oracle HTE causal characterization via the latent interactors is now within reach, thanks to (i) more extensive pre-treatment measurements, i.e., multi-modal and multi-view, and (ii) scalable representations with minimal human supervision. We then re-frame HTE identification as a Markov-blanket discovery problem on a sufficient and aligned pre-treatment representation, and introduce Neural EXposure Interaction Search (NEXIS), an iterative procedure with a provable selection guarantee. We deploy NEXIS on two anti-poverty programs in Africa, augmenting each with satellite imagery capturing previously unmeasured environmental effect modifiers, leading to new candidate prescriptive guidelines to optimize the programs' next iterations.

Riccardo Cadei, Frank Otchere, Nyasha Tirivayi +3

ISTA · UNICEF · UCLA

Causal Effect Estimation Conditional Average Treatment Effect Estimation Causal Discovery Individualized Treatment Effect Estimation

Jun 14, 2026cs.SE

SDVDiag: Multimodal Causal Discovery for Online Diagnosis in Software-defined Vehicles

The transition toward software-defined vehicles concentrates an increasing share of vehicle functionality into distributed software services, where failures propagate through service dependencies and the surface symptom is often several causal hops away from the underlying defect. Existing approaches to causal root-cause analysis in such systems address this only partially: they typically reason over a single observability modality and operate in an offline, operator-driven mode that does not match the demands of continuous vehicle operation. This paper presents SDVDiag, a multimodal causal-discovery pipeline that fuses log-based and metric-based service representations into a shared embedding space before graph construction, coupled with an anomaly-driven trigger that converts the diagnostic platform from a manually operated batch tool into a continuously running online system. Evaluation on an Autonomous Valet Parking testbed shows that the multimodal pipeline produces sparser causal graphs than a metrics-only baseline (134 vs. 182 edges on average) and consistently outperforms it in edge-weighted reward against an expert knowledge graph at every stage of human-feedback refinement, showing a 2.4-fold improvement over the baseline after 60 feedback queries. An end-to-end fault-injection scenario further demonstrates that the integrated trigger correctly recovers a true root cause located two causal hops upstream of the observable symptom.

Matthias Weiß, Athreya Hosahalli Prakash, Falk Dettinger +2

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

Causal Discovery Root Cause Analysis Fault Diagnosis

Jun 9, 2026cs.LG

Causal Ensemble Agent: Hierarchical Causal Discovery with LLM-guided Expert Reweighting

Causal discovery aims to uncover causal structures from observational data, which is crucial for real-world decision-making. However, different causal discovery algorithms can produce divergent results that conflict with each other, complicating the identification of accurate causal graphs. Traditional approaches rely on numerical values and statistical assumptions, often ignoring rich domain-specific information, such as feature descriptions, which could also help structure learning. While recent works explore using Large Language Models (LLMs) to infer causal relations via direct queries, such methods can be unreliable due to a lack of alignment with the actual data. To address these limitations, we propose Causal Ensemble Agent (CEA), a novel framework that aggregates structural insights from statistical discovery experts across different graph levels via linear opinion pooling, and uses an LLM as a meta-referee to dynamically reweight experts when the aggregated confidence is close to the decision boundary, thereby composing an improved and more complete causal graph. Extensive experiments on both synthetic and real-world datasets demonstrate that CEA achieves the strongest overall performance across a wide range of causal discovery methods, highlighting the effectiveness of using LLMs for meta-analysis in causal discovery.

Xinyu Li, Yuanyuan Wang, Haoxuan Li +7

The University of Melbourne · MBZUAI · Peking University +4

Causal Discovery Causal Structure Learning

Jun 8, 2026cs.AI

Correlation Is Not Enough: Embedding Human Metadata for Individual Causal Discovery

Ask a pretrained biomedical language model whether "cortisol 28 ug/dL" and "stock-market volatility" are related, and it returns a cosine similarity of 0.83 on a scale where 1.0 means identical. The two share no mechanism. This is not a corner case: every off-the-shelf biomedical encoder we tested (BioBERT, PubMedBERT, BioM-ELECTRA) scores unrelated cross-domain pairs between 0.76 and 0.92 when the answer should be near zero. Accuracy on cross-domain discrimination is 0%. Retrieval systems survive this, because a language model downstream filters the noise. A Large Behavioural Model (LBM), a foundation model whose subject is a person rather than a sentence, does not: it reasons over a graph of a user's life and treats embedding proximity as evidence that two events are causally linked. False proximity writes a false causal edge, and everything downstream inherits the error. Here, embedding geometry is not a tuning knob; it is correctness. We report the fix. A contrastive pass over 72,034 pairs raises PubMedBERT BIOSSES correlation from 0.633 to 0.828 and within-vs-across-domain separation from 1.05x to 1.63x. A second pass, BODHI, mines hard negatives from edges absent in a biomedical knowledge graph and lifts separation to 2.30x and the discrimination gap to +0.392, at a 4.5% BIOSSES cost. On an Intel Xeon 6737P with AMX, OpenVINO cuts single-query latency from 1367 ms to 10 ms (133x) and reaches 555 sentences/sec. One finding contradicts standard advice: FP16 beats INT8 on this silicon at every serving batch size, and we explain why. The same model on a no-AMX Ice Lake instance runs 13-27x slower. We release the benchmark suite, training corpora, the BODHI generator, and the OpenVINO scripts.

Suraj Biswas, Saurabh Gupta, Pritam Mukherjee

¹ Assessli Research · ² Dots-In Research, Bengaluru, India

Contrastive Learning Sentence Embeddings Causal Discovery

Jun 6, 2026stat.ML

Beyond Additivity: Causal Discovery in Location-Scale Noise Models with Hidden Variables

We study causal discovery from observational data when some variables are hidden and the data-generating process follows a location-scale noise model (LSNM). Existing methods that handle hidden confounders typically assume additive noise, but in practice, causes often modulate not just the mean but also the variance of their effects. We prove that acyclic directed mixed graphs (ADMGs) satisfying a bow-free condition are identifiable under LSNM with hidden variables, establishing the first identifiability result for causally insufficient models beyond noise additivity. We further provide sufficient conditions for identifying causal direction even when the bow-free assumption is violated. Our two-stage algorithm, LSNM-UV, is sound and complete, and experiments demonstrate improved performance over additive baselines on heteroscedastic data.

Mariyam Khan, Shohei Shimizu, Thong Pham

University of Bergen · *Work conducted while a student trainee at RIKEN AIP · 2The University of Osaka +2

Graph Structure Learning Causal Discovery Causal Identifiability Causal Discovery with Latent Confounding

Jun 5, 2026cs.LG

Network Recovery from Cascade Data: A Debiased Jacobian-Based Machine Learning Approach

Many important outcomes unfold as dynamic cascades, including product adoption, disease spread, financial distress, and information diffusion. A central challenge is to recover the hidden influence network behind these cascades. Existing methods typically assume a specific diffusion model, and their performance degrades substantially when that assumption is misspecified. We propose CascadeNet, a Jacobian-based machine learning framework for network recovery that does not require specifying a diffusion mechanism. The key idea is that the underlying influence structure can be characterized by the Jacobian of the one-step transition function. CascadeNet first constructs a flexible estimator of the transition function, and further applies Neyman-orthogonal debiasing via the Riesz representer, so that the debiased Jacobian is

\sqrt{n}

-consistent and asymptotically normal, enabling formal inference on the network structure. We validate CascadeNet in both a simulation exercise and a real-world empirical application. In simulations, where the data-generating process is known, CascadeNet achieves the highest network recovery accuracy across nine common data-generating processes. In an empirical application to COVID-19 transmission across Spain's 52 provinces, CascadeNet recovers transmission networks that are significantly correlated with the true inter-province mobility network, whereas networks recovered by baseline methods show no significant alignment with the ground truth.

Lei Huang

MIT Sloan School of Management

Causal Discovery

Jun 5, 2026cs.CV

polyDAG: Polynomial Acyclicity Constraints for Efficient Continuous Causal Discovery in Visual Semantic Graphs

Modern image-analysis pipelines often convert images into structured semantic variables, such as facial attributes, object concepts, and scene descriptors. Learning directed dependencies among these variables can produce interpretable visual semantic graphs, but continuous directed acyclic graph learning is limited by the cost of enforcing acyclicity. We present polyDAG, a polynomial acyclicity framework for efficient continuous causal discovery in visual semantic graphs. polyDAG replaces the matrix-exponential acyclicity constraint with a finite polynomial trace constraint and proves that the new constraint is zero exactly for acyclic graphs. We further derive a geometric-series implementation that avoids the explicit summation loop while preserving the same acyclicity condition. Experiments on synthetic Erdos-Renyi graphs and CelebA facial visual attributes show that polyDAG improves efficiency and structure recovery. Averaged over the revised synthetic protocol with d in {100, 200, 500}, polyDAG reduces mean structural Hamming distance from 318.4 to 285.4 and improves mean F1 score from 0.725 to 0.756. At 100 nodes, the geometric variant runs in 3.44 seconds compared with 5.16 seconds for the exponential baseline, corresponding to a 33.4 percent speedup. Code and data are publicly available at https://github.com/wenhaoz-fengcai/polyDAG.

Wenhao Zhang, Ramin Ramezani, Tao Han +2

School of Automation and Intelligent Sensing (Zhang, Han) and School of Computer Science (Guo), Shanghai Jiao Tong University, Shanghai, China · Department of Computer Science, University of California, Los Angeles, CA, USA · The Chinese University of Hong Kong, Shenzhen, China

Causal Discovery Causal Structure Learning

Jun 4, 2026cs.LG

Causal Atlases from Entropic Inference: Bayesian Networks beyond Optimal DAGs

Data-driven causal relationship identification is pertinent to advancing understanding of complex systems both within and beyond science. Bayesian networks offer a probabilistic method for modelling generic causal relationships via directed acyclic graphs (DAGs). However, typical techniques for constructing Bayesian networks rely on optimization, which can be ill-suited for learning causal relationships because the underlying data may admit multiple chains of causation. More data-faithful representations of causal relationships would provide frameworks for constructing multiple causal maps that are consistent with the variability that is inherent in underlying data. Here, we show that entropy-based inference generates atlases of plausible causal relationships that are consistent with underlying data. On simulated noisy data of 2- and 20-node linear structural equation models, we sample a maximum-entropy ensemble of graphs that allow us to quantify the inherent structural ambiguity in underlying causal relationships. Our method shows that "optimized" DAGs can contain causal artifacts are not consistent across equivalently accurate topologies.

Hazhir Aliahmadi, Irina Babayan, Greg van Anders

Department of Physics, Engineering Physics and Astronomy, Queen’s University, Kingston ON, Canada

Structural Causal Models Bayesian Networks Causal Discovery

Jun 4, 2026cs.LG

Causal Modeling of Selection in Evolution

Understanding potential selection in data is crucial for causal discovery; we argue that "selection" in common narratives takes two forms, which we term static and evolutionary selection, respectively. Static selection refers to a one-shot filtering process where observed data consist of a subset of the population of interest, as in survey volunteer bias. Evolutionary selection, in contrast, operates through repeated rounds of differential fitness in reproduction, where observed data constitute the latest generation shaped by a historical trajectory, as in immune adaptation, antibiotic resistance, and social norm emergence. Existing methods largely conflate these two forms and rely on an identical graphical model of selection. We show that this model is valid for static settings but fails to characterize data under evolution, yielding false discovery results. To address this, we introduce a new model that specifically characterizes evolutionary selection, and develop a sound and complete procedure for identifying such models from data across one or multiple environments or generations. Experimental results validate the method's ability to uncover the relevant mechanisms underlying evolution from data.

Haoyue Dai, Zeyu Tang, Peter Spirtes +1

Carnegie Mellon University · Stanford University · Mohamed bin Zayed University of Artificial Intelligence

Structural Causal Models Causal Discovery Causal Structure Learning Data Selection Causal Identifiability

Jun 3, 2026cs.LG

LMT: A Bayesian Framework for Causal Discovery from Textual Alarm Records in Manufacturing Systems

Textual event records, such as alarm logs, have become an increasingly common data source in engineering and manufacturing systems. Beyond identifying correlations or recurring patterns, engineers are often interested in understanding which types of events causally trigger or influence other events during system operation. Textual event descriptions may contain semantic clues about such causal relationships, and recent large language models (LLMs) provide a promising tool for extracting these signals. However, relying solely on LLM-encoded textual information is insufficient for accurate causal discovery, since semantic patterns do not directly reveal causal mechanisms and may confuse causation with correlation or frequent sequential patterns. To address these challenges, we propose \textbf{LMT}, a Bayesian causal discovery framework for engineering event data that jointly leverages textual descriptions and timestamps. Specifically, LMT first uses LLMs to extract semantic causal signals from event descriptions and constructs a prior distribution over causal graphs among event types or event clusters. It then incorporates temporal evidence through a Poisson-process-based likelihood, allowing the LLM-informed prior to be refined by timestamp-based statistical evidence. By integrating the textual and temporal information, LMT produces a causal graph that is both interpretable and data-supported. Simulation studies show that the proposed framework is effective across different settings and is especially advantageous in small-sample alarm-event scenarios.

Xiaofeng Xiao, Jianhong Chen, Qiuzhuang Sun +2

Department of Mechanical & Industrial Engineering, Northeastern University, Boston, MA, USA · College of Integrative Studies, Singapore Management University, Singapore · Department of Industrial Engineering and Management Sciences, Department of Mechanical Engineering, Northwestern University, IL, USA

Bayesian Networks Causal Discovery

Jun 3, 2026cs.CR

Preserving Data Privacy in Learning Causal Structure with Fully Homomorphic Encryption

Preserving data privacy is an important topic in structural data management and data mining. However, the issue of privacy leakage in distributed causal structure learning is a persistent challenge, especially in cases where data transmission and computation are required. In this paper, we propose a method based on fully homomorphic encryption (FHE) that performs calculations on ciphertexts, keeping data encrypted in transition and computation. Nevertheless, adopting FHE to causal structure learning is challenging due to the high computation cost and limited support on division as well as logarithm operations in FHE. To tackle this challenge, we propose a series of novel techniques including (i) circuit simplification for better efficiency, (ii) approximation of division and logarithm through Newton-Raphson Reciprocal and Taylor expansion, and (iii) a batching technique with SIMD-acceleration to enhance the whole learning process. Additionally, our method can be easily extended beyond FHE by demonstration of its portability to support differential privacy. Empirical results show that our method achieves high consistency and comparable causal structure with the plaintext version in the datasets tested. Last, our method is efficient and practical to complete learning causal structures in tens of minutes even under the privacy protection of FHE.

Jian Yang, Yuan Tong, Qinbin Li +2

Hong Kong University of Science and Technology (Guangzhou) · Hong Kong University of Science and Technology · University of California, Berkeley

Causal Discovery Causal Structure Learning Homomorphic Encryption Privacy-Preserving ML

Jun 2, 2026cs.LG

CauTion: Knowing When to Trust LLMs for Ensemble Causal Discovery

Causal discovery from observational data remains challenging due to the fundamental limitations of purely statistical methods, such as statistical distinguishability within equivalence classes and sensitivity to finite sample sizes. While large language models (LLMs) offer a promising source of domain knowledge to complement statistical inference, existing LLM-augmented methods are vulnerable to LLM errors and incur high token costs. Moreover, reliance on a single data-centric algorithm can make results sensitive to algorithm-specific biases. To address these limitations, we propose CauTion, a framework that reliably integrates LLM domain knowledge into an ensemble of statistical causal discovery algorithms through consensus filtering and LLM reliability estimation. CauTion proceeds in three stages. First, an algorithm ensemble utilizes a consensus voting to resolve up to 96% of edges on which algorithms agree, achieving near-perfect accuracy on the filtered consensus edges. Second, a trust-calibrated arbitration mechanism estimates the relative reliability of the LLM and the algorithms via an annotation-free trust calibration procedure, which is then utilized to govern a trust-weighted voting process that restricts LLM arbitration exclusively to edges with unreliable algorithmic evidence. Third, a cycle repair step is applied to guarantee the final causal graph is validly acyclic. Experiments on six datasets demonstrate that CauTion consistently outperforms both data-centric and LLM-augmented baselines, with larger gains on larger graphs and strong robustness to LLM errors. Code is available at https://github.com/OpenCausaLab/CauTion.

Bo Peng, Kaiwen Wu, Sirui Chen +3

Shanghai AI Laboratory · Shanghai Innovation Institute · Shanghai Jiao Tong University +2

Causal Discovery

Jun 2, 2026cs.LG

Learning Temporal Causal Structure via Smooth Differentiable Optimization

Causal discovery with instantaneous effects in multivariate time series is challenging, as the instantaneous structure must be acyclic. Prior methods enforce this by either separating instantaneous and lagged estimation into multi-stage pipelines or imposing algebraic acyclicity constraints via complex augmented Lagrangian optimization, both of which incur high computational cost. In this work, we propose a different approach: we learn a differentiable permutation of variables using the Gumbel--Sinkhorn operator and triangularize the instantaneous coefficient matrix of a Structural Vector Autoregressive (SVAR) model in the learned order. This converts acyclicity from a hard constraint into a parameterization and keeps it valid throughout optimization. In doing so, our method enables unified, continuous optimization with gradient-based learning, leading to improved efficiency in time--series causal discovery. Across three real-world benchmarks, our method achieves the best overall performance compared with 12 baselines in both discovery accuracy and efficiency. On the large-scale benchmark, it further demonstrates strong scalability, achieving more than a 6x speedup over competing methods.

Tong Zhao, Ce Guo, Wayne Luk +2

Time-Series Causal Discovery Causal Discovery

Jun 1, 2026cs.AI

Consistency evaluation of benchmarks used for causal discovery

In graphical causal model, causal discovery aims to construct a causal graph based on numerical data and domain knowledge in plain text. However, the evaluation of causal discovery methods remains a challenge in the area as the progress of domain researches often makes benchmark causal graphs contain mis-aligned knowledge. This problem especially affects the evaluation of large language model (LLM) based causal discovery methods as they are sensitive to the new discoveries in the literature. This work is the first to systematically study the quality of benchmark causal graphs. Specifically, we design a pipeline that automatically retrieves relevant research papers from scientific databases, and prompts LLMs to check the consistency between the benchmark causal graphs and domain research papers. We evaluate 11 popular real-world benchmarks, for which our pipeline in total proceeds 38,081 domain papers. Our results show that popular benchmarks vary significantly in their consistency with domain research, with clear implications for causal discovery research.

Yuzhe Zhang, Chihui Chen, Lina Yao +1

Independent researcher · Australia · UNSW +1

Causal Discovery Benchmark Validity

May 30, 2026cs.LG

On the Recoverability of Causal Relations from Bulk Gene Expression Data

Bulk gene expression profiling, which aggregates pooled RNA across cells within a biological sample, remains important in the single-cell era because it is typically less noisy, more sensitive, and more cost-effective than single-cell assays. Accordingly, a growing body of computational methods seeks to recover causal relations among genes from bulk expression data. However, aggregation is a lossy, non-invertible coarsening of the underlying cellular system, and it remains unclear whether and under what conditions causal relations are recoverable from aggregated bulk gene expression data. To answer this, we formalize recoverability under aggregation through two notions of consistency: functional-form consistency and conditional-independence consistency. We then derive necessary and sufficient conditions for recoverability, showing that these properties are preserved only under linear aggregations (e.g., sum/mean) coupled with affine structural equations. To assess the practical plausibility of these conditions, analyses of four bulk and four single-cell gene expression datasets further reveal that the estimated pairwise regulatory functions among genes deviate from linearity in both data types, providing limited empirical support for the linearity assumptions required for recoverability. Together, these results caution against recovering causal relations from aggregated bulk expression data without strong additional assumptions.

Gongxu Luo, Boyang Sun, Kun Zhang

Mohamed bin Zayed University of Artificial Intelligence · Carnegie Mellon University

Structural Causal Models Causal Discovery Causal Identifiability Gene Regulatory Network Inference

May 29, 2026cs.LG

TabCausal: Pretraining Across Causal Environments for Tabular Causal Discovery

Causal discovery aims to recover directed causal relations from observational and interventional data, providing a basis for mechanistic understanding and reliable decision-making. Causal discovery foundation models (CDFMs) seek to amortize this problem by mapping a dataset directly to a causal graph in a single forward pass, avoiding per-dataset testing, search, or optimization. However, existing CDFMs remain limited, often failing to consistently match strong classical methods, and we find that a key bottleneck is how causal pretraining tasks are constructed. Based on this observation, we propose TabCausal, a data-driven CDFM trained with broad causal pretraining over diverse graph priors, structural mechanisms, noise models, dimensions, sample sizes, and intervention regimes. A dynamic task construction strategy composes these causal environments into varied discovery tasks, enabling more transferable structural learning from observational and mixed-interventional data. On large-scale synthetic benchmarks, TabCausal achieves better macro-averaged performance than a diverse set of causal discovery baselines. To further bridge abstract synthetic generators and realistic causal reasoning scenarios, we introduce a protocol-guided and LLM-audited semantic causal environment benchmark, where domain-grounded SCMs generate interpretable observational and interventional datasets for out-of-distribution analysis. Across both synthetic and semantic environments, TabCausal demonstrates robust structure recovery, especially under interventional evidence, highlighting broad causal pretraining as a key ingredient for transferable amortized causal discovery.

Zi-Rong Li, Si-Yang Liu, Tian-Zuo Wang +1

Nanjing University

Causal Foundation Models Synthetic Data Pretraining Structural Causal Models Causal Discovery

May 28, 2026cs.LG

Test Time Training for Supervised Causal Learning

Supervised Causal Learning (SCL) has shown promise in causal discovery by framing it as a supervised learning problem. However, it suffers from significant out-of-distribution generalization challenges. We reveal three limitations of previous SCL practices: a significant performance gap between synthetic benchmarks and real-world data, fragility to distribution shifts, and failure in compositional generalization, collectively questioning its real-world applicability. To address this, we propose Test-Time Training for Supervised Causal Learning (TTT-SCL), a novel framework that dynamically generates training sets explicitly aligned with any specific test instance. We demonstrate the correlation between TTT-SCL and score-based methods, and design an efficient module for generating training sets based on the classic scoring function. Experiments on synthetic benchmarks, pseudo-real and real-world datasets demonstrate that TTT-SCL significantly outperforms existing SCL and traditional causal discovery methods.

Zizhen Deng, Jiaru Zhang, Rui Ding +5

Peking University · The work was done during his internship at Microsoft. · Shanghai Jiao Tong University +2

OOD Generalization Causal Discovery Test-Time Training Causal Inference

May 28, 2026cs.LG

The Good, the Bad, and the Ugly of Markov Boundary for Tabular Prediction

Under standard graphical assumptions, the Markov boundary of a target variable is the smallest set of features that renders every other feature redundant. Once the boundary is observed, the target is conditionally independent of the rest of the table. This is a tempting object for tabular prediction, since it names exactly the columns a model should need. Yet modern regressors are still trained on the full feature set. We ask whether the Markov boundary is genuinely useful for prediction on SCM3K, a 3,450-task synthetic SCM benchmark with feature counts from 40 to 1000 and six SCM families, evaluated with six regressors. The answer is more nuanced than the theory suggests. Restricting a regressor to the oracle boundary often improves prediction substantially, and the improvement grows as the feature space becomes larger and sparser. But the natural pipeline of recovering the boundary with causal discovery and training on the recovered mask does not deliver. Existing estimators exhaust the compute budget before reaching the regime where the boundary helps most, and even where they run they rarely beat the full feature set. We trace this to three causes. Discovery optimizes structural recovery rather than prediction. False negatives and false positives carry sharply asymmetric predictive cost. The exact boundary is only one of many feature sets that beat all features. We then develop what these facts imply for prediction-aligned feature selection and for tabular models that learn to use causal structure.

Shu Wan, Abhinav Gorantla, Huan Liu +1

Arizona State University Tempe, United States

Structural Causal Models Causal Discovery Feature Selection Tabular Prediction

May 26, 2026cs.AI

Why LLMs Fail at Causal Discovery and How Interventional Agents Escape

Causal discovery is a cornerstone of scientific reasoning, yet whether large language models can perform it reliably remains an open question. Recent benchmarks show that even fine-tuned models plateau on simple causal graphs and degrade as complexity grows, but why they fail has not been established. We prove the failure is fundamental: supervised fine-tuning, direct preference optimization, and in-context learning all produce predictors that cannot distinguish between causal graphs generating similar observational data, and any attempt to do so requires the model's internal representations to grow unboundedly, violating the very conditions under which these methods work. We formalize this as a kernel obstruction theorem, establishing that the limitation is intrinsic to the learning paradigm, \emph{not any particular model or dataset}. We propose Agentic Causal Bayesian Optimization (A-CBO), wherein a frozen language model serves as an interventional oracle answering targeted queries about intervention effects, while an external Bayesian loop concentrates beliefs over candidate graphs in logarithmically many rounds. Because the decision operates outside the space where the obstruction applies, A-CBO provably converges while the underlying model remains unchanged. On Corr2Cause, A-CBO matches fine-tuned baselines without any training. On Extended Corr2Cause, a new benchmark scaling to 24 variables with 18K test samples, A-CBO significantly outperforms both fine-tuning and preference optimization, with the advantage growing

Amartya Roy, Sonali Parbhoo

SIRE, IIT Delhi and Robert Bosch GmbH, India · Imperial College London

Causal Discovery Causal Reasoning in Language Models Causal Identifiability Causal Interventions in Language Models

May 26, 2026cs.AI

ORCA: An End-to-End Interactive Copilot for Optimized Root Cause Analysis

Causal analysis is a crucial task in many domains, including manufacturing, social science, and medicine. However, despite recent progress, the conceptual and methodological complexity of causal methods makes them largely inaccessible to domain experts. This gap prevents experts from leveraging these advances and hinders researchers who lack access to real-world data for validation. To bridge this divide, we introduce ORCA, a copilot for end-to-end causal analysis. ORCA orchestrates agents to understand the user's goals and guide them through the most appropriate causal analysis workflow, from fully automatic to highly user-guided execution. It features causal discovery, causal effect estimation, explainability and Root-Cause-Analysis (RCA). ORCA evaluates and compares performance, generates key metrics and diagrams, and generates insights through structured reports. We highlight its effectiveness across several real-world use-cases.

Phi Nguyen Xuan, Nicholas Tagliapietra, Lavdim Halilaj +2

Bosch Global Software Technologies Company Limited, Vietnam · Robert Bosch GmbH, Germany · Computer Science Department, TU Darmstadt, Germany +2

AI-Assisted Decision Making Causal Discovery Tool-Using Agents Root Cause Analysis