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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Aug 5, 2026cs.LG

Adversarial Causal Intervention Falsification

Generative models can reproduce an observational distribution while encoding an incorrect causal structure. We study a sequential game in which a structural causal generator proposes observational and interventional distributions, while an adversarial experimentalist selects interventions intended to maximally falsify the generator. The discriminator is therefore not merely a real-versus-synthetic classifier: it is indexed by an intervention and tests whether the generator reproduces the corresponding post-intervention law. We introduce Adversarial Causal Intervention Falsification (ACIF), formulate oracle and implementable versions of the game, and distinguish three objects that are often conflated: observational fit, interventional equivalence over an admissible query class, and point identification of a structural causal model. For finite model and intervention classes, we prove: (i) an exact reduction of the adversarial objective to a worst-intervention integral probability metric; (ii) identification up to interventional equivalence, with point identification under a separating intervention family; (iii) existence of mixed-strategy equilibria; (iv) finite-sample uniform convergence and margin-based model-selection guarantees; and (v) a logarithmic elimination guarantee for a disagreement-driven sequential design under a balanced-separation condition. We also give a complete linear-Gaussian example in which two observationally indistinguishable causal directions are separated by a single well-chosen intervention. The framework clarifies what an adversarial causal discriminator can and cannot certify, and provides a principled bridge between causal generative modeling, active causal discovery, and experimental design.

Mojtaba Eslami

University of Calgary

Structural Causal Models Causal Discovery Causal Identifiability Causal Inference

Aug 5, 2026cs.LG

SVI-DAG: A Structured Variational Inference Approach to Bayesian Causal Discovery

Bayesian causal discovery seeks to determine the posterior distribution of causal theories, which are interpreted as directed acyclic graphs (DAGs) that explain the observed data. The resulting posterior allows systematic reasoning regarding epistemic uncertainty within these theories. Nonetheless, finding such graphs is difficult due to identifiability problems and limited observational data. Furthermore, precisely approximating posterior over graphs is challenging given vast range of potential DAGs. Recent Bayesian approaches have addressed some of these challenges, yet they remain limited as they fail to encode dependencies between edges, and lack principled ways to incorporate domain knowledge as inductive biases during the search process. To overcome these limitations, we propose SVI-DAG, a structured variational inference approach to Bayesian causal discovery using observational data and prior beliefs that uses normalizing flows to model dependencies between edges, supporting expressive and multimodal posterior learning over DAGs. To mitigate mode seeking behaviour in evidence lower bound optimization and promote mode coverage, we use stein variational gradient descent to update the node potentials using a kernel in acyclicity space. We evaluate SVI-DAG against 5 state-of-the-art Bayesian DAG learning methods and demonstrate superior performance in uncertainty quantification while remaining competitive in terms of structural accuracy.

Shrenik Zinage

Massachusetts Institute of Technology · This work was conducted while the author was a PhD student at Purdue University, independently of the author’s dissertation research.

Causal Discovery Variational Inference

Aug 4, 2026cs.LG

GENESIS: Towards Explainable Causal Discovery

Causal Discovery (CD) from observational data faces two fundamental challenges. First, purely statistical methods often lack the power to resolve structural ambiguities in low-sample regimes. Second, although LLM-assisted hybrid approaches improve structure recovery through semantic reasoning, the influence of that reasoning on individual edge decisions remains largely opaque. Consequently, existing hybrid methods fail to satisfy a fundamental requirement: explaining why a particular edge is included or excluded in the learned directed acyclic graph (DAG). This is critical in real-world applications, where no ground-truth DAG exists and every structural decision must be independently justified. We formalize this requirement as decision traceability, requiring every inferred edge to be supported by auditable statistical evidence, Markov Blanket consistency, or explicit domain reasoning. We propose GENESIS, an explainable hybrid CD framework that decomposes graph construction into interpretable decision points. GENESIS first identifies and scores three-node structural motifs, including chains, forks, and colliders, to establish transparent structural priors, then progressively refines the graph by integrating these priors with observational evidence, invoking domain knowledge only when statistical evidence is insufficient. By design, every edge decision is resolved through an auditable source of evidence. Experiments show that GENESIS achieves 100% decision traceability across all settings, establishing explainability as a first-class objective in causal discovery. Despite this additional requirement, GENESIS consistently outperforms purely statistical CD methods on the majority of benchmark datasets across all sample regimes in terms of Structural Hamming Distance (SHD), while achieving performance comparable to state-of-the-art LLM-assisted approaches.

Abhinav Thorat, Ravi Kumar Kolla, Vishak K Bhat +2

User Engagement Research, Sony Research India

Causal Discovery Causal Structure Learning Causal Interpretability

Aug 3, 2026cs.LG

GoT-CD: Graph-of-Thoughts Causal Discovery and the Fragility of Post-hoc Path-Specific Fairness Audits

Causal discovery recovers directed structure from observational data and is increasingly used in clinical settings to support mechanism reasoning and fairness audits of predictive models. Path-specific counterfactual fairness asks whether a protected attribute influences an outcome through illegitimate pathways, but these estimands are defined relative to a supplied causal graph and therefore inherit whatever errors the discovery step introduces. Discovery methods are routinely scored on aggregate structural metrics that weight all edges equally, and no established evaluation asks whether the specific pathway an audit depends on survives discovery---or what the audit reports when that pathway is missing. Here we show that full-graph Graph-of-Thoughts reasoning yields acyclic discovered graphs that are structurally competitive with large language model (LLM) baselines, yet that structural fidelity alone does not guarantee fairness-faithful audits. We introduce GoT-CD, in which the reasoning unit is a complete candidate edge set: multiple graphs are generated in parallel, scored by a deterministic validity function, and merged under a hard union constraint that forbids invented edges, with greedy projection enforcing a DAG before commitment. GoT-CD returns a valid DAG on all five reported benchmarks and achieves the best DAG-valid F1 score among LLM methods on Asia, Alzheimer's, and COVID-Respiratory datasets. On an Alzheimer's benchmark with known unfair path, a post-hoc path-specific audit shows that five of eight discovered graphs recover no path from the sensitive attribute to the outcome and therefore report a null overall effect while mediated effects persist, necessitating downstream path-specific fairness analysis along with structural discovery.

Nitish Nagesh, Elahe Khatibi, Thomas Dean Hughes +3

Department of Computer Science, University of California, Irvine, Irvine, CA, USA · University of Orléans, Orléans, France

Algorithmic Auditing Algorithmic Fairness Counterfactual Fairness Causal Discovery

Jul 31, 2026cs.LG

AutoCause: A Python framework that automates expert decisions in environmental time-series causal discovery

Environmental time-series causal discovery requires expert decisions about method choice, conditional-independence tests, lag horizons, sample-size adequacy, multiple-testing control, and evidence interpretation. Applied inconsistently across datasets, these choices yield graphs that cannot be compared, reproduced, or audited. We present AutoCause, an open-source Python workflow that records each decision, derives defaults from an extended causal-audit module, and admits domain-informed overrides. The workflow wraps four established causal-discovery methods from three families, adds non-causal reference models, and grades links by method-count support. On 145 datasets from DGP-Atlas, TimeGraph, and a topology-derived CausalRivers reference, the methods recover complementary parts of the reference graphs. Majority-supported links are more precise than single-method links on the synthetic benchmarks but not against river topology. AutoCause converts inconsistent expert practice into an auditable, repeatable analysis; causal interpretation remains with the analyst. Available at https://github.com/marcoruizrueda/autocause.

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

ISR-Lisbon, Instituto Superior Técnico, Av. Rovisco Pais 1, Lisbon, 1049-001, Portugal · Digital Scholarship at Oxford, University of Oxford, Oxford, OX1 3BG, United Kingdom · Jet Propulsion Lab., Caltech, Pasadena, CA 91109, California, USA

Time-Series Causal Discovery Causal Discovery Scientific Workflow Automation

Jul 31, 2026cs.CL

Evidence-Type Competition: When Can Interventional Data Teach Language Models Causal Direction?

Interventional data is widely regarded as the gold standard for teaching models causal reasoning. We test this assumption in a fully controlled synthetic environment pitting observational correlation against causal effect, and find it fails instructively. In Simpson's-paradox worlds, where the two have systematically opposite signs, increasing the fraction of interventional samples in pretraining does not improve causal direction: the magnitude of the model's do()-response grows monotonically, yet its sign is copied from the observational context. What governs whether interventional evidence is used is not the training mixture but the evidence type present in the context at inference time. Under an identical training recipe, a purely observational context induces systematic sign reversal in 29/50 worlds, a mixed context in 19/50, while aligned interventional probes alone yield 41/50 correct. Erasing observational evidence from the context immediately releases the suppressed causal interpolation ability (ratio_true = +0.56); a four-state content manipulation shows the switch is content-mediated and graded. The suppression is stable across training seeds (11/11 strong reversals persist on a matched-protocol second seed) and robust as a rate at 0.93B parameters (31.8% vs. 6% reversals in the matched probe-only arm), even as absolute gains shrink four-fold. An external audit on CLadder exposes a learned positive-effect prior with a two-layer structure: sign-randomized retraining removes it in-distribution but not out-of-distribution. We summarize: the capability lives in the weights; the switch lives in the context, and activation patching localizes the switch to the middle layers' observational rows. We further quantify the sampling noise floor of probe-based causal evaluation and an evidence-averaging protocol that cuts sign errors from 26% to 9%.

Xining Xun

Tsingjiao Information Science (Beijing) Co., Ltd.

Causal Discovery Causal Reasoning in Language Models Causal Interpretability Causal Interventions in Language Models

Jul 30, 2026cs.CL

Causal Discovery with Inverted Self-attention for Multivariate Time Series

Causal discovery in multivariate time series data is challenging due to complex interactions, high dimensionality, and nonlinear dependencies among variables. Existing methods often struggle to capture these complexities, resulting in inaccurate causal structures. To address this issue, we propose a novel framework that leverages self-attention mechanisms within the transformer architecture for causal discovery. Our approach introduces a novel inverted causal self-attention mechanism (CSAM) that emphasizes latent and indirect causal relationships by inverting tokens and inducing sparsity in attention scores, focusing on significant causal interactions and reducing spurious correlations. Additionally, we develop a global causal algorithm to identify global causal links, providing a holistic metric for causal influence, along with a causal verification module to ensure robustness in the identified causal relationships, enhancing the reliability of our framework. Experiments on both linear and nonlinear datasets, along with ablation studies and sensitivity analyses, show that our framework outperforms existing methods, demonstrating its potential for causal discovery in complex multivariate time series.

Yusen Liu, Yong Wang, Yifan Yin +3

School of Computer Science, University of Technology Sydney, Sydney, Australia · TianFu YongXing Laboratory, Chengdu, China · Faculty of Data Science, City University of Macau, Macau, China +1

Time-Series Causal Discovery Causal Discovery Time Series Transformers

Jul 29, 2026cs.LG

EvoCause: LLM-Guided Evolution of Causal Graphs for Root Cause Analysis

Modern telecommunication, cloud, and microservice systems emit correlated alarm cascades when components fail. Root cause analysis (RCA) aims to identify the small set of alarms that initiate each cascade. A common approach learns a causal graph from observational logs and predicts all zero-in-degree alarms in each incident-induced subgraph. However, the learned graph remains fixed and cannot benefit from expert diagnoses of historical incidents. We close this loop with EvoCause. Expert labels constrain which alarms should be source nodes but do not specify the edge edits needed to satisfy those constraints. EvoCause uses a large language model (LLM) to propose semantically plausible graph edits, while deterministic code validates node identities and acyclicity and retains the best graph on a labeled alignment set. At test time, the refined graph alone produces transparent predictions without an LLM call. We also release TeleRCA, an expert-annotated benchmark from a production telecommunication network containing

485{,}681

alarm events spanning

194

alarm types over

5{,}621

resources. On synthetic data, EvoCause initialized with the PC causal discovery algorithm outperforms the unrefined PC baseline, raising Node F1, Case EM, and Graph F1 by

11.59

,

9.40

, and

4.59

percentage points, respectively, while reducing nSHD by

0.2379

. On TeleRCA, replacing human-readable alarm titles with anonymous identifiers lowers Node F1 and Case EM by

6.12

and

8.04

percentage points, respectively, indicating that alarm-name information contributes to graph refinement.

Lei Zan, Keli Zhang, Shifeng Xie +7

Huawei Noah’s Ark Lab · Guangdong University of Technology, Peng Cheng Laboratory

Causal Discovery Root Cause Analysis

Jul 27, 2026cs.LG

Causal-TS: A Python Library for Causal Discovery in High-Dimensional and Nonstationary Time Series

We describe Causal-TS, an open-source Python library for causal discovery in high-dimensional and nonstationary multivariate time series. Causal-TS provides four specialized algorithms-CDNOTS, CDNOTS+, CEDAR, and GRACE-along with wrappers for GES, Granger, LASSO-VAR, and LGES, all sharing a unified conditional independence (CI) test layer with GPU acceleration via PyTorch. A regime discovery pipeline detects structural breaks via pluggable changepoint detectors and runs discovery per regime with regime-specific parameters. A command-line interface, synthetic data generators, and optional DoWhy integration provide an end-to-end pipeline from raw time series to causal effect estimates. The library is pip-installable, tested on Python 3.10--3.12, and available at https://github.com/bloomberg/causal-ts.

Mohammad Fesanghary

Bloomberg LP, New York, NY, USA

Time-Series Causal Discovery Causal Discovery Causal Inference Conditional Independence Testing

Jul 24, 2026stat.ML

Amortized Bayesian Causal Discovery of Extended Factor Graphs

Learning causal graphs from interventional data is a challenging problem with broad applications. In molecular biology, for example, a central goal is to uncover gene regulatory networks from large-scale perturbation data. An ideal algorithm for this task should scale to thousands of nodes, incorporate interventions even when their targets are unknown, quantify uncertainty, and provide identifiability guarantees. However, existing approaches---e.g. approaches using score-based optimization or approximate Bayesian inference---often fail to meet all of these criteria. To address these limitations, we develop Amortized Bayesian Causal Discovery of Extended Factor Graphs (ABCDEFG). Our method guarantees exact acyclicity, scales to graphs with thousands of nodes, and naturally handles interventions even when their targets are unknown. Additionally, ABCDEFG estimates a posterior distribution whose maximum a posteriori estimate provably identifies the true causal graph up to an equivalence class. On simulated datasets, ABCDEFG achieves state-of-the-art accuracy, producing a well-calibrated posterior distribution while outperforming previous score-based and approximate Bayesian methods. Applied to large-scale single-cell perturbation data, ABCDEFG identifies both established and novel gene targets of growth factors.

Yichen Gu, Yuxuan Song, Weizhou Qian +2

Department of Electrical and Computer Engineering University of Michigan Ann Arbor, MI 48109, USA · Department of Computational Medicine and Bioinformatics University of Michigan, Ann Arbor Ann Arbor, MI 48109, USA · Department of Statistics University of Michigan, Ann Arbor Ann Arbor, MI 48109, USA +1

Causal Discovery Probabilistic Graphical Models Causal Identifiability Gene Regulatory Network Inference Causal Intervention

Jul 22, 2026cs.LG

CEDAR: Causal Edge Discovery for Autoregressive Processes

We propose CEDAR (Causal Edge Discovery for Autoregressive Processes), a constraint-based method for lagged causal edge discovery in sparse autoregressive time series. CEDAR screens candidate cross-variable lags using AR(1)-residualized, U-centered distance correlation, then applies two targeted conditional-independence tests per significant cross-variable lag candidate and accepts at most one lag per ordered pair. A stable MCI pruning step removes indirect edges, and optional deterministic C-nodes adjust for specified trend-like nonstationarity. In sparse regimes where few lags survive screening, CEDAR requires

O(d^2)

CI tests after screening while retaining edge-level interpretability. CEDAR is most effective when data are scarce and variables exhibit lag-1 self-dynamics; methods with richer conditioning sets become preferable as

T

grows or when higher-order autoregressive or simultaneous multi-lag effects are common.

Mohammad Fesanghary

Bloomberg LP

Time-Series Causal Discovery Causal Discovery Autoregressive Modeling

Jul 22, 2026cs.LG

Local Causal Structure Learning in the Presence of Latent Variables and Selection Bias

Discovering the direct causes and effects of a target variable from observational data is a fundamental problem in causal discovery, with broad applications in domains such as gene regulatory analysis and biomedical research. Existing causal discovery methods either learn a global causal structure, which incurs substantial computational cost, or assume the absence of latent variables and selection bias, assumptions that are often violated in real-world settings. Motivated by these challenges, we study local causal structure learning in the presence of latent variables and selection bias. Specifically, we first characterize a local region that enables target-specific causal discovery without recovering the entire global structure. We then establish a theoretical bridge between causal information learned from the observed distribution induced on this local region and the corresponding information in the global causal structure. Building on these foundations, we propose LoCaLS, a local causal structure learning algorithm that is sound and complete under standard assumptions and identifies the same direct causes and effects of a target variable as those identifiable by global causal discovery methods, while allowing for latent variables and selection bias. Extensive experiments on random and real-world structures demonstrate that the proposed method consistently achieves higher structural accuracy than existing local methods while requiring substantially less computational effort than state-of-the-art global methods. Furthermore, applications to two real-world gene expression datasets reveal biologically plausible target-specific causal structures, demonstrating its practical applicability in large-scale biological data analysis.

Zheng Li, Hao Zhang, Ruxin Wang +3

Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China. · School of Computer Science, Guangdong University of Technology, Guangzhou, China. · Peng Cheng Laboratory, Shenzhen, China. +3

Causal Discovery Causal Structure Learning Causal Discovery with Latent Confounding

Jul 20, 2026cs.LG

Causal Discovery on Irregular Time Series

Causal discovery methods have shown strong performance in temporal systems, but they typically rely on regular and discrete lag structures, limiting their applicability to regularly sampled data. However, many real-world tasks require dealing with irregularly sampled streams of events, such as sensor streams, healthcare data, and financial transactions. In this work, we propose an extension of PCMCI+, a state-of-the-art method for causal discovery on regular multivariate time series, to allow for handling irregular time series. Instead of modelling causal relations through fixed-lag dependencies, our method aggregates causal influence over predefined temporal windows. We evaluate our method on synthetic irregular event streams with known causal structures under different signal-to-noise ratios, showing that it consistently recovers the underlying causal graph and substantially outperforms the standard PCMCI+ on irregularly sampled data.

Martim Penim, Ricardo Ribeiro Pereira, Jacopo Bono +3

1Feedzai, Portugal · 3DCC, Faculdade de Ciêncidas da Universidade do Porto, Portugal · 2Instituto Superior Técnico, Universidade de Lisboa, Portugal +1

Irregular Time-Series Modeling Time-Series Causal Discovery Causal Discovery Causal Structure Learning

Jul 13, 2026stat.ML

Falsifying Causal Graphs With Outlier Events

True causal relationships are rarely known, and inferring causal graphs from data is hard. A fundamental challenge is how to assess whether a given causal graph is good in the absence of a ground truth. We propose falsifying candidate causal graphs based on whether they can explain the propagation of an outlier event. Our approach leverages a key principle: weak outliers rarely cause strong ones. While this principle has previously been used in root cause analysis to identify root causes without prior knowledge of the graph, we turn it on its head and use it to falsify candidate causal graphs whose implied outlier propagation is inconsistent with the data. To this end, we present the first statistical tests for the hypothesis that a candidate graph is the true causal graph, and show they have false positive control, power guarantees against incorrect causal graphs, and can operate with a single outlier sample.

William Roy Orchard, Philipp M. Faller, Dominik Janzing

University of Cambridge, Cambridge, UK · Karlsruhe Institute of Technology, Karlsruhe, Germany · Amazon Research, Tübingen, Germany

Causal Discovery Statistical Hypothesis Testing

Jul 13, 2026cs.LG

Relaxing Faithfulness with Intervention-Only Causal Discovery

Causal discovery algorithms learn a network that describes the causal dependencies among random variables. A common workflow involves first utilizing conditional independence properties on observational data to determine partially directed causal relationships, then applying interventions to orient the unknown causal directions. A critical assumption for the first step is faithfulness: a requirement that causally linked variables exhibit statistical dependence. Many natural systems include buffering and stabilizing pathways that cancel out to achieve systemic robustness. This cancellation of pathways violates faithfulness, leading causal discovery algorithms to incorrectly remove causal dependencies. In this paper, we argue that hard interventions contain information about the presence/absence of causal linkage that is overlooked in the first stage of structure discovery. We show that a mild assumption -- called intervention-immediacy faithfulness -- that allows cancellations, is sufficient to nonparametrically identify causal structures with hard interventions. These results position interventions as the primary carriers of information about causal structure, which should take precedence over conditional independence testing. To flip the paradigm, we also specify equivalence classes when the identification criteria are not met due to limitations in the scope of interventions.

Bijan Mazaheri, Jiaqi Zhang, Caroline Uhler

Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire, USA · Schmidt Center, Broad Institute of MIT and Harvard, Cambridge, Massachusetts, USA · Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

Causal Discovery Causal Identifiability Causal Intervention

Jul 13, 2026cs.LG

DAG-FM: A Foundation Model for Causal Discovery under Heterogeneous Causal Mechanisms

Causal discovery from observational tabular data remains fundamentally challenging, primarily due to the heterogeneity of underlying causal mechanisms and the high-dimensional combinatorial search space of Directed Acyclic Graphs (DAGs). In this paper, we propose \textbf{DAG-FM}, a novel foundation model architecture that amortizes causal discovery. Unlike direct matrix prediction, DAG-FM decomposes the causal discovery process into two auto-regressive stages using two specialized Transformer-based sub-modules: a leaf-node predictor and a parent-node predictor. To effectively model complex row-column interactions, we adopt a robust tabular interaction block to output feature-wise representations. Crucially, to handle diverse and unknown Functional Causal Model (FCM) assumptions in real-world scenarios, we introduce Mixture-of-Leaf-Experts (MoLE), allowing the model to dynamically route and adapt to identifiable mechanism families. Through an iterative inference algorithm, DAG-FM seamlessly extracts causal orderings and constructs valid DAGs. Extensive experiments demonstrate that DAG-FM achieves state-of-the-art performance on both synthetic benchmarks and complex real-world datasets, significantly outperforming traditional classical algorithms and recent foundation models in both accuracy and scalability.

Yikang Chen, Zhengkang Guan, Haoyuan Qian +3

1Zhejiang University · 2Tsinghua University

Causal Foundation Models Tabular Foundation Models Structural Causal Models Causal Discovery

Jul 13, 2026cs.LG

CDFM: Towards a General-Purpose Causal Discovery Foundation Model

Causal discovery, the process of recovering underlying causal structures from observational data, is a fundamental pursuit across scientific disciplines. Over the past decades, numerous algorithms have been developed to tackle this challenge through workflows tailored to the specific causal mechanisms underlying each type of dataset, demonstrating effectiveness across a wide range of applications. However, as the volume and heterogeneity of real-world data continue to grow, this dataset-specific approach inevitably leads to a fragmented, test-driven paradigm that struggles to scale to the demands of modern scientific discovery. To address this, we formulate the Causal Discovery Foundation Model (CDFM) as a unified, general-purpose framework for zero-shot structural inference. To ensure reliable generalization across unknown domains, we first investigate the theoretical boundaries of causal identifiability, revealing the indispensable role of causal prior mechanisms in this process. Building on these insights, we formulate a principled variational framework that treats unknown causal mechanisms as latent variables and mathematically decomposes the intractable marginal likelihood into distinct, tractable learning modules. The variational decomposition provides a conceptual design principle for the architecture design of CDFM, while comprehensive causal knowledge guides the large-scale synthesis of our pretraining data. By pretraining on a massive, highly diverse space of synthetic structural causal models, CDFM successfully internalizes complex statistical asymmetries. Extensive experiments demonstrate that CDFM consistently outperforms traditional algorithms, driving a paradigm shift toward a general-purpose causal discovery foundation model.

Jie Qiao, Ruichu Cai, Zijian Li +6

School of Computer Science, Guangdong University of Technology, Guangzhou, China · College of Mathematics and Computer, Shantou University, Shantou, China · Department of Computer Science and Technology, Tsinghua University, Beijing, China

Causal Foundation Models Causal Discovery

Jul 11, 2026stat.ML

Integrating Background Knowledge for Scalable Causal Discovery

Expert background knowledge is often available in practical applications of causal discovery. Such constraints on the true causal graph can help causal discovery in terms of identifiability of causal effects and accuracy of the learned structure, but also in reducing the space of candidate causal graphs. As causal discovery can become computationally expensive for large number of variables, it is crucial to utilize background knowledge effectively during the causal discovery process. However, most current methods only use background knowledge in a postprocessing step after causal discovery to refine the learned graph. In this work, we develop a framework for utilizing background knowledge during the causal discovery process, focusing especially on scalable causal discovery methods that recover only a subset of the whole graph. We implement our framework for multiple algorithms and empirically show that utilizing background knowledge can both reduce computational requirements and increase the quality of the learned structures.

Mátyás Schubert, Theofanis Aslanidis, Tom Claassen +1

University of Amsterdam · Radboud University Nijmegen · Saarland University

Causal Discovery Causal Structure Learning

Jul 10, 2026cs.AI

How Does Bayesian Causal Discovery Fail? Characterising Structural Consequences in Linear Gaussian Networks under Latent Confounding

Bayesian causal discovery is widely used for its ability to quantify epistemic uncertainty over directed acyclic graphs (DAGs) through posterior inference. However, its behaviour under latent confounding remains poorly understood, as existing work typically notes that confounding breaks identifiability without characterising how the posterior distribution over DAGs responds. In this work, we analyse posterior behaviour under latent confounding in linear Gaussian causal models, focusing on additive latent confounding between exactly two observed variables. We derive a critical correlation threshold above which the score function favours graphs with a spurious edge between the confounded variables, and show that this threshold decreases with sample size -- more data lowers the correlation required for the spurious edge to be favoured. Beyond this threshold, we characterize two distinct posterior failure regimes determined by the local structure around the confounded variables. Our findings are supported by exact posterior computations on multiple graph structures, demonstrating both the predicted failure regimes.

Debargha Ghosh, Silja Renooij, Anna V. Kononova

Department of Information and Computing Sciences, Utrecht University · Leiden Institute of Advanced Computer Science, Leiden University

Structural Causal Models Bayesian Networks Causal Discovery Causal Discovery with Latent Confounding

Jul 10, 2026cs.CL

DKCD: Domain Knowledge-Enhanced Causal Discovery from Unstructured Data

Causal discovery from unstructured data is a challenging yet underexplored task in high-expertise domains such as healthcare, finance, and education. Existing methods typically leverage the general knowledge of large language models (LLMs) to identify causal factors from unstructured data and annotate them into structured data for causal graph construction. However, they remain limited by two key challenges (CHs): (CH1) insufficient identification of latent factors, which are implicit in the data yet essential for causal discovery, due to the lack of domain-specific knowledge; and (CH2) unreliable factor annotation, caused by the lack of domain-grounded reasoning, which propagates errors to the resulting causal graphs. To address these challenges, we introduce a novel Domain Knowledge-enhanced Causal Discovery framework (DKCD) for causal discovery from unstructured data in high-expertise domains with three interconnected components: (1) Knowledge Mining: It retrieves relevant domain knowledge based on observable factors to support subsequent causal reasoning. (2) Knowledge-guided Causal Reasoning: Reasoning with relevant knowledge, it discovers latent causal factors to address CH1 and generates key causal clues for more accurate data annotation to address CH2. (3) Causal Structure Discovery: It constructs the final causal graphs based on a more complete factor set and accurate annotations. Experiments on two domain-specific datasets show that DKCD significantly improves both causal factor identification and causal graph construction.

Xin Li, Jin Li, Shoujin Wang +2

University of Technology Sydney · Sydney, NSW, Australia

Causal Discovery Causal Structure Learning Causal Reasoning

Jul 7, 2026cs.LG

Learning Sparsest Linear Causal DAGs with Latent Confounders via Higher-Order Cumulants

Recovering the exact directed acyclic graph (DAG) in linear non-Gaussian acyclic models with latent confounders (LvLiNGAM) remains a challenging problem. Although LvLiNGAM is identifiable only up to an observational equivalence class, each equivalence class is characterized by a unique sparsest DAG. Recovering the sparsest DAG from finite samples, however, remains difficult. Although existing methods are asymptotically consistent, they do not provide an explicit finite-sample procedure for recovering the unique sparsest DAG, nor do they handle models with an arbitrary number of latent confounders. In this paper, we propose a finite-sample method for recovering the sparsest DAG without imposing any restriction on the number of latent confounders. Simulation studies and real-data analyses demonstrate that the proposed method achieves superior finite-sample performance compared with existing approaches.

Ming Cai, Hisayuki Hara

Graduate School of Informatics, Kyoto University, Kyoto, Japan · Institute for Liberal Arts and Sciences, Kyoto University, Kyoto, Japan

Structural Causal Models Causal Discovery Causal Discovery with Latent Confounding

Jul 5, 2026stat.ML

Causal ASCEND: Scalable Two-tier Causal Discovery on High Dimensional Multi-omics Data

Biological systems exhibit a hierarchical structure, characterised by directed flow from upstream regulators to downstream effects. Although this ordering provides a natural scaffold for causal inference, most causal discovery and GRN methods either ignore the tiered organisation or condition on all upstream variables, which becomes infeasible for high-dimensional omics data. We present ASCEND (Ancestral Scalable Causal discovEry via iNherited Descent), a constraint-based framework that leverages known two-tiered structure to enable genome-scale causal discovery. ASCEND introduces a divide-and-conquer strategy that maintains dynamically updated ancestral conditioning sets for each downstream variable, dramatically reducing the number of conditional independence tests required, and achieves polynomial-time complexity where traditional approaches face exponential blow-up. Through extensive simulations and real biological data, we demonstrate that ASCEND accurately recovers ancestral relationships, scales properly and much faster, and outperforms existing gene regulatory network inference methods in both causal precision and computational efficiency. The algorithm's ability to resolve directionality makes it particularly suited for integrating multi-omic data where upstream regulators (e.g., SNPs, methylation sites) and downstream responses (e.g., gene expression) are measured jointly.

Stephen Asiedu, David Watson

Department of Informatics, King’s College London, Bush House, 30 Aldwych, WC2B 4BG, London, United Kingdom

Causal Discovery Gene Regulatory Network Inference Genomics

Jul 5, 2026cs.LG

Knowledge-Informed Local Causal Discovery of Optimal Adjustment Sets

Local causal discovery is a scalable alternative to global structure learning. However, it can struggle to identify valid adjustment sets in data-scarce settings because of finite-sample uncertainty, incomplete local neighborhoods, and unresolved Markov equivalence. Although many application domains provide structured background knowledge, its integration into local causal discovery remains limited. We propose b-LOAD, a knowledge-informed extension of the LOAD algorithm for local discovery of optimal adjustment sets. b-LOAD incorporates prior edge constraints directly into the local structure-learning procedure and uses Meek's rules to expand the discovery frontier dynamically, yielding a knowledge-constrained partially directed graph over the relevant local subgraph. This strategy helps prevent structurally relevant nodes introduced by prior knowledge from being excluded by local search. We prove that, under sound background knowledge, the procedure monotonically refines the admissible equivalence class and can enlarge the set of identifiable causal queries, enabling recovery of optimal adjustment sets that are not identifiable from observational conditional-independence information alone. Empirically, b-LOAD improves downstream causal effect estimation relative to purely data-driven and standard knowledge-augmented baselines, particularly in data-scarce and structurally complex regimes. Results on real-world biological networks show that locally targeted prior knowledge provides the largest gains and remains beneficial under moderate structural noise. These findings position b-LOAD as a scalable approach for converting fragmented domain knowledge into more reliable causal-effect estimation.

Seong Woo Ahn, Alessandro Leite, José Lucas De Melo Costa +3

Laboratoire Interdisciplinaire des Sciences du Numérique, Université Paris-Saclay, CNRS, CentraleSupélec, France · LITIS UR 4108, INSA Rouen Normandy, University of Rouen Normandy, France

Causal Effect Estimation Causal Discovery Causal Identifiability

Jul 5, 2026cs.LG

MDL Meets Latent Confounders: LNML-based Causal Discovery

Causal discovery with nonlinear mechanisms and latent confounders remains challenging. Existing methods often rely on either linear assumptions or causal sufficiency, limiting their applicability. We propose an MDL-based causal discovery framework that explicitly accounts for latent confounders while allowing flexible nonlinear mechanisms by minimizing the luckiness normalized maximum likelihood (LNML) code-length. The causal relationship between each variable pair is determined by selecting the shortest code-length of the causal model, and we introduce the notion of

Δ

-pseudo-collinearity to identify dependencies induced by latent confounders. Based on these ideas, we develop a greedy algorithm, termed Pseudo-Collinearity Guided Causal Discovery (PCG-CD). Experiments on synthetic and real-world datasets demonstrate that the proposed method accurately recovers directed causal relationships and effectively detects latent confounders.

Zhongyi Que, Shin Matsushima, Kenji Yamanishi

Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, Japan · Graduate School of Arts and Sciences, The University of Tokyo, Tokyo, Japan

Minimum Description Length Causal Discovery Causal Discovery with Latent Confounding

Jul 4, 2026cs.LG

Order-based Causal Discovery for Multistage Processes

Causality has become an increasingly important tool for gaining a deeper understanding of complex systems. Among various causal analysis methods, causal discovery, which identifies causal relationships among variables from data, has been widely used to uncover underlying causality in diverse processes. However, while multistage processes are prevalent in many fields, existing causal discovery methods may produce counterintuitive results, given the known process knowledge, and may not be computationally efficient for handling large datasets typical of multistage processes. To address this gap, we propose a novel causal discovery method called Order-based Causal Discovery for Multistage Processes (OCDM). OCDM is designed to infer the causal structure of multistage data while preserving their inherent hierarchical and sequential structure by explicitly incorporating process knowledge into the causal discovery process. Specifically, we propose a structural knowledge-informed order-inferring algorithm that infers the causal order of variables by incorporating information about the stage from which each variable originates, based on an order-based causal discovery framework naturally suited for inherently ordered multistage data. Furthermore, to eliminate spurious edges from the initial causal graph generated based on the inferred causal order, we introduce a novel pruning technique using stochastic gated neural networks, which offers greater computational efficiency compared to existing methods. Through experiments on various datasets, we demonstrate that OCDM effectively infers the causal structure of multistage processes, outperforming existing methods.

Eun-Yeol Ma, Junsub Jung, Heeyoung Kim

Department of Industrial and Systems Engineering, Korea Advanced Institute of Science and Technology, Daejeon 34141, South Korea

Causal Discovery

Jul 3, 2026cs.LG

Statistically Meaningful Geometry and Gauge Symmetry Breaking: A Geometric Foundation for Scientific Discovery and Intelligence Emergence

The rapid scaling of over-parameterized machine learning architectures, particularly LLMs, raises a profound crisis: do these systems exhibit genuine intelligence, or are they merely sophisticated statistical pattern matchers? Classical flat Euclidean statistics cannot differentiate continuous interpolation from the autonomous discovery of novel causal laws. To resolve this, we introduce Statistically Meaningful Geometry (SMG), a framework modeling over-parameterized learning systems as infinite-dimensional non-parametric Orlicz fiber bundles. We prove that under persistent out-of-distribution (OOD) stimuli governed by unmodeled causal mechanisms, continuous optimization fails. Unmodeled variance is rejected by the visible horizontal base manifold, leaking into the unobservable vertical fiber space and generating an accumulation of Active Acausal Tension. Driven by the statistical manifold's non-linear curvature, this tension inevitably strikes a conjugate focal boundary (

T_{\text{crit}} = π^2 / K_{\text{max}}

), triggering localized volumetric collapse and a catastrophic matrix singularity (

[G_f]^{-1} \to \infty

). We demonstrate this geometric breakdown acts as the strict non-equilibrium trigger for a Gauge Symmetry Break (GSB). The system purges hidden tension from unobservable gauge redundancies, spontaneously crystallizing a new, mathematically independent horizontal coordinate axis. This non-parametric phase transition registers as a discrete

+1.0

integer step-jump in observable Structural G-Entropy. By decoupling parameter charts and subjecting emergent axes to a Minimal Energy Path Criterion and a Causal Invariance Filter, we distinguish genuine discovery from malignant hallucinations. Ultimately, SMG provides a parameter-free, falsifiable dashboard to mathematically certify true intelligence, transforming AI for Science into an engine of autonomous paradigm shifts.

Bing Cheng, Yi-Shuai Niu, Howell Tong +1

Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China · Beijing Institute of Mathematical Sciences and Applications (BIMSA), Beijing, China · Department of Statistics, London School of Economics and Political Science, London WC2A 2AE, UK +3

AI for Science Causal Discovery Autonomous Scientific Discovery Statistical Learning Theory

Jul 2, 2026cs.MA

CausalSteward: An Agentic Divide-Conquer-Combine Copilot for Causal Discovery

Learning causal models from high-dimensional data is a significant challenge, particularly in real-world settings where violations of core assumptions lead to causal identifiability issues. Although massive amounts of prior knowledge are available, and contain valuable causal information, effectively integrating this knowledge into the causal discovery process remains an open problem. We introduce CausalSTeward (CAST), a novel human-in-the-loop framework for interactively assembling large causal models. CausalSteward is a multi-agent collaborative system that tackles high-dimensional causality through a divide-and-conquer approach where large clusters of variables are iteratively partitioned and then separately analyzed. Our framework fuses prior knowledge with a data-driven approach by using tailored tools such as retrieval augmented generation and conditional independence tests. Finally, we use this work to examine the capabilities and limitations of causal reasoning in multi-agent frameworks, and how the human-in-the-loop can contribute to accurate and trustworthy results.

Nicholas Tagliapietra, Gian Lorenzo Marchioni, Moritz Willig +3

1 : Computer Science Department, TU Darmstadt, Germany · 2 : Bosch Center for Artificial Intelligence, Renningen, Germany · 5 : LUISS University, Rome, Italy +2

Causal Discovery Multi-Agent Collaboration Human-in-the-Loop AI Multi-Agent Reasoning

Jun 27, 2026eess.IV

A Neuroimaging Simulation Framework for Developing and Evaluating Causal AI

Causally linking disease-related factors to image-derived biomarkers provides a powerful pathway to understanding disease mechanisms. Despite growing interest in applying causal artificial intelligence (AI) approaches for this task, these methods still need to be adapted for complex medical images, and especially, neuroimaging. However, the lack of ground-truth data presents a barrier to development. To bridge this gap, we developed and tested a method for generating synthetic neuroimages, which adhere to a user-specified causal structure describing the non-image to image variable relationships, permitting the creation of ground-truth neuroimaging datasets. In the simulated T1-weighted magnetic resonance images, anatomical variability is modeled by sampling from a subspace estimated from real data and deforming a template image to create unique simulated subjects. Causal relationships are encoded via precise volumetric changes of any region-of-interest without unwanted global artifacts. We achieved relative volume errors of 0.3-2.66% for the targeted regions-of-interest and demonstrate their statistically significant causal relationships, while maintaining mean absolute errors for non-target brain regions between 0.034-0.397ml. An initial evaluation of causal discovery methods exposes their limited ability to suppress spurious connections, highlighting the need for image-appropriate methods. Our framework is the first to enable the generation of realistic synthetic 3D neuroimages with explicit causal control that can serve as the missing ground-truth data necessary for the objective benchmarking and development of causal AI methods.

Eryn Libert-Scott, Emma A. M. Stanley, Vibujithan Vigneshwaran +3

Biomedical Engineering Graduate Program, University of Calgary, Calgary, AB, Canada · Department of Radiology, the Hotchkiss Brain Institute, the Alberta Children’s Hospital Research Institute, and Department of Clinical Neuroscience, all at the University of Calgary, Calgary, Alberta, Canada · Department of Computing, Imperial College London, London, U.K. +1

Image Generation Causal Discovery Medical Image Synthesis Neuroimaging Medical Image Benchmarks

Jun 23, 2026cs.CV

RetiSEM: Generalising Causal Models for Fragmented Biomedical Data

Learning causal models from fragmented biomedical data is challenging because clinical, molecular, and imaging variables are often incomplete or not jointly observed. We propose RetiSEM, a domain-constrained structural equation modelling (SEM) framework for causal graph recovery and mediation analysis under limited multimodal resources. This proposed work organises variables into biologically informed blocks, applies forbidden-edge constraints, and decomposes pathway-level effects into TE, NDE, and NIE components. We evaluate RetiSEM across ten synthetic benchmark scenarios that vary in dimensionality, nonlinearity, causal depth, and pathway structure, together with a fragmented real-world setting that combines NHANES clinical variables with externally derived retinal representations. This approach achieves lower structural error and higher causal accuracy than unconstrained baselines across the synthetic benchmarks. In the real-data analysis, retinal variables behave mainly as downstream biomarker-like indicators, with smaller but detectable indirect effects. These findings support our strategy as an interpretable framework for testing structured causal hypotheses in limited-resource biomedical AI. The code and resources for this work are publicly available at: https://github.com/Inamullah-Colab/ReitSEM.

Inam Ullah, Imran Razzak, Shoaib Jameel

University of Southampton, Southampton, SO18 1PB, Hampshir, United Kingdom · Mohamed bin Zayed University of Artificial Intelligence, United Arab Emirates

Latent Variable Models Structural Causal Models Causal Mediation Analysis Causal Discovery Causal Inference

Jun 22, 2026cs.LG

GRACE: Gated Refinement for Accurate Causal Edge Discovery in High-Dimensional Time Series

From climate teleconnections to gene regulation, modern time-series datasets encompass tens or hundreds of interacting variables, making causal discovery increasingly challenging. Constraint-based methods offer statistical rigor but their nonlinear CI tests are infeasible at scale, while score-based alternatives avoid CI testing but require arbitrary thresholds to binarize continuous edge scores. We propose GRACE (

\textbf{G}

ated

\textbf{R}

efinement for

\textbf{A}

ccurate

\textbf{C}

ausal

\textbf{E}

dge discovery), which refines constraint-based discovery using Hard Concrete gates with

L_0

regularization: each candidate edge has an independent gate whose values concentrate near 0 or 1, yielding a clean bimodal separation that makes the binary decision robust, unlike the narrow, overlapping score distributions produced by

L_1

and attention-based methods. A fast linear CI skeleton provides high-recall candidates; a single gated model then prunes false positives by learning which edges genuinely improve prediction, with automatic regularization adapted to problem dimensions and skeleton density. Systematic experiments on synthetic benchmarks, spanning diverse graph topologies (scale-free, Erdős-R'enyi, small-world) and dimensionalities up to

d=100

, show that GRACE substantially improves F1 over its base CI method while maintaining high precision, and outperforms attention-based and score-based alternatives. GRACE matches or exceeds expensive nonlinear CI tests at a fraction of the cost (

75\times

faster). On a real-world river flow dataset, where rainfall confounders, variable propagation lags, and distributional shifts violate standard assumptions, a temporal bootstrap variant of GRACE recovers 9 of 11 causal edges along the Elbe River with only 1 false positive (

F_1 = 0.86

, AUROC

{} = 0.99

), reducing the skeleton's 106 false positives by 99%.

Mohammad Fesanghary, Abhinav Havaldar

Time-Series Causal Discovery Causal Discovery Causal Inference