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

Oct 8, 2026stat.ML

Score-Based Learning of Cluster DAGs from Interventions

Graphical approaches to causal abstraction transform a low-level causal directed acyclic graph (DAG) over many measured variables into a smaller, high-level DAG whose nodes cluster the original variables and whose edges summarize the causal relations between clusters. Such cluster DAGs are easier to interpret, but learning them requires finding the clusters and recovering the edges between them. Madaleno et al. (2026) learn the interventional coarsening (the cluster DAG that merges variables the interventions cannot distinguish) in two constraint-based phases: first the clusters, then the edges. We introduce COARSE, the first score-based method for this task: it keeps the two-phase structure but, under linear Gaussian assumptions, swaps the constraint-based edge phase for a score-based one. We show that the interventions themselves identify a causal order over the clusters, and learning the edges reduces to a single local search per cluster under a cluster-level BIC score. We prove that the procedure runs in polynomial time and, provided the variables affected by each intervention are correctly identified, that it is consistent. On synthetic and real-world interventional data, COARSE matches state-of-the-art edge recovery given enough samples, with an edge phase up to two orders of magnitude faster, including on dense graphs with hundreds of nodes.

Gaetano Tedesco, Alex Markham

Informatics Institute, University of Amsterdam · Department of Mathematical Sciences, University of Copenhagen

Causal Structure Learning Causal Discovery Causal Abstraction Graph Coarsening Causal Intervention

Oct 7, 2026cs.LG

AdaPS-LiNGAM: Adaptive Predecessor Selection for Linear Non-Gaussian Acyclic Models under Small-Sample Settings

Causal discovery becomes particularly challenging when the available sample size is small relative to the number of variables. This challenge also arises in the linear non-Gaussian acyclic model (LiNGAM), an identifiable framework for causal discovery from observational data. DirectLiNGAM estimates a causal order, which arranges variables so that causes precede their effects, by sequentially identifying an exogenous variable and removing its linear effect from the remaining variables. We establish a structural limitation of this procedure: when the number of variables exceeds the sample size, repeated residualization necessarily becomes degenerate before the full causal order can be determined. Our analysis further reveals that each residual can be reconstructed using only a graph-determined subset of variables already placed earlier in the causal order, termed the active boundary. This result motivates AdaPS-LiNGAM (Adaptive Predecessor Selection LiNGAM), which reconstructs each residual directly from the original observations using an adaptively chosen sparse subset of those earlier variables. The same subset-selection principle is also applied to the final pruning step for edge estimation. Experiments on synthetic data demonstrate that AdaPS-LiNGAM provides accurate causal-structure recovery in sample-limited settings and degrades more gradually as the sample size decreases.

Shun Yanashima, Kentaro Kanamori, Hirofumi Suzuki

Artiﬁcial Intelligence Laboratory, Fujitsu Limited, 4-1-1 Kamikodanaka, Nakahara-ku, Kawasaki, 211-8588, Kanagawa, Japan.

Causal Discovery Causal Structure Learning Structural Causal Models

Oct 7, 2026cs.AI

DrugTargetWorld: A Synthetic Biobank for Training and Benchmarking AI Scientists

Drug target discovery requires distinguishing molecules that causally drive disease from those that are merely associated with it. Training and evaluating AI agents to perform this workflow end-to-end is difficult because real world biobanks lack known causal ground truth and participant-level data is access controlled. We introduce DrugTargetWorld, a framework that procedurally generates simulated biobanks, or "worlds," with known but concealed causal structure. Each world contains genotypes, proteins, health records, outcomes, and synthetic magnetic resonance imaging (MRI) for 54,000 participants. Agents must construct a disease phenotype, identify causal driver proteins, infer the beneficial direction of modulation, and optionally conduct virtual 'wet lab' experiments. We evaluated nine agents in 540 episodes across 20 cardiovascular worlds and three experimental budgets. Opus 5 and GPT-5.6 Sol achieved the highest mean composite scores, 39.98 and 35.38 of 100, respectively, and both recovered 64% of causal drivers on average. However, no agent reliably distinguished misleading non-causal proteins, and performance remained limited by the integrative judgments required to connect phenotype construction, causal evidence, and intervention decisions. By making each world's causal structure known to the evaluator but hidden from the agent, DrugTargetWorld turns end-to-end drug target discovery into a scalable training and evaluation problem with verifiable reward.

Samuel Margolis, Paul Schmiedmayer, Alan Huang +12

Department of Biomedical Data Science, Stanford University, Stanford, CA 94305, USA · Department of Medicine, Stanford University, Stanford, CA 94305, USA · Division of Computational Medicine, Department of Medicine, Stanford University, Stanford, CA 94305, USA +1

Drug Discovery AI Agent Benchmarks Synthetic Benchmark Generation Causal Discovery Synthetic Data Generation

Oct 6, 2026cs.LG

Directional Evidence Guided Search-Space Reduction for Exact DAG Learning

Learning a directed acyclic graph (DAG) from observational data is a challenging combinatorial problem due to the exponential growth in the number of candidate parent-set configurations. Existing exact score-based methods often require computationally intensive combinatorial search, whereas constraint-based methods can become unreliable or computationally demanding as graph size and conditioning-set complexity increase. We develop a non-parametric hybrid framework, referred to as DECO (Directional Evidence-guided Configuration Optimization), that extracts dependency and directional evidence from observation data to construct admissible parent sets prior to exact optimization. It reduces the optimization search space by eliminating empirically unsupported parent configurations while preserving flexibility for all plausible edge orientations. Theoretical analysis establishes an exponential reduction in the admissible parent-set configuration space and quantifies how bounded edge-level omission affects the probability of retaining the true parent structure. Experiments on benchmark Bayesian networks and synthetic discrete and continuous DAGs demonstrate substantial search-space reduction while achieving competitive structure-recovery performance, with favorable structural Hamming distance across many evaluated settings. These results show that directional evidence can provide an effective preprocessing mechanism for reducing the computational burden of exact DAG learning without requiring a fixed parametric structural~model.

Upala Junaida Islam, Abdelmonem Elrefaey, Rong Pan

School of Computing and Augmented Intelligence, Arizona State University, Tempe, AZ 85281, USA.

Causal Discovery Causal Structure Learning Bayesian Networks

Oct 5, 2026cs.LG

GO-Based Clustering for Learning Cluster-Level Causal Gene Regulatory Networks

Discovery of causal relationships in high-dimensional Gene Regulatory Networks (GRN) is computationally challenging and often difficult to interpret due to dense connections. Therefore, grouping genes together into functional modules can improve tractability and biological interpretability. However, existing cluster level causal discovery methods assume access to a predefined admissible partitions, requiring the graph over clusters to be acyclic. Constructing such partitions is therefore challenging. In this work, we introduce GO-based Clustering for Causal Discovery (GO4CD), an algorithm that uses Gene Ontology (GO) to construct biologically meaningful gene partitions at multiple levels of granularity, while favoring those more likely to be admissible for causal discovery. GO4CD groups together genes participating in a shared biological process, and propagates gene annotations through the ontology hierarchy to achieve different granularity of partitions. Furthermore, we integrate GO4CD with Causal Learning over Clusters (CLOC) algorithm and evaluate recovery of true Markov equivalence class both with an oracle of conditional independencies and on simulated gene expression data using multivariate conditional independence tests. We evaluate GO4CD on multiple E.coli regulatory subnetworks and find that it is inadmissible in 18.1% of the cases, compared with 65.3-82.3% for the semantic-similarity baselines. Our results indicate that GO4CD is substantially better suited to learning causal GRNs defined over biologically meaningful gene clusters.

Azlaan Mustafa Samad, Wei Zhang, Adèle H Ribeiro

L3S Research Center, Leibniz University Hannover, Lower Saxony Center for Artificial Intelligence and Causal Methods in Medicine (CAIMed), Hannover, Germany · Institute for Causal and Explainable Artificial Intelligence in Life Sciences, Center for Computational Life Sciences, RWTH Aachen University, Germany

Clustering Causal Discovery Causal Structure Learning Gene Regulatory Network Inference

Sep 30, 2026cs.AI

Inferring Causal Relations between Two Sequences of Events with Language Models

Causal AI is a branch of Artificial Intelligence which helps understand and reason about cause and effect relationships, not just patterns or correlations. Causal discovery aims to infer elements of the underlying causal structure--often represented as a directed graph--from observational and, when available, interventional data. While causal discovery is the fundamental step for moving beyond mere associations toward genuine understanding, and thus the basic building block of causal AI, it becomes intrinsically difficult when causal relations must be inferred from single observations. In such situations, standard causal discovery methods cannot be used and one has to identify causal relations from limited amount of information. This is typically the case for, e.g., sequences of events produced by different alarms which need to be analyzed on the fly to detect abnormal phenomena, which are usually rare. We show in this study that it is possible to leverage the predictive power of Large Language Models (LLMs) to infer causal relations between only two sequences of events. This approach, which is validated on both synthetic and real data, provides better results than standard causal discovery algorithms on several time series data, even though these data were converted into smaller, single observed sequences.

Nishchal Prasad, Eric Gaussier, Emilie Devijver +3

INRIA, Univ. Grenoble Alpes, CNRS, LIG · Univ. Grenoble Alpes, CNRS, Grenoble INP, LIG · Univ. Grenoble Alpes, CNRS, Inria, Grenoble INP, LIG +1

Time-Series Causal Discovery Causal Discovery Causal Reasoning in Language Models

Sep 30, 2026stat.ML

Discrete Score Matching Enables Causal Discovery from Count Data

Count data pose a challenge for score-matching-based causal discovery: derivatives are unavailable, and simply replacing them with finite differences does not generally suffice for causal discovery. We generalize SCORE's constant-curvature criterion (Rolland et al., 2022) by conditioning on the node's value, yielding the conditional curvature score (CCS) for ordering. We also extend curvature-based parent recovery through the off-diagonal curvature score (OCS), enabling directed acyclic graph (DAG) recovery with both scores constructed from score functions for continuous data and concrete scores for counts. In the bivariate setting, zero CCS exactly characterizes a semiparametric generalized linear model (GLM) conditional form in which the conditional family need not be specified in advance, unlike in classical GLMs. For bivariate semiparametric GLM DAGs under our regularity condition, canonical-parameter nonlinearity is necessary and sufficient for identifiability. In multivariate DAGs, this nonlinearity enables DAG recovery through CCS and OCS. Our framework identifies a new class of semiparametric GLM DAGs that strictly contains the nonlinear Gaussian ANM class identified by SCORE. We introduce DISCO (DIscrete SCOre), a count-DAG recovery algorithm that estimates CCS and OCS using discrete diffusion. Experiments demonstrate accurate DAG recovery across Poisson, negative binomial, binomial, and mixed-family settings, as well as scalability to 1,000-node DAGs on a single GPU.

Euijong Song, Hyewon Park, Gunwoong Park

Department of Statistics Seoul National University, Korea · Interdisciplinary Program in Artificial Intelligence; Institute for Data Innovation in Science, Seoul National University, Korea

Score Matching Causal Discovery Causal Identifiability Generalized Linear Models

Sep 29, 2026cs.LG

Differentiable Structure Learning for Cyclic Linear Gaussian Models with Latent Confounders

We study causal structure learning from observational data in linear Gaussian structural causal models in the presence of directed cycles and an unknown number of exogenous latent confounders, bounded by a given maximum. We derive the covariance of the observed variables and introduce marginal quasi-equivalence, which characterizes when different causal models share a full-dimensional subset of the observational distributions they can generate. We formulate structure learning as minimization of the Gaussian negative log-likelihood with a logarithmically scaled complexity penalty that counts directed edges and latent variables. For a fixed number of observed variables and a fixed upper bound on latent variables, we establish consistency of global score minimizers up to marginal quasi-equivalence under algebraic faithfulness, structural minimality, and model-overlap assumptions. We parameterize the inclusion of directed edges and candidate latent variables using Bernoulli gates, whose continuous probabilities are optimized jointly with the structural coefficients. Averaging the penalized negative log-likelihood over these gates yields an objective with a closed-form differentiable complexity penalty. We prove that this expected objective has the same global infimum as the corresponding discrete structure-learning objective. Experimental results show that our approach achieves lower recovery error than previous methods in several experimental settings.

Sadegh Khorasani, Ali Najar, Saber Salehkaleybar +1

School of Computer and Communication Sciences, EPFL, Lausanne, Switzerland · Leiden Institute of Advanced Computer Science (LIACS), Leiden University, Leiden, The Netherlands · College of Management of Technology, EPFL, Lausanne, Switzerland

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

Sep 29, 2026cs.AI

Demistifying Data and Simulator Assumptions in Supervised Causal Discovery

Supervised causal discovery learns to infer causal structure for a new dataset from training datasets paired with structural labels. These training pairs are typically simulated, making the simulator both a source of supervision and a carrier of assumptions about causal graphs, mechanisms, and noise. Understanding the resulting predictions therefore requires examining how these assumptions supplement the information available in observational data, which may be compatible with multiple causal graphs. This paper examines that relationship across representative methods available through June 2026. We organize these methods by prediction target, prediction granularity, encoder, structural decoder, and training regime to relate what each method predicts to how it uses data and simulator-based supervision. Using this framework, we distinguish two questions: whether the target is identifiable under the assumed model class, and whether a trained predictor generalizes beyond its training distribution. Restrictions on mechanisms and noise can make otherwise ambiguous causal directions identifiable, but predictive accuracy under those restrictions does not establish transfer when they change. This distinction motivates evaluation that matches metrics to the identifiable graph target and tests changes in graphs, mechanisms, and noise between training and deployment. Extending such evaluation to real data also requires documenting the external causal evidence and uncertainty behind benchmark reference graphs. Together, these analyses guide method comparison and identify open questions in transfer, test-time adaptation, and uncertainty assessment.

Pingchuan Ma, Rui Ding, Bojun Huang +1

Zhejiang University of Technology, China · Microsoft Research Asia · Sony Research +1

Causal Discovery Causal Structure Learning Causal Identifiability Cross-Dataset Generalization

Sep 28, 2026cs.AI

DoAtlas-2: A Foundation for Self-Evolving Causal Biomedical Discovery

We introduce DoAtlas-2, a foundation for self-evolving causal biomedical discovery that organizes knowledge around causal mechanisms and advances through external evidence from human populations. DoAtlas-2 integrates 771 research resources covering more than 720,000 participants in 48 countries, from longitudinal clinical phenotypes, medical imaging, and continuous physiological signals to eight molecular layers, together with an evidence network of approximately 4.7 million literature-derived records over 93,566 concepts and 149,383 candidate causal relations. DoAtlas-2 autonomously formulates research questions from evidence gaps and unresolved mechanisms, prespecifies their causal designs, and generates validated analyses. Supporting, challenging, and unresolved results continuously revise mechanistic interpretations, the causal evidence state, and the discovery frontier, so that DoAtlas-2 self-evolves within a closed loop of hypothesis generation, empirical testing, and renewed discovery. DoAtlas-2 has systematically evaluated 2,031 research questions. In the Human Phenotype Project (HPP), it formulated 4,014 candidate pathway questions across vascular, early-glycemic, and hepatic-metabolic systems, and screening of the first 1,079 yielded statistical support for 756. Representative studies identify blood pressure as a convergence node linking adiposity, hepatic, and lipid phenotypes to vascular outcomes, and show that an adiposity-inflammation-blood-pressure pathway is largely attenuated by joint adjustment for body mass index (BMI) and smoking. The discovered vascular network constitutes a completely interpretable predictive foundation, admitting exact attribution of every prediction and closed-form mediation effects. DoAtlas-2 thereby unifies causal mechanism discovery, population-evidence testing, and interpretable prediction within one continuously evolving foundation.

Yulong Li, Rong Xia, Yuxuan Zhang +12

MBZUAI

Causal Discovery Causal Attribution Autonomous Scientific Discovery Biomedical KGs

Sep 28, 2026stat.ME

Forecast-Necessary Causal Discovery for Nonlinear Political Panel Data: Feedback, Functional Form, and the Dynamics of Democratization

A non-significant coefficient in a dynamic panel model need not imply the absence of a relationship. It may instead reflect heterogeneous effects averaged toward zero, reciprocal dynamics overlooked by a recursive specification, or relationships masked by the omission of correlated covariates. Standard linear estimators cannot distinguish among these possibilities. We develop an inferential workflow for political panel data that resolves this ambiguity by combining flexible autoregressive estimation, forecast-necessity testing, functional characterization, and same-data linear benchmarking. The workflow first identifies relationships required for out-of-sample prediction, then characterizes their functional form across political contexts, and finally, distinguishes differences arising from estimator flexibility from those due to model specification. Applied to the causal sequence model of democratization on the V-Dem panel of 113 countries, the workflow reproduces the model's central finding - the protective belt of civil society, the rule of law, and institutionalized parties - while recovering reciprocal relationships from democracy to its institutional supports that a linear model cannot detect. Most importantly, three weak published direct effects, of which two are null, and one is marginally significant, receive three different diagnoses: one dissolves under the full specification, one reflects heterogeneous effects averaged toward zero, and one was masked by the reduced variable set. The workflow corrects the published record in both directions, removing one relationship and recovering two. More broadly, the workflow provides a framework for evaluating dynamic political theories under a model class capable of representing nonlinear and reciprocal mechanisms while preserving relationship-level interpretation and explicit inferential standards.

Michael Coppedge, Dmitry Zaytsev, Valentina Kuskova

Department of Political Science, University of Notre Dame, Notre Dame, IN, USA · Kellogg Institute, University of Notre Dame, Notre Dame, IN, USA · Lucy Family Institute for Data & Society, University of Notre Dame, Notre Dame, IN, USA

Time-Series Causal Discovery Causal Discovery Causal Structure Learning

Sep 28, 2026stat.ML

The Statistical Cost of Causal Discovery with Feedback

What determines the unavoidable sample cost of learning cyclic causal structure? For cyclic linear non-Gaussian models, we study exact condensation recovery from observational data: identifying the strongly connected component (SCC) partition and all edges between components. We establish the first information-theoretic lower bounds on sample complexity for this target. For

p

variables, maximum SCC size

s_{\max}

, and maximum external-parent count

d_B

, any estimator requires order

s_{\max}\log(ep/s_{\max})+d_B\log(ep/d_B)

samples in the worst case over a regular model class. These bounds distinguish the costs of SCC membership and external-parent selection. Under principal invertibility and without correlation faithfulness, we establish a population block-exogeneity principle that identifies unknown root SCCs through residual independence and inclusion minimality. A sparse-adjustment characterization shows that small adjustment sets suffice to identify SCCs and their direct external parents, without regressing on all previously recovered variables. These characterizations yield BlockExo, which attains a structurally matching sample bound without knowing

s_{\max}

or

d_B

under suitable conditions. Simulations support the structural dependence of our sample bound and demonstrate BlockExo's sample-efficient recovery in comparisons with other methods for cyclic causal discovery.

Sunmin Oh, Seungsu Han, Gunwoong Park

Department of Statistics; Institute for Data Innovation in Science, Seoul National University, Korea · Department of Operations Research and Financial Engineering, Princeton University, USA · Department of Statistics; Interdisciplinary Program in Artificial Intelligence; Institute for Data Innovation in Science, Seoul National University, Korea.

Sample Complexity Causal Discovery Causal Structure Learning

Sep 22, 2026cs.LG

xWhyL: Causal Interactive Learning

Explanations are central to causal reasoning, and cognitive science has long established that the human drive to explain is itself a mechanism for learning about causality. Despite this, learning from those abductive signals is largely ignored in artificial intelligence. While explainable AI (XAI) increasingly draws on causal models to generate explanations, the converse direction about what explanations can do for causality remains largely unexplored. To fill this gap, we propose xWhyL, a formal framework connecting causality and XAI by learning causal models from explanations. We develop a mathematical theory that translates explanations into a learning signal complementary to observational data, and demonstrate how it enables overcoming the limits of observational causal discovery. As explanations can be derived from incorrect beliefs and clash with data, a tension we call the Causal Tug-of-War, we prove conditions under which our framework rejects misspecified explanations rather than absorbing them. Our practical instantiation, Causal Interactive Learning (CIL), shows how expert explanations can efficiently support causal discovery and distinguish correct from incorrect explanations.

Nicholas Tagliapietra, Florian Peter Busch, Moritz Willig +4

Bosch Center for Artificial Intelligence, Germany · Computer Science Department, Technical University of Darmstadt, Germany · Hessian Center for AI (hessian.AI), Darmstadt, Germany

Causal Discovery Causal Structure Learning

Sep 21, 2026cs.LG

Hessian Rank Constraint for Learning Structure of Nonlinear Latent Variable Models

Uncovering latent variables and their causal relations from observed data is a fundamental yet challenging problem. Existing methods often rely on restrictive assumptions, such as linear relations or invertible mixing functions. To better address this problem under general nonlinear mixing procedures, we propose a condition called the cross-Hessian Rank Constraint (HRC), which serves as a primitive rank-based tool for nonlinear latent causal discovery. In particular, we show that a rank-based property arises from the cross-Hessian of the observed-data log-density in the nonlinear case, revealing information about the latent variables, and reduces to the Tetrad constraints in the linear Gaussian case. More specifically, when two groups of observed variables are d-separated by a set of lower-dimensional latent variables, the rank of this cross-Hessian is equal to the dimension of the latent variables, under a mild affine derivative assumption on the conditional log-density derivatives. This assumption can be naturally satisfied when the noise level is low or the relevant nonlinearity is moderate. As a downstream application, we instantiate HRC in the pure one-factor measurement setting for locating latent variables and recovering their causal structure up to Markov equivalence. Experimental results on synthetic and real-world datasets support the theoretical claims.

Zijian Li, Ruichu Cai, Feng Xie +7

Mohamed bin Zayed University of Artificial Intelligence, Abu Dhabi, UAE · Carnegie Mellon University, Pittsburgh, PA, USA · Guangdong University of Technology, Guangzhou, China +3

Latent Variable Models Causal Discovery Causal Structure Learning Causal Discovery with Latent Confounding

Sep 20, 2026cs.LG

Decoupled Causal Discovery

Causal discovery from observational data is a fundamental yet challenging task in scientific research. While existing approaches are primarily based on conditional independence tests, structure scores, or restrictive functional assumptions, we propose Decoupled Causal Discovery (DCD), a novel decoupling-based perspective that does not rely on these methodologies. DCD directly identifies the Markov boundary (MB) by decoupling non-target variables via weighting functions, such that only variables within the MB preserve dependence with the target under the decoupled distribution. Building on this, DCD iteratively constructs the Completed Partially Directed Acyclic Graph (CPDAG) by exploiting structural asymmetries within the MBs. We establish the theoretical identifiability, soundness, and completeness of DCD. Empirical evaluations demonstrate that DCD achieves strong performance, particularly excelling in challenging noise regimes.

Zhengkang Guan, Fei Wu, Kun Kuang

College of Computer Science and Technology Zhejiang University

Causal Discovery Causal Structure Learning Causal Identifiability

Sep 20, 2026cs.LG

ITSY: Causal Discovery From Irregular Time-Series Data

Structural causal models for time series recover contemporaneous and lagged effects, but most methods require complete observation windows and become misspecified when samples are missing. We introduce ITSY, the first continuous-optimization method for causal discovery from irregular time series under a linear model. ITSY reformulates the structural equation so that prediction uses the nearest available history rather than the possibly missing current slice, and jointly imputes missing values while learning both graphs. A weighted reconstruction objective corrects the noise transformation induced by this reformulation. Across synthetic regimes varying missingness, scale, graph density, and noise, and on a real world benchmark, ITSY consistently improves graph recovery over representative SCM-based baselines, demonstrating the effectiveness of the proposed method. The results establish a focused solution for irregular linear first-order dynamics and clarify the assumptions required for nonlinear or higher-order extensions.

Wenbo Xu, Yue He, Yunhai Wang +2

Renmin University of China, China · Zhejiang University, China

Irregular Time-Series Modeling Structural Causal Models Time-Series Causal Discovery Learning with Missing Data Causal Discovery

Sep 17, 2026cs.LG

Epidemiological Causal Graph Identification: Challenges, Identifiability and Algorithms

Causal discovery from observational data is fundamental to statistics and machine learning, yet determining causal direction without interventions necessitates structural assumptions. Existing identifiability research primarily focuses on continuous variables under additive noise models, often neglecting mixed datasets containing ordinal scales, counts, and continuous measurements. This paper investigates causal discovery in Directed Acyclic Graphs (DAGs) where nodes follow either an ordinal distribution (via an ordered logit model) or a regular one-parameter exponential family distribution. We prove that the edge direction between an ordinal and an exponential family node is distributionally identifiable for generic parameter values. Our findings generalize previous Ordinal-Poisson results to the broader exponential family. Computationally, we introduce a score-based exhaustive search and a masked continuous optimization framework using DAGMA for larger graphs. Numerical results validate the theory, recovering edge orientations within a Markov equivalence class that are unidentifiable under classical structural equation models.

Sambit Mishra, Yingying Wang, Christine K. Johnson +1

University of Southern California · University of California, Davis

Structural Causal Models Causal Discovery Causal Identifiability

Sep 17, 2026cs.AI

MaSCoD: A Multi-Agent Framework for Structural-Context-Guided Candidate Causal Graph Generation

Large language models (LLMs) have been applied to causal discovery, but candidate-graph generation rarely treats premature omission of potentially relevant causal relations as an explicit design objective. We propose MaSCoD, a multi-agent framework that organizes candidate third variables and local structural patterns before direct-edge judgment. We evaluate MaSCoD on Auto-MPG, DWD, and Sachs using GPT-5.4 as the primary backbone and GPT-4o for replication. MaSCoD exhibits a dataset- and backbone-dependent retention-selectivity profile rather than uniform superiority. Across all six dataset-backbone settings, Full, which supplies structural hypotheses before direct-edge judgment, achieved higher mean Recall and F1 than No Phase 1, which instead constructs them within the judgment procedure, while also increasing false-positive rates. Additional reference-edge retention over all evaluated baselines was observed on DWD with GPT-5.4 and on Sachs with GPT-4o, rather than uniformly across settings. Partial ablations showed that supplying both information components did not always outperform supplying only one. For GPT-5.4, stage-wise analysis showed that the Full-No Phase 1 retention gap was already present after direct-edge judgment, while reconciliation introduced additional reference-edge loss for Full on Sachs. These findings support structural pre-organization as an explicit design and evaluation target for omission control and motivate evaluating context construction jointly with its utilization in judgment.

Yudai Nakada, Yuichiro Nishiura, Jin Michael Splichal

SCSK Corporation Tokyo, Japan

Multi-Agent LLM Systems Causal Discovery Causal Structure Learning

Sep 16, 2026cs.LG

On the Identifiability of Mixed Ordinal and Exponential Family Causal DAGs under Linear Parametric Models

The problem of identifiability in linear parametric models (LPMs) whose nodes follow either an ordered logit model or a regular one-parameter exponential family is evaluated. The results go beyond classical structural equation models as well as results for nodes with observations from a homogeneous family of distributions. The main result establishes that the orientation of every edge joining an ordinal node to an exponential-family node is identifiable from the joint distribution alone at every parameter value, provided the ordinal node has at least three categories and the exponential-family node at least three points of support, with no restriction on the sufficient statistic. Converses show that both requirements are necessary: the three-category requirement is binding only for affine sufficient statistics, and the three-point requirement is binding under the canonical link. The guarantee extends to orienting every such mixed ordinal-exponential family edge of a given

d

-node undirected skeleton. Numerical experiments illustrate the theoretical results by successfully separating orientations within a Markov equivalence class, which are indistinguishable by conditional independence alone.

Sambit Mishra, Urbashi Mitra

Ming Hsieh Department of Electrical and Computer Engineering University of Southern California Los Angeles, CA 90089, USA

Structural Causal Models Causal Discovery Causal Structure Learning Causal Identifiability

Sep 15, 2026stat.ME

Causal Discovery via Transformed Low-Rank Quantile Surfaces

We propose Low-Rank Quantile Surfaces (LRQS), a bivariate causal model in which, in the causal direction, an unknown monotone transformation of the conditional quantile surface admits a low-rank functional decomposition. LRQS subsumes location-scale noise models and post-nonlinear heteroscedastic noise models, while allowing multiple quantile bases to represent changes beyond location-scale effects. We prove generic identifiability of LRQS: the transformed quantile surface is low rank in the causal direction, whereas reverse representability under the corresponding constraints occurs only for exceptional, fine-tuned cause marginals. We provide a simple-yet-powerful causal score using a nonparametric fitting procedure that alternates between rank-constrained approximation of discretized quantile surfaces and isotonic estimation of the unknown monotone transformation. Experiments on synthetic mechanisms with higher-rank distributional shape variation and strong nonlinear distortions, together with standard bivariate benchmarks, show that LRQS is especially effective when conditional distributional shape or observation distortion goes beyond existing location-scale assumptions.

Ryo Kamimura, Thong Pham

1Shiga University · 3RIKEN AIP · 2The University of Osaka

Causal Discovery Causal Identifiability

Sep 14, 2026cs.LG

Fundamental Dynamical Units for Physics-Informed Structural Inference from Perturbation Time-Series in Networked Systems

In networked dynamical systems, the parameter of primary mechanistic interest is signed interaction structure. Recovering this structure from perturbation time-series data is a fundamental identification problem, compounded by three coupled obstacles: the combinatorial complexity of interaction architectures, ambiguity of causal attribution under limited interventions, and state-dependent dynamics that confound structural inference. Each obstacle is structural in origin and calls for a structural solution. We address these challenges by adopting a reductionist approach, introducing Fundamental Dynamical Units (FDUs): signed three-node interaction patterns as composable primitives that convert the interaction hypothesis space into a finite, constructive, and tractable representation. We show that local interaction structure determines the perturbation conditions required to disentangle direct from relayed influence, making intervention design a structural consequence of the FDU representation. We embed FDU-regularized structural inference within a physics-informed neural ordinary differential equation (ODE) whose governing-equation constraint transforms structural hypotheses into verifiable dynamical predictions, enabling joint recovery of interaction structure and perturbation-resolved trajectories. Validated on synthetic benchmarks with known ground truth, the framework supports structural commitment, expressed through FDU primitives, motif-prescribed intervention design, and physics-informed learning, as a principled basis for mechanistically interpretable inference in networked dynamical systems.

Nima Nouri

Artificial Intelligence for Science Innovation, AstraZeneca, Waltham, MA, USA

Time-Series Causal Discovery Causal Discovery Causal Structure Learning

Sep 10, 2026cs.LG

CausalArena: Benchmarking Causal Discovery in the Foundation Model Era

Causal discovery aims to uncover causal structures from data and is fundamental to scientific reasoning and intervention-based decision making. Its evaluation relies heavily on structural causal models (SCMs), which specify a causal graph together with the mechanisms that generate data, yet existing studies differ substantially in graph families, mechanisms, and evaluation protocols. The emergence of causal discovery foundation models (CDFMs) further complicates evaluation: performance may reflect not only causal discovery ability, but also overlap between pretraining environments and test SCMs, making results on fixed synthetic benchmarks difficult to interpret. We introduce CausalArena, a unified and evolvable benchmark for causal discovery under a common protocol. Synthetic SCMs supply controlled breadth over structures and mechanisms; semantic operational SCMs provide human-auditable, semantically grounded environments beyond standard synthetic generators; and formula-grounded SCMs test discovery under explicit scientific mechanisms. Public real-world datasets provide an additional external-validity check. Experiments across classical, neural, and pretrained methods reveal substantial ranking shifts across SCM families and protocols, showing that strong performance in one benchmark regime does not reliably transfer to others. These results highlight benchmark diversity and pretraining--evaluation overlap as central challenges for evaluating causal discovery in the foundation model era.

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

School of Artificial Intelligence, Nanjing University

Causal Foundation Models Structural Causal Models Causal Discovery Synthetic Data Evaluation

Sep 3, 2026cs.LG

Federated Causal Discovery via Regression-Directed Cumulants

In this paper we study linear non-Gaussian acyclic models (LiNGAM) when used in federated environments. These causal models allow one to go beyond Markov equivalence. However, in many domains data are scarce, and increasing the sample size by centralising data from different clients is not advisable due to regulations such as the GDPR. The federated environment offers an attractive option to balance privacy and causal discovery accuracy. Unfortunately, the standard centralised estimator in the LiNGAM setting, i.e., DirectLiNGAM, cannot be straightforwardly federated. Higher-order cumulant tensors offer a way around this obstacle: they depend only on the joint distribution of the variables involved and add exactly across independent sample groups, so a single communication round suffices in horizontal, vertical, and hybrid partitions. However, FedISHC, i.e., the current federated method along these lines, breaks down under near-symmetric noise. To overcome the above limitation, we introduce the FedRCD family of causal discovery algorithms, and investigate three variants that trade off communication rounds against algebraic noise; two of them are exact federated counterparts of the centralised high-order cumulant (HC) and HC-LiNGAM algorithms, and the single-round variants further effectively support exact unlearning at any granularity, from a single observation to a whole client. Numerical experiments show that at sample sizes typical of real deployments, the entire cumulant-based federated family does not actually rank variables by the population asymmetry that the scores encode at zero. It ranks them by a variance ladder induced by the DAG along its directed paths, the cumulant counterpart of varsortability. Marginal standardisation collapses every cumulant method to near-random ordering, while scale-invariant DirectLiNGAM, not federable under this protocol, is unaffected.

Pablo Torrijos, Fabio Stella, José A. Gámez +1

Departamento de Sistemas Inform´aticos Universidad de Castilla-La Mancha Albacete, Spain · Dipartimento di Informatica, Sistemistica e Comunicazione Universit`a degli Studi di Milano Bicocca Milano, Italy · Departamento de Sistemas Inform´aticos2026 Universidad de Castilla-La Mancha Albacete, Spain

Structural Causal Models Causal Discovery

Sep 3, 2026cs.LG

Guide, Not Bind: Why Defeasible Priors Fail in Augmented Lagrangian Causal Discovery

Differentiable causal discovery methods increasingly encode expert priors as forbidden-edge constraints enforced by an Augmented Lagrangian (ALM) penalty, on the assumption that a data-adaptive relaxation mechanism will discount and eventually override a rule the data consistently contradicts. We show this design, which we call \emph{guide, not bind}, fails for two independent, precisely characterized reasons, and that directly repairing both restores it only partially. First, sequential penalty-ramping ALM suppresses a wrongly-forbidden true edge before any counterfactual check can detect it: we give three necessary conditions any adaptive relaxation must satisfy to avoid this (Proposition~\ref{prop:conditions}), prove that DADU---the natural relaxation rule this paper introduces as the object of study---violates all three (Corollary~\ref{cor:dadu_failure}), and confirm the failure across 3{,}072 training runs spanning graphs from 4 to 32 nodes, where a single wrong prior suppresses a true edge in 87--97% of trials under DADU. Second, and independent of any fix to the mechanism, we prove in closed form that the standard correlation-matching objective ties a true edge and its reverse to an identical cost of exactly

2r^2

(Lemma~\ref{lem:tie}), not because the underlying equal-variance model is unidentifiable, but because normalizing to correlation discards exactly the variance information that would make it identifiable; covariance matching instead separates the two directions by a provable margin of at least

w_0^4

(Lemma~\ref{lem:separation}).

Sairam Sundararaman, Sara Girdhar, Manit Narasimha Murthy +2

Department of Computer Science (AI & ML) PES University · Department of Computer Science2026 PES University · Department of Computer Science PES University

Causal Discovery Causal Identifiability Augmented Lagrangian Method

Sep 1, 2026cs.LG

Replicating TRACE: A Practitioner's Guide to Its Threshold and Particle Budget

TRACE (Math & Lienhart, arXiv:2602.01135) reads causal graphs over event types out of a pretrained autoregressive sequence model by thresholding a per-position conditional-mutual-information estimate at a fixed tau. We independently replicate its headline synthetic result: with tau selected on a validation split, mean per-sequence F1 against exact interventional truth reaches 0.90-0.91 at vocabulary size 1000 (paper: 0.91) and 0.86-0.91 from 100 to 2000. First, the optimal threshold is pinned to the truth margin, not to any constant: at every size the errors at tau* straddle the delta = 0.05 margin defining ground truth (missed true edges lie just above it, accepted false ones just below), and the blind optimum lands near delta/2 times the estimator's calibration, confirmed out of sample at 5000. Second, at a single global threshold TRACE mostly recovers a direct, adjacent-influence graph: lag-1 true edges are recalled at 0.97-0.99, while true edges at lag 2 or more read orders of magnitude lower---the reading-scale price of randomizing mediating positions, which an exact test of direct causal effect requires when the truth is unknown. A per-lag threshold family recovers a third to a half of lag-2 truth; on lag-uniform data one validated threshold recalls every lag at 0.40-0.87, 8-26 pp below an atomic-intervention control at lags 3-6. Third, the default lag decay of the paper's synthetic benchmark concentrates about 85% of interventional truth at lag 1 and pushes the rest below the estimator's noise floor, so headline F1 there certifies lag-1 recovery only and conflates the benchmark's skew with the algorithm's own limit; a flatter decay separates the two. Fourth, F1 saturates from N = 2 particles at the selected threshold---a property of the threshold's margin over the noise floor, not of the estimator, which converges as N^(-1/2). We distill five practitioner rules.

Alex Chadyuk, Alicia Zhang, Roy Kucukates

LotusFlare Inc.

Time-Series Causal Discovery Causal Discovery

Aug 14, 2026cs.CY

Meteorology-driven Causal Nowcasting of Fugitive Landfill Emissions from Measured Coupling Timescales

Which meteorological processes control exposure to fugitive gases downwind of a source, and on what timescales, have largely been inferred from dispersion theory and partial field evidence. Here we show that the meteorological drivers of elevated hydrogen sulphide (H

_2

S) exposure at a long-monitored European landfill, and the timescales over which each acts, can be identified directly from monitoring data. Wind direction, wind speed and atmospheric pressure form the causal core, with the share of directed information carried by pressure increasing with aggregation scale. The recovered timescales are consistent with those expected from the underlying atmospheric processes. We use these driver timescales to initialise CAIRN (Causal-Anchored Inference for Receptor Nowcasting), a machine-learning nowcaster with fast and slow memory components. Trained on past exceedances of WHO guideline levels, CAIRN nowcasts them from surface weather measurements and the calendar alone, without hand-engineered features. Combining four such nowcasters produces a site-level, tiered alert that agrees substantially with that generated by a direct sensor network and tracks an independent record of community odour reports. Meteorological variables can therefore serve as an inference-time proxy for exposure relative to WHO guideline levels, and they link atmospheric dynamics to community impact as an episode unfolds.

Timothy C. Pearce, David J. T. Smith, Alec Dobney +1

Biomedical Engineering Research Group, School of Engineering, University of Leicester, Leicester, United Kingdom. · Environmental Hazards and Emergency Department, UKHSA, Nottingham, United Kingdom.

Causal Discovery Air Quality Prediction

Aug 12, 2026cs.LG

Interpretable Causal Discovery via Causal-Effect Constraints

Causal discovery aims to uncover the underlying causal relationships given data generated from a system. The goal, however, is not merely to predict causal edges given data, but also to be able to interpret and explain either observed or hypothesized phenomena, such as a particularly large causal effect. We consider this task of conditional causal discovery and cast it as a Bayesian inference problem, in which we target the posterior over causal graphs and parameters conditional on an event such as a causal-effect constraint. Unfortunately, this poses a computational challenge: existing approaches to Bayesian causal discovery struggle when the event has small posterior mass. To address this, we adapt rare-event estimation techniques to perform inference the joint graph-parameter space. Our method gradually drives a particle population toward the constrained region while maintaining samples that approximate the conditional posterior. Empirical evaluation on synthetic graphs validates the accuracy of our approach at small and large scales, and we show in a case study on the Sachs protein dataset how our method can be used to aid scientific exploration by providing pathway-level summaries.

Cixuan Zhang, Guy Van den Broeck, Benjie Wang

Computer Science Dept., Yale University, New Haven, Connecticut, USA · Computer Science Dept., University of California, Los Angeles, Los Angeles, California, USA

Bayesian Inference Causal Discovery Causal Explanation Rare-Event Estimation

Aug 11, 2026stat.ML

Conditional Independence Tests for Constraint-Based Causal Discovery: A Survey

Conditional Independence (CI) tests are the statistical engine of constraint-based causal discovery: in algorithms such as PC (Peter-Clark) and FCI (Fast Causal Inference), skeleton pruning and key orientations follow directly from CI decisions. This survey reviews CI testing with emphasis on assumptions, robustness, and scalability in high-dimensional and mixed-type settings common in biomedical domains. The survey organizes widely used CI methods into six families: partial-correlation, contingency-table, regression, nearest-neighbor, kernel, and machine-learning-based. Special emphasis is provided on the robustness layers that address the limitations of these families. For each family, the survey examines when CI decisions reflect the data-generating distribution and when they fail. By this, we link test-level properties, including power decay with conditioning set size and asymmetric type I/II error consequences, to graph-level errors in skeleton recovery and v-structure orientation. The survey also compares adoption across major R and Python libraries and summarizes open challenges, including mixed-type CI testing without discretization, small-sample error control, and strategies for improving scalability of CI-testing.

Pavel Averin, Theodoros Moysiadis, Ioannis Katakis

Department of Computer Science School of Sciences and Engineering University of Nicosia 2417, Nicosia, Cyprus

Causal Discovery Causal Inference Conditional Independence Testing Statistical Hypothesis Testing

Aug 9, 2026cs.HC

Human-Guided Causal Knowledge Injection for Virtual Cells

Virtual cells employ machine learning models to simulate and predict cellular behaviors, serving as a critical computational framework for investigating health and disease. Injecting causal graphs into virtual cells can improve the interpretability, but such graphs are usually not available in real-world applications. Recently, many methods have been proposed to construct causal graphs from data, which group genes based on their similarities to form concepts and extract their causal relationships. However, since this automatic process is unsupervised, the causal graphs usually contain errors. In this paper, we propose a human-guided causal knowledge injection method for virtual cells. We developed a gene-similarity-aware causal graph visualization supported by a hybrid optimization algorithm to help explore both the causal relationships between concepts and the similarities between genes. Based on the exploration, we further developed a counterfactual analysis strategy supported by a counterfactual visualization and a causal path visualization to help validate and refine causal graphs. The effectiveness of our method is demonstrated through two real-world case studies, the extraction of scientifically meaningful causal insights, and positive feedback from domain experts.

Pengcheng Wang, Changjian Chen, Zhuo Tang +4

Causal Discovery Gene Regulatory Network Inference

Aug 8, 2026cs.LG

Support Selection Beyond Smooth DAG Exactness: Completion Geometry,Score Margins, and Selective Certificates

Smooth acyclicity constraints answer whether a weighted support is a DAG, whereas structure learning asks which support change should be made. Existing analyses establish degeneracy for particular constraint formulas but do not isolate what follows from smooth exactness itself. At a DAG boundary, we show that minimal cycle completions generate a squarefree monomial ideal containing every restricted Taylor jet of an exact representation. If the smallest completion has

q

edges, the first possible response has order

q

for a vector residual and

2q

for a nonnegative scalar. Exponentially many constant-scale cyclic manifolds exhibit the same lack of ranking away from the boundary for NOTEARS and DAGMA. We derive the exact selection time for an isolated cycle. When

Ψ'(h)\asymp h^ν

, the feasibility-only time is

T_0(\varepsilon)=Θ(\varepsilon^{-(2ν+1)})

; a score margin changes the leading dynamics at scale

T_0^{-1}

for

ν>0

, while

ν=0

has a logarithmic boundary layer requiring

γT_0\log(1/\varepsilon)\to0

. Experiments verify this law, and a truth-free separation statistic predicts selection time on 320 official NOTEARS/DAGMA trajectories (Spearman

-0.52

and

-0.66

, permutation

p<10^{-4}

). For finite samples, a parent-set confidence family and forced-opposite queries certify skeleton and unshielded-collider labels shared by every population optimum of a frozen score. Across 320 runs, every regret bound covers an independent oracle-score audit. None of 3,042 certified skeleton or 2,396 collider labels disagrees with the oracle-score optimum, although 4.4% and 5.5%, respectively, disagree with the generating graph. These results separate DAG feasibility, score-based support selection, and causal identification.

Rui Wu, Zongyuan Chen, Hong Xie

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

Causal Discovery Causal Structure Learning Constrained Optimization