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

May 4, 2026cs.LG

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

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

Gideon Stein, Niklas Penzel, Tristan Piater +1

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

Time-Series Causal Discovery Causal Discovery

May 3, 2026stat.ML

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

External priors of unknown reliability create a brittle trade-off in causal discovery: blind trust amplifies errors, blind rejection wastes signal. Real priors are also heterogeneously reliable -- physical laws are trustworthy, LLM-suggested edges are speculative -- yet existing methods either ignore priors or impose them through globally uniform trust. We propose PRCD-MAP, a soft prior-consumption layer that assigns per-edge trust to an imperfect prior and uses it to modulate a prior-aware

\ell_1

and prior-weighted

\ell_2

regularizer in a MAP objective. Trust is calibrated by empirical Bayes on a Laplace-approximated marginal likelihood and propagated along the prior graph by an MLP, so data-confirmed neighborhoods boost trust and contradictions suppress it. PRCD-MAP enjoys a population-level safety guarantee: it is

\varepsilon

-safe in expectation over the prior-generation distribution, with

\varepsilon\leq C\cdot\mathrm{acc}(1{-}\mathrm{acc})\cdot d^2/T

at the parametric

T^{-1}

rate and vanishing at the prior-quality endpoints. When the prior is uninformative, learned trust provably collapses to its floor and the method recovers a no-prior baseline. Empirically, on real CausalTime data PRCD-MAP exploits informative LLM priors (LLM-prior gain

+0.067/+0.089

AUROC on AQI/Medical over a no-prior PRCD-MAP backbone; combined backbone+prior lead

+0.123/+0.043

over PCMCI+), auto-attenuates on the anonymous-variable Traffic stress test, and retains a lead at

d{=}300

; against BayesDAG, the closest soft-Bayesian baseline, PRCD-MAP wins on every CausalTime dataset under a matched

W_0

-only protocol. A four-way ablation isolates each component: EB calibration and MLP trust propagation jointly carry the plurality of the gain, with positive sign on every dataset. Extensions to nonlinear (NAM) and cross-sectional settings show the calibrated-trust principle is setting-agnostic.

Xihang Shan, Da Zhou

School of Mathematical Sciences Xiamen University Fujian, China

Time-Series Causal Discovery Bayesian Inference Causal Discovery

May 1, 2026cs.LG

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

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

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

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

Time-Series Causal Discovery Climate Science Causal Discovery Causal Structure Learning

Apr 29, 2026cs.LG

Causal Learning with Neural Assemblies

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

Evangelia Kopadi, Dimitris Kalles

Hellenic Open University Greece

Neural Processes Causal Discovery Causal Structure Learning Biologically Plausible Learning Causal Interpretability Local Learning

Apr 28, 2026cs.LG

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

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

Rui Wu, Hong Xie

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

Causal Discovery Causal Structure Learning

Apr 27, 2026cs.AI

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

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

Zhou Ziheng, Huacong Tang, Jinyuan Zhang +9

University of California, Los Angeles · Peking University · Amazon

AI Agents for Scientific Discovery Circuit Discovery Causal Discovery AI Agent Benchmarks

Apr 26, 2026cs.LG

Causal Representation Learning from General Environments under Nonparametric Mixing

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

Ignavier Ng, Shaoan Xie, Xinshuai Dong +2

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

Causal Representation Learning Causal Discovery Causal Structure Learning Causal Identifiability

Apr 26, 2026cs.AI

Causal Discovery as Dialectical Aggregation: A Quantitative Argumentation Framework

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

Sheng Wei, Yulin Chen, Beishui Liao

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

Causal Discovery Computational Argumentation

Apr 24, 2026cs.LG

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

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

Zongyu Li

Causal Effect Estimation Causal Discovery Causal Abstraction Causal Discovery with Latent Confounding

Apr 21, 2026cs.AI

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

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

John Alderete, Sebastian Benthal, Connie Xu +1

Amigo AI · Simon Fraser University · International Computer Science Institute

Causal Discovery LLM Agents Causal Interventions in Language Models LLM Reasoning

Apr 20, 2026cs.CL

Implicit Causal Graph Construction in Text via Chain Discovery

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

Liesbeth Allein, Marie-Francine Moens

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

Causal Discovery Causal Reasoning in Language Models Causal Inference

Apr 16, 2026cs.CL

ClimateCause: Complex and Implicit Causal Structures in Climate Reports

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

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

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

Relation Extraction Climate Science Causal Discovery Causal Reasoning

Apr 16, 2026cs.AI

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

LLM-empowered agent simulations are increasingly used to study social emergence, yet the micro-to-macro causal mechanisms behind macro outcomes often remain unclear. This is challenging because emergence arises from intertwined agent interactions and meso-level feedback and nonlinearity, making generative mechanisms hard to disentangle. To this end, we introduce \textbf{\textsc{CAMO}}, an automated \textbf{Ca}usal discovery framework from \textbf{M}icr\textbf{o} behaviors to \textbf{M}acr\textbf{o} Emergence in LLM agent simulations. \textsc{CAMO} converts mechanistic hypotheses into computable factors grounded in simulation records and learns a compact causal representation centered on an emergent target

Y

. \textsc{CAMO} outputs a computable Markov boundary and a minimal upstream explanatory subgraph, yielding interpretable causal chains and actionable intervention levers. It also uses simulator-internal counterfactual probing to orient ambiguous edges and revise hypotheses when evidence contradicts the current view. Experiments across four emergent settings demonstrate the promise of \textsc{CAMO}.

Xiangning Yu, Yuwei Guo, Yuqi Hou +2

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

Causal Discovery Causal Structure Learning Multi-Agent Systems Large Language Model-Based Social Simulation Emergent Behavior in Multi-Agent Systems

Mar 27, 2026cs.LG

Identification of Bivariate Causal Directionality Based on Anticipated Asymmetric Geometries

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

Alex Glushkovsky

Causal Discovery

Mar 5, 2026cs.LG

Learning Causal Structure of Time Series using Best Order Score Search

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

Irene Gema Castillo Mansilla, Urmi Ninad

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

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

Feb 16, 2026cs.LG

Use What You Know: Causal Foundation Models with Partial Graphs

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

Arik Reuter, Anish Dhir, Cristiana Diaconu +6

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

Causal Foundation Models Causal Discovery Causal Inference

Feb 13, 2026cs.LG

Uncertainty Quantification in Federated Granger Causality Learning

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

Ayush Mohanty, Nazal Mohamed, Nagi Gebraeel

Georgia Institute of Technology Atlanta, GA 30332

Time-Series Causal Discovery Causal Discovery Federated Graph Learning

Feb 9, 2026cs.LG

CauScale: Neural Causal Discovery at Scale

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

Bo Peng, Sirui Chen, Jiaguo Tian +2

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

Efficient Neural Network Inference Causal Discovery

Nov 18, 2025stat.ML

Skewness-Robust Causal Discovery in Location-Scale Noise Models

To distinguish Markov equivalent graphs in causal discovery, it is necessary to restrict the structural causal model. Crucially, we need to be able to distinguish cause

X

from effect

Y

in bivariate models, that is, distinguish the two graphs

X \to Y

and

Y \to X

. Location-scale noise models (LSNMs), in which the effect

Y

is modeled based on the cause

X

as

Y = f(X) + g(X)N

, form a flexible class of models that is general and identifiable in most cases. Estimating these models for arbitrary noise terms

N

, however, is challenging. Therefore, practical estimators are typically restricted to symmetric distributions, such as the normal distribution. As we showcase in this paper, when

N

is a skewed random variable, which is likely in real-world domains, the reliability of these approaches decreases. To approach this limitation, we propose SkewD, a likelihood-based algorithm for bivariate causal discovery under LSNMs with skewed noise distributions. SkewD extends the usual normal-distribution framework to the skew-normal setting, enabling reliable inference under symmetric and skewed noise. For parameter estimation, we employ a combination of a heuristic search and an expectation conditional maximization algorithm. We evaluate SkewD on novel synthetically generated datasets with skewed noise as well as established benchmark datasets. Throughout our experiments, SkewD exhibits a strong performance and, in comparison to prior work, remains robust under high skewness.

Daniel Klippert, Alexander Marx

Department of Statistics, TU Dortmund University, Germany · Research Center Trustworthy Data Science and Security, University Alliance Ruhr, Germany.

Causal Discovery

Oct 25, 2025stat.ML

MetaCaDI: A Meta-Learning Framework for Causal Discovery from Multiple Environments with Unknown Interventions

Uncovering the causal mechanisms of complex real-world systems remains a significant challenge, as these systems often entail high data collection costs and involve unknown interventions. We introduce MetaCaDI, the first framework to cast the identification of unknown interventions as a meta-learning problem, explicitly leveraging a jointly learned causal graph. MetaCaDI is a Bayesian framework that learns a shared causal structure across multiple environments and is optimized to rapidly adapt to new, few-shot intervention target identification tasks. A key innovation is our model's analytical adaptation, which uses a closed-form solution to bypass expensive and potentially unstable gradient-based bilevel optimization. Extensive experiments on synthetic and complex gene expression data demonstrate that MetaCaDI significantly outperforms state-of-the-art methods. It excels at identifying intervention targets from as few as 3 samples - where existing methods collapse to random chance - while robustly recovering the shared causal graph, proving its effectiveness in data-scarce scenarios.

Hans Jarett Ong, Yoichi Chikahara, Tomoharu Iwata

Nara Institute of Science and Technology, Nara, Japan · NTT Communication Science Laboratories, Kyoto, Japan

Meta-Learning Causal Discovery Causal Structure Learning Data-Efficient Learning

Oct 22, 2025cs.LG

Learning Granger Causality under Latent Confounding via Intervention-Induced Heterogeneity

Granger causality characterizes directed predictive dependencies in multivariate time series, but recovering such dependencies becomes challenging in the presence of latent confounding. Cross-environment invariance provides a natural source of information in heterogeneous settings, yet invariance alone can be insufficient: when latent-to-observed mechanisms remain stable, hidden confounders can induce predictive dependencies that are just as invariant as genuine Granger-causal relations. We show that interventions provide an additional source of identifying information by inducing structured variation in observed mechanisms, while stable latent pathways need not exhibit the same cross-environment changes. In practice, however, neither the intervened environments nor the affected mechanisms are known. We propose GRACE, a framework for learning Granger causality under latent confounding from intervention-induced heterogeneity. GRACE decomposes multivariate dynamics into a shared Granger mechanism, sparse environment-specific deviations that capture edge-level interventions, and a latent component that accounts for confounding. Under a linear generative model, we show that GRACE can recover which environments intervene on a given edge when the edge is perturbed in at least one but fewer than half of the environments and the intervention effect is sufficiently large to survive sparsity shrinkage; the recovered intervention pattern then provides a certificate for the corresponding Granger causal edge. Experiments on synthetic and real-world time series demonstrate improved Granger causal structure recovery under latent confounding and unknown interventions.

Ziyi Zhang, Shaogang Ren, Xiaoning Qian +1

Texas A&M University · University of Tennessee at Chattanooga · Brookhaven National Laboratory

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

Sep 2, 2025stat.ML

Design of Experiment for Discovering Directed Mixed Graph

We study the design of interventions for causal discovery in simple structural causal models whose causal graphs are directed mixed graphs (DMGs) that may contain directed cycles and bidirected edges representing latent confounding. In such case, observational conditional-independence (CI) information may not identify even the graph skeleton, while CI alone cannot generally detect a bidirected edge coexisting with a directed edge. To this end, we propose a stage-wise framework based on tailored separating systems. Separating-system interventions first recover descendant relations and strongly connected components (SCCs). The SCCs are then ordered by ancestry, and an SCC-Anc separating system recovers the directed subgraph. Given this subgraph, further systems use CI tests interpreted through

d

- or

σ

-separation to recover non-adjacent bidirected edges, whose endpoints share no directed edge, and do-see comparisons to recover those coexisting with exactly one directed edge. Under our assumptions, the framework recovers the directed subgraph and every bidirected edge except double-adjacent ones, whose endpoints are connected by a directed edge in each direction. We develop algorithms for unrestricted and

M

-bounded settings, with each experiment targeting at most

M

variables in the latter. For recovering the directed subgraph and non-adjacent bidirected edges, our upper bounds on the number and maximum size of experiments match corresponding worst-case lower bounds up to logarithmic factors.

Haijie Xu, Chen Zhang

Department of Industrial Engineering Tsinghua University

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

Jun 24, 2025cs.LG

Tags for DAGs: Graph Refinement with Meta-Informed Relations

Causal discovery has shifted from data-centric methods to hybrid strategies that integrate semantic knowledge from experts or large language models (LLMs). Such external information is vital for identifying causal structures beyond the Markov Equivalence Class (MEC), which data alone cannot resolve. However, expert availability is often limited, and LLMs frequently misidentify causal directions in specialized domains. To overcome such shortcomings, we propose a tag-based approach that leverages semantically meaningful labels while deriving causal directionality directly from data. Using variable-level tag assignments from available sources (e.g., LLMs), our tags for DAGs method learns from identifiable data structures to extract higher-level causal relations. These are then used to orient undirected edges, enabling causal discovery to move beyond the MEC without reliance on fallible external knowledge.

Florian Peter Busch, Moritz Willig, Florian Guldan +2

Computer Science Department, Technical University of Darmstadt · Hessian Center for AI (hessian.AI) · German Research Center for AI (DFKI) +2

Causal Discovery Causal Structure Learning

Feb 27, 2025cs.LG

Multi-View Causal Discovery without Non-Gaussianity: Identifiability and Algorithms

Causal discovery is a difficult problem that typically relies on strong assumptions on the data-generating model, such as non-Gaussianity. In practice, many modern applications provide multiple related views of the same system, which has rarely been considered for causal discovery. Here, we leverage this multi-view structure to achieve causal discovery with weak assumptions. We propose a multi-view linear Structural Equation Model (SEM) that extends the well-known framework of non-Gaussian disturbances by alternatively leveraging correlation over views. We prove the identifiability of the model for acyclic SEMs. Subsequently, we propose several multi-view causal discovery algorithms, inspired by single-view algorithms (DirectLiNGAM, PairwiseLiNGAM, and ICA-LiNGAM). The new methods are validated through simulations and applications on neuroimaging data, where they enable the estimation of causal graphs between brain regions.

Ambroise Heurtebise, Omar Chehab, Pierre Ablin +2

Inria, CEA, University of Paris-Saclay, France · University of Carnegie Mellon, Pittsburgh PA, USA · Apple +1

Structural Causal Models Causal Discovery Causal Identifiability

Feb 11, 2025stat.ML

The observational partial order of causal structures with latent variables

For two causal structures with the same set of visible variables, one is said to observationally dominate the other if the set of distributions over the visible variables realizable by the first contains the set of distributions over the visible variables realizable by the second. Knowing such dominance relations is useful for adjudicating between these structures given observational data. Here, we consider the problem of determining the partial order of equivalence classes of causal structures with latent variables relative to observational dominance. We provide a complete characterization of the dominance order in the case of three visible variables, and a partial characterization in the case of four visible variables. Our techniques also help to identify which observational equivalence classes have a set of realizable distributions that is characterized by nontrivial inequality constraints, analogous to Bell inequalities and instrumental inequalities. We find evidence that as one increases the number of visible variables, the equivalence classes satisfying nontrivial inequality constraints become ubiquitous. (Because such classes are the ones for which there can be a difference in the distributions that are quantumly and classically realizable, this implies that the potential for quantum-classical gaps is also ubiquitous.) Furthermore, we find evidence that constraint-based causal discovery algorithms that rely solely on conditional independence constraints have a significantly weaker distinguishing power among observational equivalence classes than algorithms that go beyond these (i.e., algorithms that also leverage nested Markov constraints and inequality constraints).

Marina Maciel Ansanelli, Elie Wolfe, Robert W. Spekkens

Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario Canada N2L 2Y5 · Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1

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

Jul 10, 2024stat.ML

Towards Complete Causal Explanation with Expert Knowledge

We study the problem of restricting a Markov equivalence class of maximal ancestral graphs (MAGs) to only those MAGs that contain certain edge marks, which we refer to as expert or orientation knowledge. Such a restriction of the Markov equivalence class can be uniquely represented by a restricted essential ancestral graph. Our contributions are several-fold. First, we prove certain properties for the entire Markov equivalence class including a conjecture from Ali et al. (2009). Second, we present several new sound graphical orientation rules for adding orientation knowledge to an essential ancestral graph. We also show that some orientation rules of Zhang (2008b) are not needed for restricting the Markov equivalence class with orientation knowledge. Third, we provide an algorithm for including this orientation knowledge and show that in certain settings the output of our algorithm is a restricted essential ancestral graph. Finally, outside of the specified settings, we provide an algorithm for checking whether a graph is a restricted essential graph and discuss its runtime. This work can be seen as a generalization of Meek (1995) to settings which allow for latent confounding.

Aparajithan Venkateswaran, Emilija Perković

Microsoft · Redmond, WA 98052, USA · Department of Statistics +2

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

Apr 9, 2024cs.LG

CausalBN-Bench: A Comprehensive Benchmark for Causal Learning Capability of LLMs

The ability to understand causality significantly impacts the competence of large language models (LLMs) in output explanation and counterfactual reasoning, as causality reveals the underlying data distribution. However, the lack of a comprehensive benchmark currently limits the evaluation of LLMs' causal learning capabilities. To fill this gap, this paper develops CausalBN-Bench based on data from the causal research community, enabling comparative evaluations of LLMs against traditional causal learning algorithms. To provide a comprehensive investigation, we offer three tasks of varying difficulties, including correlation, causal skeleton, and causality identification. Evaluations of 19 leading LLMs reveal that, while closed-source LLMs show potential for simple causal relationships, they significantly lag behind traditional algorithms on larger-scale networks (

>50

nodes). Specifically, LLMs struggle with collider structures but excel at chain structures, especially at long-chain causality analogous to Chain-of-Thought techniques. This supports the current prompt approaches while suggesting directions to enhance LLMs' causal reasoning capability. Furthermore, CausalBN-Bench incorporates background knowledge and training data into prompts to thoroughly unlock LLMs' text-comprehension ability during evaluation, whose findings indicate that, LLM understand causality through semantic associations with distinct entities, rather than directly from contextual information or numerical distributions.

Yu Zhou, Xingyu Wu, Jibin Wu +2

Department of Data Science and Artificial Intelligence, The Hong Kong Polytechnic University, Hong Kong SAR 999077, China · College of Computer Science, Chongqing University, Chongqing 400044, China

LLM Evaluation Causal Discovery Causal Structure Learning Causal Reasoning in Language Models Causal Reasoning

Nov 13, 2023cs.LG

Causal Discovery in Mixtures of Populations

Causal discovery aims to learn causal structures up to certain symmetries. Diverse populations or changing environments give rise to heterogeneous data in the following sense: each population/environment is a ``source'' which idiosyncratically determines the forms of causal effects. From this perspective, the source is a latent common cause for every observed variable. While some methods for causal discovery can work around latent confounding in special cases, a global confounder poses a significant challenge. The only known ways to deal with latent global confounding involve making assumptions that limit structural equations and/or noise functions. We demonstrate that globally confounded causal structures can still be identified with arbitrary structural equations and noise functions, so long as the number of latent classes remains small relative to the size and sparsity of the underlying DAG. The approach relies on agglomerating variables into large-enough matrices of moments, whose ranks directly reveal graphical properties of the causal structure. We also provide a statistical test to test the rank of these matrices.

Bijan Mazaheri, Spencer Gordon, Yuval Rabani +1

Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire, USA · Fragment Data Technologies, San Francisco, California, USA · Department of Computer Science, Hebrew Univeristy of Jerusalem, Jerusalem, Israel +1

Latent Variable Models Causal Discovery Causal Identifiability Causal Discovery with Latent Confounding