Causal Structure Learning

Follow this topic Ask about this topic

Momentum

14 papers in the last four weeks, with none the four weeks before. 0.1% of all new papers.

Jul 13Week of Sep 28

Latest papers 81

Jul 3, 2026stat.ME

CaSPECT: Discovering Causally Homogeneous Subgroups via Directed Spectral Clustering

We propose \textbf{CaSPECT}, a causal spectral clustering framework for discovering causally homogeneous subgroups from observational data. Rather than clustering in covariate space, CaSPECT defines similarity through the topology of a learned directed acyclic graph (DAG); a bootstrap-stabilised PC algorithm recovers the causal skeleton; a novel \emph{Orientation Validation Score} (OVS) combines PC bootstrap evidence with DirectLiNGAM to orient edges robustly; directed edges are weighted by backdoor-identified average treatment effects estimated via OLS or double machine learning. Chung's directed Laplacian provides a spectral embedding in which individuals close together share the same causal propagation pathways. We establish almost-sure consistency of the full pipeline and validate the method through a controlled simulation study and on LaLonde CPS1, IHDP, and 401(k) datasets, where CaSPECT recovers a positive and statistically significant treatment effect within the causally comparable subpopulation and corrects for severe confounding without requiring a pre-specified propensity score model.

Arghya Pratihar, Shinjon Chakraborty, Swagatam Das

1*Electronics and Communication Sciences Unit, Indian Statistical Institute, India. · 2Indian Statistical Institute, India.

Causal Effect Estimation Causal Structure Learning Spectral Clustering Graph Clustering Causal Inference

Jul 1, 2026stat.ML

Characterizing and Identifying Separable Graphical Models

We study a broad class of graphical models whose independencies correspond to vertex separation in mixed graphs with directed, undirected, and bidirected edges, that are capable of encoding independence structures arising from feedback, latent and selection mechanisms. In particular, we introduce separable graphs, in which each missing edge implies the existence of a separating set for its endpoints, and essentially separable graphs, those graphs separation equivalent to a separable graph. We show that these models include many existing graph families used to define graphical models an provide several characterizations of separable graphs and essentially separable graphs. We also provide multiple characterizations of separation equivalence for separable graphs. One is a graphical characterization in terms of ordinary graph properties, extending earlier results for specific subfamilies Another is a separational characterization depending only on graph separation properties. Finally, we provide a canonical representation for the equivalence classes of essentially separable graphs and develop an algorithm that, under suitable assumptions, identifies the equivalence class of any essentially separable graph.

Christopher Meek, Kayvan Sadeghi

Department of Statistics, University of Washington · Department of Statistical Science, University College London

Causal Structure Learning Probabilistic Graphical Models

Jun 30, 2026cs.CV

Additive Causal Construction for Transferable and Reconfigurable Cross-System Learning in Multi-Source Image Fusion

In multi-source image fusion scenarios, heterogeneous inputs are typically driven by distinct generative mechanisms and can be viewed as a composition of multiple causal systems. However, cross-system discrepancy (CSD) and cross-system entanglement (CSE) commonly arise during the fusion process, often leading to significant performance degradation under out-of-distribution (OOD) predictions. To address the CSD and CSE issues, we propose the additive causal construction (ACC) framework, which characterizes information fusion at two levels: firstly, it establishes causal "anchors" shared among multiple systems through intervention consistency to enable causal graph transferability (CGT); and secondly, it formalizes the fusion process as causal construction and models the reliability of constructed paths through uncertainty quantification to ensure causal graph reconfigurability (CGR). Building upon this, we revisit the traditional causal representation learning (CRL) with ACC and propose ACC-CRL as a learnable instantiation of the framework. The method explores joint causal content representations across systems via content-mechanism decoupling, and performs response alignment under shared anchors to mitigate CSD. Furthermore, it incorporates structural uncertainty to adaptively regulate the fusion process, thereby suppressing unstable CSE. We conduct systematic experiments on synthetic data (ColorMNIST) and real-world multi-center medical imaging tasks (microvascular invasion (MVI) prediction). The results demonstrate that the proposed method significantly improves OOD generalization while maintaining in-distribution (ID) performance, validating the effectiveness and robustness of the ACC-CRL strategy based on mechanism alignment and uncertainty modeling in open environments.

Zhizhong Fu, Wei Zhou, Zhaoyang Jiang +5

School of Life Science and Technology, University of Electronic Science and Technology of China, Chengdu 610054, China. · Department of Radiology, Huzhou Maternity & Child Health Care Hospital, Huzhou 313000, China. · Department of Radiology, Huzhou Maternity & Child Health Care Hospital Affiliated to Huzhou Normal University,Huzhou 313000,China. +3

Multi-Source Image Fusion Causal Representation Learning OOD Generalization Causal Structure Learning Cross-Domain Transfer Learning

Jun 26, 2026cs.LG

Disentangling Continuous-Time Latent Dynamics: Identifiability of Latent SDEs via Diffusion Shifts

Causal representation learning for time series has developed strong identifiability results in discrete-time latent causal models, but identifiability in continuous-time latent stochastic differential equation (SDE) models remains largely open. We address this gap using environment-induced shifts in diffusion covariance. We study additive-noise latent SDEs observed through an unknown nonlinear diffeomorphism, with shared drift but environment-specific diffusion covariance. We show that two diagonal diffusion regimes with pairwise distinct coordinate-wise variance ratios identify the latent coordinates up to permutation, coordinate-wise scaling, and a possible constant shift, without any sparsity assumption on the drift. We first prove this result for linear Ornstein-Uhlenbeck systems and then extend it to general additive-noise latent SDEs. Under mild smoothness, the instantaneous drift-Jacobian causal graph is identifiable up to the same permutation. We propose a two-stage estimator for latent disentanglement and optional graph recovery; experiments on synthetic systems confirm the predicted identifiability boundary, and an application to Hardanger Bridge monitoring data illustrates the approach on real sensor trajectories.

Yuanyuan Wang, Wenjie Wang, Haoxuan Li +2

Mohamed bin Zayed University of Artificial Intelligence · The University of Melbourne · Peking University +1

Stochastic Differential Equations Causal Representation Learning Representation Identifiability Parameter Identifiability Causal Structure Learning Causal Identifiability

Jun 25, 2026cs.LG

A Causal Foundation Model for Structure and Outcome Prediction

We introduce TabPFN-CFM, a causal foundation model that can handle multiple causal problems. TabPFN-CFM predicts both causal structure and outcomes from observational data, supports queries on all three levels of Pearl's Causal Hierarchy and uses known graph structure when available to improve predictions. TabPFN-CFM is trained on synthetic datasets, and generalises to real datasets, demonstrating improved performance over both structural and outcome prediction baselines.

Max Zhu, Martino Mansoldo, Ching-Hao Wang +1

University of Cambridge, United Kingdom · GSK.ai.

Causal Foundation Models Causal Structure Learning Causal Inference

Jun 21, 2026cs.CL

Words as Difference Makers: How Large Language Models Determine Causal Structure in Text

Because large language models (LLMs) are impressively successful in predicting text, it appears that they must have access to a 'world model' representing causal and definitional structure. However, the dominant formalisms of modern causal inference -- Judea Pearl's interventionist approach and the Neyman-Rubin potential outcomes framework -- struggle to illuminate how LLMs learn causal structure. I resolve this puzzle by arguing that LLMs employ a specific inductive approach based on a difference-making logic -- sometimes called variational induction. I demonstrate how central aspects of this logic are realized during training, where LLMs require enormous amounts of text data from a wide range of contexts to identify difference- and indifference-makers within word sequences. Furthermore, I analyze specific architectural features of LLMs -- such as token embeddings and self-attention -- to determine their roles in variational induction. The difference-making logic of LLMs fundamentally parallels the experimental method, where causal relations are derived by systematically varying individual circumstances to determine their influence on a phenomenon.

Wolfgang Pietsch

tum

Causal World Models LLM Interpretability Causal Structure Learning Causal Reasoning in Language Models LLM Training

Jun 19, 2026cs.LG

A Framework for Directed Acyclic Hypergraph Learning

Continuous optimization methods for learning Directed Acyclic Graphs (DAGs) operate on weighted adjacency matrices and are therefore limited to pairwise causal relationships. We propose a framework for learning Directed Acyclic Hypergraphs (DAHGs) from observational data, capturing joint parental influences that pairwise models cannot represent. Our approach rests on three components: (i) a generalized linear structural equation model (SEM) with multiplicative interaction terms whose non-zero weights correspond one-to-one with directed hyperedges; (ii) a weighted adjacency tensor representation whose acyclicity is characterized via nilpotency under the tensor t-product; and (iii) a differentiable acyclicity constraint derived through the Fourier decomposition of the t-product, which reduces tensor nilpotency to slice-wise matrix nilpotency and enables least-squares learning via the augmented Lagrangian method.

Zhiyuan Dong, Carlos Mundo-Levano, Wei Qian +2

Institute for Financial Services Analytics, University of Delaware, Newark, DE 19716, USA · Department of Electrical and Computer Engineering, University of Delaware, Newark, DE 19716, USA · Department of Applied Economics AND Statistics, University of Delaware, Newark, DE 19716, USA +1

Structural Causal Models Causal Structure Learning Hypergraph Learning

Jun 19, 2026cs.LG

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

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

Zhengkang Guan, Yikang Chen, Yi He +5

College of Computer Science and Technology Zhejiang University

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

Jun 16, 2026stat.ML

Fast Nonparametric Conditional Independence Testing via Two-Stage Regression

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

Eric V. Strobl

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

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

Jun 10, 2026cs.CV

From Prompts to Tokens: Internalizing Causal Supervision in Vision-Language Model for Multi-Image Causal Reasoning

Visual causal reasoning is essential for understanding and intervening in the physical world, requiring identification of causal variables from visual inputs and reasoning over intervention effects. Despite recent progress, large vision--language models (VLMs) remain brittle at such tasks, especially for interventional and counterfactual queries over multi-image inputs. Most existing explorations inject causal knowledge via textual prompts, leaving causal mechanisms external to model execution and limiting reliable control during inference. To address this problem, we propose BridgeVLM, which internalizes visual causal reasoning by inducing a causal graph from multi-image inputs and converting it into structured Causal Tokens executed by RAMP layers injected into the LLM decoder for causal message passing. We further introduce a unified training interface M3S for fine-grained causal supervision from different granularities (local/global level). BridgeVLM achieves 54.4% accuracy on intervention tasks on CausalVLBench (vs. 33.2% with prompt-level supervision), improves results on Causal3D from 43.6% to 49.0%, and substantially improves causal structure learning on CausalVLBench (

F_1

: 33.4%

\rightarrow

75.1%).

Haoping Yu, Yuanxi Li, Jing Ma

Department of Computer & Data Sciences, Case Western University, Cleveland, OH, US.

Visual Reasoning Causal Structure Learning Causal Reasoning in Language Models VLM Reasoning

Jun 9, 2026cs.LG

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

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

Xinyu Li, Yuanyuan Wang, Haoxuan Li +7

The University of Melbourne · MBZUAI · Peking University +4

Causal Discovery Causal Structure Learning

Jun 9, 2026cs.LG

KG-SoftMAP: Soft Knowledge-Graph Priors for Bayesian Network Structure Learning from Sparse Discrete Data

Learning Bayesian network (BN) structure from sparse discrete data is hard: when each instance records only a few variables, most variable pairs lack the joint observations needed for reliable scoring, and data-only methods recover little structure. Imperfect domain knowledge, expressible as a weighted directed knowledge graph (KG), is often available. KG-SoftMAP encodes such a KG as a finite-strength, confidence-weighted edge prior and maximizes a MAP objective that adds this logit-form prior to the BDeu score. With an informative but imperfect KG, KG-SoftMAP recovers partial directed structure even at observation rate rho=0.05, with directed F1 (DF1) of 0.19-0.32 across benchmarks. At higher observation rates within this sparse grid, DF1 reaches 0.44-0.66 at rho=0.20 and 0.46-0.64 at rho=0.40. Across the same three rates, KG-SoftMAP without the KG prior averages DF1 0.00, 0.19, and 0.21. Stress tests that corrupt, remove, or blur the KG signal, together with checks on LLM-extracted graphs beyond canonical benchmarks, show that recovery rises and falls with KG quality. On three real sparse educational datasets without ground-truth DAGs, we evaluate prediction, calibration, and KG-consistency. On Short Answer Feedback (SAF), KG-SoftMAP+VE reaches Fail-class F1 0.75 versus 0.78 for logistic regression while also providing an inspectable concept graph, calibrated Fail probabilities, and posterior queries from partially observed concept evidence. The remaining datasets sharpen the operating picture: weak heuristic KG signal leaves prediction unchanged, while an independent expert ontology moves the learned graph toward expert relatedness.

Guoliang Xu, James E. Corter

Columbia University

Graph Structure Learning Bayesian Networks Bayesian Inference Causal Structure Learning

Jun 5, 2026cs.CV

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

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

Wenhao Zhang, Ramin Ramezani, Tao Han +2

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

Causal Discovery Causal Structure Learning

Jun 4, 2026cs.LG

LLM Explainability with Counterfactual Chains and Causal Graphs

Causal graphs provide a high-level language for making mechanisms transparent. Recent work uses Large Language Models (LLMs) to recover causal graphs of external-world processes. Instead, in this paper, we use causal graphs to model LLM inference itself, providing stakeholders with a transparent view of how the model perceives and organizes high-level concepts to produce a prediction. We propose a four-phase method for constructing such graphs. Given a target LLM and a set of textual examples, our method discovers class-discriminative, human-interpretable concepts and maps each input to LLM-perceived concept states. We then introduce an MCMC-inspired counterfactual augmentation procedure that expands the sparse observational data through chains of counterfactuals. This enables stable causal discovery with

σ

-CG, yielding informative, interpretable graphs. We apply our method to three LLMs across disease diagnosis, sentiment analysis, and LLM-as-a-judge classification tasks. We evaluate the learned graphs for predictive fidelity and structural stability, and the MCMC-inspired augmentation for convergence and downstream utility. Our results show that the discovered causal graphs capture meaningful dependencies consistent with LLMs' reasoning. Together, this paper provides a foundation for concept-level explainability of LLMs.

Nirit Nussbaum-Hoffer, Nitay Calderon, Liat Ein-Dor +1

Faculty of Data and Decision Sciences, Technion · IBM Research

LLM Reasoning with Graphs LLM Interpretability Causal Structure Learning Concept-Based Explanations Causal Reasoning in Language Models Counterfactual Data Augmentation+1

Jun 4, 2026stat.ML

EML-CD: Causal Mechanism Recovery via EML Symbolic Trees in Structure Learning

Neural network (NN)-based nonlinear causal discovery methods recover DAG structure but leave each causal mechanism as a black box. Waxman et al. argued that extracting causal mechanisms from NN weights is ill-posed. We propose EML-CD, a framework that integrates the EML operator (capable of composing elementary functions from a single binary operator) into causal structure learning, with interpretable mechanism recovery as the primary objective. EML-CD represents each edge mechanism as a gated EML binary tree and automatically discovers closed-form causal equations. Analytical Jacobians can be directly computed from the output equations, enabling quantitative understanding of causal effects. On real data (Sachs protein signaling, d=11), EML-CD achieves SHD=11.2 +/- 0.4 (5-seed mean; baselines are single deterministic runs), on par with PC/GES within seed variance and below CAM, while attaching closed-form equations to each detected edge (precision 0.756, recall 0.365). In a controlled bivariate test with known mechanisms, EML-CD recovers 10 of 11 elementary function families faithfully (held-out shape correlation >= 0.96; only high-frequency sine is partial). On a symbolic synthetic benchmark, EML-CD attains a substantially lower and more stable held-out mechanism f-MSE than a fixed SINDy dictionary (mean 3.67 vs. 7644, the latter inflated by catastrophic extrapolation on one seed), although its structure recovery (SHD 14.0) only matches the dictionary and stays below specialized optimizers; on the Causal Chambers light-tunnel subset, a depth-2 model improves F1 over linear OLS-BIC (0.444 vs. 0.273).

Sota Asanuma

SoftBank Corp.

Structural Causal Models Causal Structure Learning Causal Interpretability Symbolic Regression

Jun 4, 2026cs.LG

Causal Modeling of Selection in Evolution

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

Haoyue Dai, Zeyu Tang, Peter Spirtes +1

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

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

Jun 3, 2026cs.CR

Preserving Data Privacy in Learning Causal Structure with Fully Homomorphic Encryption

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

Jian Yang, Yuan Tong, Qinbin Li +2

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

Causal Discovery Causal Structure Learning Homomorphic Encryption Privacy-Preserving ML

Jun 3, 2026cs.AI

Trivium: Temporal Regret as a First-Class Objective for Causal-Memory Controllers

Many current agentic systems and LLM pipelines correct mistakes by optimizing outcome reward. This addresses only the what of failure: when an outcome diverges from prediction, the why and when of the mismatch are not systematically logged, reviewed, or corrected, so the same error can recur episode after episode. We argue that this is a structural problem, not merely a model-capacity one. We propose long-horizon temporal regret as a first-class objective alongside outcome regret and epistemic regret over the working causal model. Temporal regret captures when failure persists: how long a miscalibrated causal model is tolerated before correction. Epistemic regret captures why failure persists: residual uncertainty or error in the working causal model. Together, the three regrets give a falsifiable account of what, why, and when a long-lived agent can fail. Modeling the agent as a stream of E episodes, we prove three conditional results under explicit causal-probing, persistence, and detectability assumptions. First, under observationally equivalent confounding, outcome-only learning cannot distinguish causal from spurious structure without an intervention channel, so temporal miscalibration can persist linearly even after outcome regret is driven to zero. Second, with a persistent causal log and budgeted probes, total probe complexity is logarithmic in the episode horizon, inducing O(log E) temporal regret. Third, under K detectable change-points, the rate extends to O(K log E). We instantiate Trivium and pre-register five falsifiable predictions. On CausalBench-Seq, Trivium follows the predicted logarithmic envelope while outcome-only baselines grow linearly. A pilot real-LLM stream provides preliminary external-validity evidence across one full E = 500 run and three E = 100 frontier-model pilots. Self-learning here means revising an external causal model, not retraining LLM weights.

Edward Y. Chang

Computer Science Stanford University

Lifelong Learning Agents Causal Structure Learning Memory-Augmented Agents

Jun 1, 2026stat.ML

Identifiable Markov Switching Models with Instantaneous Effects and Exponential Families

Temporal systems often exhibit non-stationary behaviour, such as seasonal climate variation or glucose fluctuations in patients with type-1 diabetes. One way to model non-stationarity is through discrete latent regimes, i.e., stationary segments of time. Such systems induce a Markov Switching Model (MSM), a class of Hidden Markov Models with autoregressive dependencies among latent regimes and observed variables. Identifying latent regimes is challenging in the presence of frequent regime switches and nonlinear and non-Gaussian dynamics, particularly when there are instantaneous effects between the variables, e.g., due to slow rates of measurements. In this work, we establish the identifiability of both latent regimes and regime-dependent causal structures under temporal regime dependencies, nonlinear lagged and instantaneous effects, and independent noise from the exponential family. Our identifiability theory subsumes non-temporal mixtures of causal models. Furthermore, we introduce FlowMSM, a regime detection framework that can be paired with any stationary causal discovery method to recover regime-dependent causal structures. Experiments on synthetic benchmarks and a financial economics dataset demonstrate the effectiveness of our approach to detect latent regimes and discover causal structures from non-stationary time series.

Roel Hulsman, Carles Balsells-Rodas, Sara Magliacane

University of Amsterdam · 2Adyen · 3Imperial College London +1

Time-Series Causal Discovery Regime-Switching Dynamical Systems Causal Structure Learning Causal Identifiability Non-Stationary Time Series

May 26, 2026stat.ML

Iterative Causal Discovery: Per-Edge Impossibility Certificates, Tier-Aware Oracle Queries, and the $1+K$ Lower Bound

Causal-discovery algorithms return a directed graph, yet provide no principled means of distinguishing edge directions identified by the data from those assigned without an identifying assumption. Under the standard Markov and faithfulness conditions, the observational distribution identifies only a Markov equivalence class; orientations within that class are not determined by the joint distribution and cannot be recovered from additional samples alone, but require either a functional restriction or an intervention. We introduce a protocol for observational causal discovery on continuous data that attaches to each candidate edge a discrete impossibility certificate: a RESOLVED code records the identifiability theorem under which the direction was committed, while an IMPOSSIBLE code records the failure mode together with the specific question a domain expert must answer to resolve it. The bivariate cascade is extended with five gated identifiability tiers LSNM, IGCI, Stein, MDL, and PEIT that abstain when their precondition test rejects. Two oracle primitives, the meta-hub query and the node-children query, jointly establish an upper bound of

1+K

expert interactions sufficient to recover any DAG, where

K

denotes the number of non-leaf vertices. Under an ideal-oracle assumption, the bound is met exactly on the asia, sachs, child, and alarm benchmarks.

Eichi Uehara

aflo, Inc., Tokyo, Japan

Bayesian Networks Causal Discovery Causal Structure Learning Causal Identifiability

May 24, 2026cs.LG

Evolving Causal Regulatory Networks (ECR-Net)

Modern machine learning models excel at pattern recognition but remain brittle, often failing to generalize out of distribution (OOD) because they capture spurious correlations rather than the underlying causal data-generating process. Current causal discovery methods, while powerful, typically assume a static graph structure, rendering them unable to model systems that adapt or undergo structural changes across different environments. We introduce ECR-Net, Evolving Causal Regulatory Networks, a novel, bio-inspired framework for adaptive causal mechanism discovery. Our approach models the data-generating process not as a static graph, but as a dynamic system analogous to a Gene Regulatory Network (GRN), composed of localized, recursive functions where variables can activate and inhibit one another. To discover the latent structure of this network, we employ an evolutionary search algorithm that evolves a population of candidate regulatory graphs, optimizing for a fitness function that measures how well the simulated system dynamics reconstruct the observed data. The key innovation of ECR-Net is its ability to model structural adaptation, it explicitly ingests shifts in the data's statistical properties as signals of an environmental shock. In response, the evolutionary search identifies parsimonious modifications to the causal graph topology, such as link inhibitions or activations that explain the new data regime. We posit that ECR-Net represents a new class of adaptive Structural Causal Models capable of discovering how and why a system's fundamental rules change, offering a path toward robust generalization in complex, non-stationary systems.

Govind Vallabhasseri Binish, Abdhul Ahadh, Rano Roy Kavanal +1

Structural Causal Models Causal Discovery Causal Structure Learning Dynamic Graph Learning

May 21, 2026cs.LG

Learning Causal Orderings for In-Context Tabular Prediction

In-context learning for tabular data sets strong predictive standards in observational settings; it however primarily relies on correlational structure, which becomes unreliable under distribution shift or intervention. While established methods to discover causal structure exist, they are often focused on structure identifiability and decoupled from the predictive architectures that could benefit from them. To bridge these perspectives, we study how to simultaneously infer and enforce causal structure in the form of topological variable orderings into tabular prediction. Unlike standard architectures, our model TabOrder uses causal order-constrained attention, basing predictions only on features that precede a target under a learned causal order. Similar to causal discovery methods, TabOrder learns the optimal variable ordering in an unsupervised manner through a likelihood-based objective. We justify this choice under standard functional model classes and also study how sample missingness, a common challenge in tabular data, interacts with causal direction identification. Empirically, we confirm that TabOrder recovers accurate variable orderings while addressing prediction and imputation tasks, as well as gives insight into real-world biological data under intervention.

Sascha Xu, Sarah Mameche, Jilles Vreeken

CISPA Helmholtz Center

Incomplete Data Imputation Causal Structure Learning Causal Identifiability Tabular ICL

May 19, 2026cs.LG

Score-Based Causal Discovery of Latent Variable Causal Models

Identifying latent variables and the causal structure involving them is essential across various scientific fields. While many existing works fall under the category of constraint-based methods (with e.g. conditional independence or rank deficiency tests), they may face empirical challenges such as testing-order dependency, error propagation, and choosing an appropriate significance level. These issues can potentially be mitigated by properly designed score-based methods, such as Greedy Equivalence Search (GES) (Chickering, 2002) in the specific setting without latent variables. Yet, formulating score-based methods with latent variables is highly challenging. In this work, we develop score-based methods that are capable of identifying causal structures containing causally-related latent variables with identifiability guarantees. Specifically, we show that a properly formulated scoring function can achieve score equivalence and consistency for structure learning of latent variable causal models. We further provide a characterization of the degrees of freedom for the marginal over the observed variables under multiple structural assumptions considered in the literature, and accordingly develop both exact and continuous score-based methods. This offers a unified view of several existing constraint-based methods with different structural assumptions. Experimental results validate the effectiveness of the proposed methods.

Ignavier Ng, Xinshuai Dong, Haoyue Dai +3

Carnegie Mellon University · University of California, San Diego · Mohamed bin Zayed University of Artificial Intelligence

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

May 19, 2026cs.LG

Exploiting Non-Negativity in DAG Structure Learning

This work addresses the problem of learning directed acyclic graphs (DAGs) from nodal observations generated by a linear structural equation model. DAG learning is a central task in signal processing, machine learning, and causal inference, but it remains challenging because acyclicity is a global combinatorial property. Continuous acyclicity constraints have led to important algorithmic advances by replacing the discrete DAG constraint with smooth equality constraints. However, existing formulations still involve difficult non-convex optimization landscapes and may suffer from degenerate first-order optimality conditions. Here, we restrict attention to DAGs with non-negative edge weights and exploit this additional structure to obtain a simpler characterization of acyclicity. Building on this characterization, we formulate a regularized non-negative DAG learning problem and develop an algorithm based on the method of multipliers. We further analyze the benign optimization landscape induced by non-negativity. In the population regime, we show that the true DAG is the unique global minimizer of the proposed augmented-Lagrangian formulation; moreover, the landscape contains no spurious interior stationary points, and the true DAG is the only acyclic KKT point. Numerical experiments on synthetic and real-world data show that the proposed method improves over state-of-the-art continuous DAG-learning alternatives.

Samuel Rey, Madeline navarro, Gonzalo Mateos

Dept. of Signal Theory and Communications, Universidad Rey Juan Carlos, Madrid, Spain · Dept. of Electrical and Computer Engineering, Rice University, Houston, TX 77005, USA · Dept. of Electrical and Computer Engineering, University of Rochester, Rochester, NY 14627, USA

Graph Structure Learning Structural Causal Models Causal Structure Learning Nonconvex Optimization Augmented Lagrangian Method Constrained Optimization

May 19, 2026stat.ML

A Unified Framework for Structure-Aware Clustering and Heterogeneous Causal Graph Learning

In complex multivariate systems, interactions among variables are defined by dependency structures, often encoded as directed acyclic graphs (

\text{DAGs}

). However, dependency structures can vary across subjects, and ignoring this structural heterogeneity introduces bias and obscures subpopulation-specific dependencies. To address this, we propose Directed Acyclic Graph-based Dependency Clustering via Alternating Direction Method of Multipliers (DAG-DC-ADMM), a unified framework built upon Structural Equation Modeling (SEM) that jointly learns cluster assignments and cluster-specific dependency structures. We encode acyclicity via a smooth constraint and integrate a groupwise truncated Lasso fusion penalty (gTLP) to cluster subjects based on their structural similarity. This yields a nonconvex optimization problem that incorporates sparsity, acyclicity, and structural consensus constraints. We address the nonconvexity by using the augmented Lagrangian method and solve it with an adapted version of the Alternating Direction Method of Multipliers (ADMM) for difference-of-convex programs. For certain graph structures, such as upper triangular adjacency matrices, our algorithm is guaranteed to converge to a Karush-Kuhn-Tucker (KKT) point. Experiments demonstrate that our method recovers cluster-specific causal dependency structures with a high true positive rate and a low false discovery rate. This capability enables the robust discovery of heterogeneous dependencies across subjects where the subpopulation label is unknown.

Honglin Du, Muxuan Liang, Xiang Zhong

Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL 32611, USA · Department of Biostatistics, MD Anderson Cancer Center, Houston, TX 77030, USA

Structural Causal Models Clustering Causal Discovery Causal Structure Learning Alternating Direction Method of Multipliers

May 17, 2026cs.LG

TriOpt: A Scalable Algorithm for Linear Causal Discovery

Learning causal relations from observational data is challenging because the graph search space grows super-exponentially with the number of variables. Ordering-based methods reduce this space by first identifying the topological ordering, whereas continuous optimization methods explore most likely regions of the space by casting DAG learning as a differentiable objective with an acyclicity constraint. Despite their conceptual appeal, both paradigms face significant scalability limitations in high-dimensional settings, restricting their practical applicability. In this work, we introduce a new formulation for linear causal discovery that tightly integrates these two paradigms to achieve substantial gains in scalability without sacrificing accuracy. Our approach, TriOpt, decomposes the problem into two efficient stages. First, it recovers the topological ordering by exploiting the Sherman-Morrison rank-1 downdate together with the additive structure of linear kernels, enabling fast and scalable ordering estimation. Second, given this ordering, we reformulate structure learning as a convex continuous optimization problem that entirely avoids the need for enforcing costly acyclicity constraints. We theoretically show that, under the true ordering, TriOpt exactly recovers the underlying linear DAG. Empirically, across synthetic, semi-synthetic, and real-world datasets, TriOpt achieves orders-of-magnitude speedups over state-of-the-art linear causal discovery methods in high-dimensional regimes, while maintaining comparable or superior accuracy.

Rafat Ashraf Joy, Elena Zheleva

University of Illinois Chicago

Structural Causal Models Causal Discovery Causal Structure Learning

May 14, 2026cs.LG

PACER: Acyclic Causal Discovery from Large-Scale Interventional Data

Inferring the structure of directed acyclic graphs (DAGs) from data is a central challenge in causal discovery, particularly in modern high-dimensional settings where large-scale interventional data are increasingly available. While interventional data can improve identifiability, existing methods remain limited by soft acyclicity constraints, leading to optimization over invalid cyclic graphs, numerical instability, and reduced scalability. We introduce PACER (Perturbation-driven Acyclic Causal Edge Recovery), a scalable framework for causal discovery that guarantees acyclicity by construction. PACER parameterizes a distribution over DAGs through a joint model of variable permutations and edge probabilities, enabling direct optimization over valid causal structures without surrogate penalties. The framework supports a unified likelihood-based treatment of observational and interventional data, flexible conditional density models, and the incorporation of structural prior knowledge. For linear-Gaussian mechanisms, we derive closed-form expressions for the expected interventional log-likelihood and its gradients, yielding substantial computational gains. Empirically, PACER matches or exceeds state-of-the-art methods on protein signaling and large-scale genetic perturbation benchmarks, while scaling efficiently to networks with thousands of variables and achieving up to two orders of magnitude speedups over penalty-based differentiable approaches. These results demonstrate that exact and scalable causal discovery from high-dimensional perturbation data is achievable through principled search space design.

Ramon Viñas Torné, Sílvia Fàbregas Salazar, Soyon Park +4

Swiss Federal Technology Institute of Lausanne (EPFL), Switzerland · ETH Zurich, Zurich, Switzerland · Cornell University, USA

Causal Discovery Causal Structure Learning

May 11, 2026cs.LG

A Recursive Decomposition Framework for Causal Structure Learning in the Presence of Latent Variables

Constraint-based causal discovery is widely used for learning causal structures, but heavy reliance on conditional independence (CI) testing makes it computationally expensive in high-dimensional settings. To mitigate this limitation, many divide-and-conquer frameworks have been proposed, but most assume causal sufficiency, i.e., no latent variables. In this paper, we show that divide-and-conquer strategies can be theoretically generalized beyond causal sufficiency to settings with latent variables. Specifically, we propose a recursive decomposition framework, termed DiCoLa, that enables divide-and-conquer causal discovery in the presence of latent variables. It recursively decomposes the global learning task into smaller subproblems and integrates their solutions through a principled reconstruction step to recover the global structure. We theoretically establish the soundness and completeness of the proposed framework. Extensive experiments on synthetic data demonstrate that our approach significantly improves computational efficiency across a range of causal discovery algorithms, while experiments on a real-world dataset further illustrate its practical effectiveness.

Zheng Li, Feng Xie, Shenglan Nie +3

Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China · Department of Applied Statistics, Beijing Technology and Business University, Beijing, China · College of Computer Science and Artificial Intelligence, Fudan University, Shanghai, China

Causal Discovery Causal Structure Learning Causal Discovery with Latent Confounding

May 11, 2026stat.ML

Coarsening Linear Non-Gaussian Causal Models with Cycles

Recent work on causal abstraction, in particular graphical approaches focusing on causal structure between clusters of variables, aims to summarize a high-dimensional causal structure in terms of a low-dimensional one. Existing methods for learning such summaries from data assume that both the high- and low-dimensional structures are acyclic, which is helpful for causal effect identification and reasoning but excludes many high-dimensional models and thus limits applicability. We show that in the linear non-Gaussian (LiNG) setting, the high-dimensional acyclicity assumption can be relaxed while still allowing recovery of a low-dimensional causal directed acyclic graph (DAG). We further connect identifiability of this low-dimensional DAG to existing results: LiNG models with cycles are observationally identifiable only up to an equivalence class whose members differ by reversals of directed cycles; our low-dimensional DAG, which is invariant across all members of a given equivalence class, thus forms a natural representative of the class. While existing approaches for learning this observational equivalence class over high-dimensional variables have exponential time complexity, our low-dimensional summary is learned in worst-case cubic time and comes with explicit bounds on the sample complexity. We provide open source code and experiments on synthetic data to corroborate our theoretical results.

Francisco Madaleno, Francisco C Pereira, Alex Markham

Department of Technology, Management and Economics, Technical University of Denmark · Department of Mathematical Sciences,11 University of Copenhagen

Structural Causal Models Causal Discovery Causal Structure Learning Causal Abstraction Causal Identifiability

May 8, 2026cs.LG

Mask2Cause: Causal Discovery via Adjacency Constrained Causal Attention

Leveraging deep learning for causal discovery in time series remains challenging because existing neural methods predominantly rely on component-wise architectures that fail to capture shared system dynamics or employ decoupled post-hoc graph extraction that risks overfitting to spurious correlations. We propose

\textbf{Mask2Cause}

, an end-to-end framework that recovers the underlying causal graph directly during the forecasting forward pass. Our approach introduces an Inverted Variable Embedding and an Adjacency-Constrained Masked Attention mechanism, trained with homoscedastic or heteroscedastic objectives to capture causal influences in both mean and variance. Empirical results on diverse benchmarks, from synthetic chaotic dynamics to realistic biological simulations, demonstrate state-of-the-art causal discovery with significantly reduced parameter complexity compared to standard baselines. We further show that inferred causal structures can be used to reduce parameter count of forecasting models by more than 70% on average while maintaining predictive accuracy.

Omar Muhammad, Pasupuleti Dhruv Shivkant, Deepak N. Subramani

1Indian Institute of Science, Bengaluru, India

Time-Series Causal Discovery Causal Structure Learning