Causal Discovery

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.

This paper studies causal discovery in irregularly sampled time series—a key challenge in risk-sensitive domains like finance, healthcare, and climate science, where missing data and inconsistent sampling frequencies distort causal mechanisms. The main challenge comes from the interdependence between missing data imputation and causal structure recovery: errors in imputation and structure learning can reinforce each other, leading to an inaccurate causal graph. Existing methods either impute first and then discover, or jointly optimize both via neural representation learning, but lack explicit mechanisms to ensure mutual consistency of imputation and structure learning. We address this challenge with ReTimeCausal, an EM-based framework that alternates between imputation and structure learning, which encourages structural consistency throughout the optimization process. Our framework provides theoretical consistency guarantees for structure recovery and extends classical results to settings with irregular sampling and high missingness. ReTimeCausal combines kernel-based sparse regression and structural constraints in an alternating process that updates the completed data and the causal graph in turn. Experiments on synthetic and real-world datasets show that ReTimeCausal is more effective than existing methods under challenging irregular sampling and missing data.

This paper proposes a power-enhanced panel Granger causality test (PE-PGCT) for assessing the Granger non-causality in heterogeneous and potentially high-dimensional panel data. Building on any existing panel Granger non-causality test, we show, both theoretically and empirically, that the proposed PE-PGCT boosts its power substantially. The power gains are particularly significant in situations of high-dimensional panels when the cross-sectional dimension exceeds the time dimension, as well as under sparse alternatives when the signals are sparsely distributed across panel units. We establish rigorous theoretical guarantees on the asymptotic behavior of the proposed power enhancement component, demonstrating attractive power enhancement properties that it induces negligible size distortion under the null hypothesis while delivering significant power gain under the alternatives. The empirical performances are illustrated via extensive simulation studies, as well as a real-world application.

Learning causal relationships between variables from data is a fundamental research area with many applications across disciplines. Most of the existing causal discovery algorithms rely on the assumptions that (i) the underlying system is acyclic, (ii) the exogenous noise variables are Gaussian, and (iii) that the intervention targets for the data generating experiments are known. While these assumptions simplify the analysis, they are violated in real-life systems. Most existing methods that address these issues either assume the underlying model is linear or are constrained to operate in limited interventional settings. To that end, we propose SCOUT, a novel causal discovery framework to learn nonlinear causal cyclic relationships from soft interventional data with unknown targets. Our main approach maximizes the data log-likelihood to recover the graph structure, using two normalizing-flow architectures—contractive residual flows and neural spline flows. By conducting experiments on synthetic and real-world data, we show that SCOUT outperforms state-of-the-art methods in both causal graph and unknown target recovery across various interventional and noise settings.

Generating realistic adversarial examples for tabular data remains challenging due to heterogeneous feature types and asymmetric inter-feature dependencies. Existing approaches typically rely on handcrafted constraints or undirected similarity criteria to delimit the feasible attack region, which often fail to capture the structural dependency governing tabular generation. Consequently, standard attacks typically produce perturbations that are statistically likely yet semantically inconsistent and prone to optimization stagnation via gradient masking. To address this, we propose LCSA, a white-box framework that formulates adversarial generation as optimization over structurally admissible perturbations. LCSA leverages an ensemble of heterogeneous neural Structural Causal Models to infer dependencies and introduces a structure-aware ripple mechanism. Unlike attacks that perturb features in isolation, this mechanism propagates updates downstream, acting as a structural preconditioner that conditions gradient flow to mitigate masking effects. Extensive experiments demonstrate that LCSA outperforms state-of-the-art baselines in 45 of 50 evaluated configurations, yielding adversarial examples with superior structural consistency and transferability.

Causal effect estimation is a fundamental task in many scientific fields. Selecting appropriate covariates for adjustment is crucial for obtaining unbiased causal effects. However, most existing methods either rely on learning the global causal structure, assume the absence of latent variables, or impose the pretreatment assumption-restricts covariates to those unaffected by the treatment or outcome. These assumptions are often unrealistic in real-world scenarios, and global structure learning can be computationally intensive and inefficient. To address these challenges, we first characterize the local existence boundary of adjustment sets for causal effect estimation. Based on this characterization, we develop a novel local learning method for covariate selection in nonparametric causal effect estimation. This method accommodates the presence of latent variables and eliminates the need for the pretreatment assumption. We prove that the proposed method is both sound and complete under standard assumptions. Its effectiveness is validated through extensive experiments on both synthetic and real-world datasets.

Patient-level sepsis prediction requires models that track clinical deterioration over time and integrate heterogeneous structured evidence from electronic health records. We present PathwayLLM, a trajectory-based framework that grounds prediction on temporal signals, graph-structured evidence, and pathway-level clinical information derived from statistical dependency discovery. PathwayLLM follows a three-stage design. First, each observation window is encoded from multiple structured views, including physiological measurements, temporal dynamics, a heterogeneous patient-diagnosis-medication graph, and dependency-derived pathway signals. Second, these representations are injected into a pretrained language model as auxiliary contextual embeddings so that risk prediction and evidence-conditioned explanations can be learned jointly. Third, a Clinical Trajectory LSTM with Deterioration Attention aggregates window-level representations to highlight critical deterioration points and produce patient-level risk scores. On MIMIC-IV (15,410 ICU patients; 8.45% sepsis prevalence), PathwayLLM achieves AUROC 0.891 and AUPRC 0.724, outperforming strong time-series and pretrained baselines. External validation on eICU achieves AUROC 0.842 zero-shot and 0.867 after light fine-tuning. Ablation studies indicate that trajectory aggregation and structured clinical signals are key contributors, and clinician review suggests coherent, interpretable, and clinically relevant explanations.

Modern high-throughput biological datasets containing thousands of perturbations enable large-scale discovery of causal graphs that represent regulatory interactions between genes. Differentiable causal graphical models and regression-based methods have been developed to infer gene regulatory networks (GRNs) from interventional datasets. However, existing approaches fail to capture the non-linear dynamics of biological processes such as cellular differentiation. To address this limitation, we propose $\textit{PerturbODE}$, a novel framework that employs interpretable neural ordinary differential equations (neural ODEs) to model cell state trajectories under perturbations and derive the underlying causal GRN from the neural ODE parameters, enabling downstream simulation of unseen genetic interventions. The GRN is encoded via a single-hidden-layer feedforward network, implicitly grouping genes into interpretable co-regulated modules. We demonstrate PerturbODE's efficacy in GRN inference and extension to perturbation response prediction across both simulated and real overexpression datasets.

To distinguish Markov equivalent graphs in causal discovery, it is necessary to restrict the structural causal model. A flexible class of models that is general and identifiable in most cases are location-scale noise models (LSNMs), in which the effect $Y$ is modeled based on its causes $\boldsymbol{X}$ as $Y = f(\boldsymbol{X}) + g(\boldsymbol{X})N$. To facilitate the estimation of these models, a prominent assumption is that the noise variable $N$ follows a symmetric distribution. We show that when $N$ is a skewed random variable, which is likely in real-world domains, such approaches drop in performance. To address this limitation, we propose SkewD, a likelihood-based method for causal discovery under LSNMs with skewed noise, employing a combination of heuristic search and expectation conditional maximization for parameter estimation. SkewD extends the usual normal distribution framework to the skew-normal setting, enabling reliable inference under symmetric and skewed noise. While our main focus is on bivariate cause-effect inference, we further showcase how SkewD can be extended to the multivariate setting.

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.

Causal Abstraction (CA) theory provides a principled framework for relating causal models that describe the same system at different levels of granularity while ensuring interventional consistency between them. Recent methods for learning CAs, however, assume fixed and well-specified exogenous distributions, leaving them vulnerable to environmental shifts and model misspecification. In this work, we address these limitations by introducing the first class of distributionally robust CAs and their associated learning algorithms. The latter cast robust causal abstraction learning as a constrained min-max optimization problem with Wasserstein ambiguity sets. We provide theoretical guarantees for both empirical and Gaussian environments, enabling principled selection of ambiguity-set radii and establish quantitative guarantees on worst-case abstraction error. Furthermore, we present empirical evidence across different problems and CA learning methods, demonstrating our framework’s robustness not only to environmental shifts but also to structural and intervention mapping misspecification.

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 is the most 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.

Latent or continuous chain-of-thought methods replace explicit textual rationales with a number of internal latent steps, but these intermediate computations are difficult to evaluate beyond correlation-based probes. In this paper, we view latent chain-of-thought as a manipulable causal process in representation space by modeling latent steps as variables in a structural causal model (SCM) and analyzing their effects through step-wise $\mathrm{do}$-interventions. We study two representative paradigms (i.e., Coconut and CODI) on both mathematical and general reasoning tasks to investigate three key questions: (1) which steps are causally necessary for correctness and when answers become decodable early; (2) how influence propagates across steps and how this structure compares to explicit CoT; and (3) whether intermediate trajectories retain competing answer modes and how output-level commitment differs from representational commitment across steps. We find that latent-step budgets behave less like homogeneous extra depth and more like staged functionality with non-local routing, and we identify a persistent gap between early output bias and late representational commitment. These results motivate mode-conditional and stability-aware analyses, together with corresponding training/decoding objectives, as more reliable tools for interpreting and improving latent reasoning systems. Code is available at https://github.com/J1mL1/causal-latent-cot.

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.

In this paper, we present a novel federated independence testing (FedIT) method that addresses both theoretical and practical challenges arising from client heterogeneity. We begin by revisiting existing federated independence testing methods and showing why they fail to provide valid guarantees or maintain statistical power under data distributional shift across clients. Building on this analysis, we develop a copula-based marginal alignment technique together with a stacking-based aggregation strategy that amplifies intra-client dependence while mitigating inter-client variation, resulting in a theoretically sound and powerful global test. For practicality, we further accelerate the aggregation step and incorporate a privacy-preserving mechanism. On the theoretical side, we prove both the correctness of our method and the validity of the test. Empirically, we conduct extensive experiments on both synthetic and real-world datasets, which demonstrate the superiority of our solution over existing methods.

We study the problem of recovering the parameters of a multivariate Ornstein–Uhlenbeck (OU) process from steady-state observational and interventional data. In many applications, such as large-scale gene perturbation experiments, only stationary “snapshot” measurements are available, making standard stochastic differential equation estimation methods that rely on time-series trajectories inapplicable. We first establish an identifiability result: one intervention per strongly connected component (SCC) of the drift graph suffices to recover all OU process parameters generically up to a global scaling factor. This holds provided that the SCC condensation graph is connected with a single root and certain spectral nondegeneracy assumptions hold. We propose a recursive learning algorithm that orders SCCs topologically and, for each component, isolates its marginal dynamics and solves a linear system derived from the steady-state moment equations, leveraging parameters recovered for upstream components. Building on this theoretical foundation, we propose a regularized least-squares estimator that jointly minimizes residuals of the steady-state mean and covariance equations across observational and interventional data. Experiments on synthetic and real datasets demonstrate the effectiveness of our method in recovering parameters and predicting unseen interventions.

Identifying temporal causal structure is fundamental to understanding complex systems. Neural Granger causality has emerged as a powerful paradigm for this task, leveraging the expressiveness of neural networks to model intricate nonlinear dynamics. Although complex architectures excel at predictive modeling, existing methods typically rely on simple local measures for causal discovery, which extract only partial information from the learned model and may miss global dependencies. To address this issue, we reformulate Granger causality as a feature attribution problem and propose the Information-Theoretic Shapley value (Info-Shap) to measure global feature importance. We first establish the theoretical equivalence between zero Info-Shap and Granger non-causality. On top of this, we construct two novel regularizers to suppress spurious relationships and mitigate overfitting. These regularizers are model-agnostic and can be seamlessly integrated into the training of any differentiable neural network. Through extensive experiments on synthetic and realistic datasets, we demonstrate that our method robustly recovers the underlying causal relationships, providing a flexible tool for causal discovery in high-dimensional nonlinear time series.

We study causal discovery from soft interventions in the presence of latent confounding. Beyond within-environment conditional independences, soft interventions induce cross-environment invariances that can be encoded using an augmented graph with intervention indicator nodes ($\mathcal{I}$-AUG). Taking its maximal ancestral graph (MAG) yields the $\mathcal{I}$-MAG, which characterizes the interventional Markov equivalence class. Building on this framework, we show that the FCI-inspired learner ($\mathcal{I}$-FCI) by Kocaoglu et al. (2019) is sound but not complete: it may output circle endpoints that are nevertheless compelled by the interventional equivalence class. To exploit intervention-node semantics, we propose two complementary methods. First, we introduce an enumeration-based completion procedure that is sound and theoretically complete, but whose worst-case cost depends on the number of MAGs compatible with the partial graph learned by $\mathcal{I}$-FCI. Second, we derive a set of additional local orientation rules that provably tighten $\mathcal{I}$-FCI without increasing asymptotic complexity. Both methods refine prior outputs in the controlled soft-intervention setting with latent variables.

Federated causal discovery for time series is becoming increasingly important in many application domains. In practice, intervention policies on each client often change over time, causing the local underlying causal mechanisms to drift rather than remain fixed. Moreover, different sampling frequencies across clients yield incompatible time scales in the observed data, making the resulting local causal graphs naturally heterogeneous and difficult to aggregate consistently. Accordingly, we propose Fed-CAW, a Credibility-Aware Weighting Federated causal discovery framework for time series. Specifically, we define edge-level credibility scores that quantify per-edge reliability by summarizing (i) within-client temporal stability across windows and (ii) cross-client temporal consistency after mapping heterogeneous sampling frequencies onto a unified time scale. We then aggregate privatized edge statistics under differential privacy, treating credibility scores as weights to recover a global causal graph while preserving personalized local structures without sharing raw data. Theoretically, we demonstrate the rationale for the unified time scale mapping and establish rigorous differential privacy guarantees. Experimental results on synthetic and real-world datasets demonstrate the effectiveness of our proposed method.

Causal inference in spatial domains faces two intertwined challenges: (1) unmeasured spatial factors, such as weather, air pollution, or mobility, that confound treatment and outcome, and (2) interference from nearby treatments that violate standard no-interference assumptions. While existing methods typically address one by assuming away the other, we show they are deeply connected: *interference reveals structure* in the latent confounder. Leveraging this insight, we propose the **Spatial Deconfounder**, a two-stage method that reconstructs a substitute confounder from local treatment vectors using a conditional variational autoencoder (C-VAE) with a spatial prior, then estimates causal effects with a flexible outcome model. We show that this enables nonparametric identification of direct and spillover effects under weak assumptions—without multiple treatment types or a known latent-field model. Empirically, we extend SpaCE, a benchmark suite for spatial confounding, to include treatment interference, and show that the Spatial Deconfounder consistently improves effect estimation across real-world environmental health and social science datasets. By turning local interference into a multi-cause proxy for latent spatial confounding, our framework advances robust causal inference for spatial data.