The paper introduces a novel conditional independence (CI) based method for linear and nonlinear, lagged and contemporaneous causal discovery from observational time series in the causally sufficient case. Existing CI-based methods such as the PC algorithm and also common methods from other frameworks suffer from low recall and partially inflated false positives for strong autocorrelation which is an ubiquitous challenge in time series. The novel method, PCMCI$^+$, extends PCMCI [Runge et al., 2019b] to include discovery of contemporaneous links. PCMCI$^+$ improves the reliability of CI tests by optimizing the choice of conditioning sets and even benefits from autocorrelation. The method is order-independent and consistent in the oracle case. A broad range of numerical experiments demonstrates that PCMCI$^+$ has higher adjacency detection power and especially more contemporaneous orientation recall compared to other methods while better controlling false positives. Optimized conditioning sets also lead to much shorter runtimes than the PC algorithm. PCMCI$^+$ can be of considerable use in many real world application scenarios where often time resolutions are too coarse to resolve time delays and strong autocorrelation is present.
In sports analytics, home field advantage is a robust phenomenon where the home team wins more games than the away team. However, discovering the causal factors behind home field advantage presents unique challenges due to the non-stationary, time-varying environment of sports matches. In response, we propose a novel causal discovery method, DYnamic Non-stAtionary local M-estimatOrs (DYNAMO), to learn the time-varying causal structures of home field advantage. DYNAMO offers flexibility by integrating various loss functions, making it practical for learning linear and non-linear causal structures from a general class of non-stationary causal processes. By leveraging local information, we provide theoretical guarantees for the identifiability and estimation consistency of non-stationary causal structures without imposing additional assumptions. Simulation studies validate the efficacy of DYNAMO in recovering time-varying causal structures. We apply our method to high-resolution event data from the 2020-2021 and 2021-2022 English Premier League seasons, during which the former season had no audience presence. Our results reveal intriguing, time-varying, team-specific field advantages influenced by referee bias, which differ significantly with and without crowd support. Furthermore, the time-varying causal structures learned by our method improve goal prediction accuracy compared to existing methods.
Causal discovery algorithms typically recover causal graphs only up to their Markov equivalence classes unless additional parametric assumptions are made. The sizes of these equivalence classes reflect the limits of what can be learned about the underlying causal graph from purely observational data. Under the assumptions of acyclicity, causal sufficiency, and a uniform model prior, Markov equivalence classes are known to be small on average. In this paper, we show that this is no longer the case when any of these assumptions is relaxed. Specifically, we prove exponentially large lower bounds for the expected size of Markov equivalence classes in three settings: sparse random directed acyclic graphs, uniformly random acyclic directed mixed graphs, and uniformly random directed cyclic graphs.
This paper presents an evaluation framework for agentic AI systems in mission-critical negotiation contexts, addressing the need for AI agents that can adapt to diverse human operators and stakeholders. Using Sotopia as a simulation testbed, we present two experiments that systematically evaluated how personality traits and AI agent characteristics influence LLM-simulated social negotiation outcomes--a capability essential for a variety of applications involving cross-team coordination and civil-military interactions. Experiment 1 employs causal discovery methods to measure how personality traits impact price bargaining negotiations, through which we found that Agreeableness and Extraversion significantly affect believability, goal achievement, and knowledge acquisition outcomes. Sociocognitive lexical measures extracted from team communications detected fine-grained differences in agents' empathic communication, moral foundations, and opinion patterns, providing actionable insights for agentic AI systems that must operate reliably in high-stakes operational scenarios. Experiment 2 evaluates human-AI job negotiations by manipulating both simulated human personality and AI system characteristics, specifically transparency, competence, adaptability, demonstrating how AI agent trustworthiness impact mission effectiveness. These findings establish a repeatable evaluation methodology for experimenting with AI agent reliability across diverse operator personalities and human-agent team dynamics, directly supporting operational requirements for reliable AI systems. Our work advances the evaluation of agentic AI workflows by moving beyond standard performance metrics to incorporate social dynamics essential for mission success in complex operations.
Discovering pure causes or driver variables in deterministic LTI systems is of vital importance in the data-driven reconstruction of causal networks. A recent work by Kathari and Tangirala, proposed in 2022, formulated the causal discovery method as a constraint identification problem. The constraints are identified using a dynamic iterative PCA (DIPCA)-based approach for dynamical systems corrupted with Gaussian measurement errors. The DIPCA-based method works efficiently for dynamical systems devoid of any algebraic relations. However, several dynamical systems operate under feedback control and/or are coupled with conservation laws, leading to differential-algebraic (DAE) or mixed causal systems. In this work, a method, namely the partition of variables (PoV), for causal discovery in LTI-DAE systems is proposed. This method is superior to the method that was presented by Kathari and Tangirala (2022), as PoV also works for pure dynamical systems, which are devoid of algebraic equations. The proposed method identifies the causal drivers up to a minimal subset. PoV deploys DIPCA to first determine the number of algebraic relations ($n_a$), the number of dynamical relations ($n_d$) and the constraint matrix. Subsequently, the subsets are identified through an admissible partitioning of the constraint matrix by finding the condition number of it. Case studies are presented to demonstrate the effectiveness of the proposed method.
In this note, we extend the conditional local independence testing theory developed in Christgau et al. (2024) to Ito processes. The result can be applied to causal discovery in dynamic systems.
Kernel-based hypothesis tests offer a flexible, non-parametric tool to detect high-order interactions in multivariate data, beyond pairwise relationships. Yet the scalability of such tests is limited by the computationally demanding permutation schemes used to generate null approximations. Here we introduce a family of permutation-free high-order tests for joint independence and partial factorisations of $d$ variables. Our tests eliminate the need for permutation-based approximations by leveraging V-statistics and a novel cross-centring technique to yield test statistics with a standard normal limiting distribution under the null. We present implementations of the tests and showcase their efficacy and scalability through synthetic datasets. We also show applications inspired by causal discovery and feature selection, which highlight both the importance of high-order interactions in data and the need for efficient computational methods.
Dynamic causal discovery in wireless networks is essential due to evolving interference, fading, and mobility, which complicate traditional static causal models. This paper addresses causal inference challenges in dynamic fading wireless environments by proposing a sequential regression-based algorithm with a novel application of the NOTEARS acyclicity constraint, enabling efficient online updates. We derive theoretical lower and upper bounds on the detection delay required to identify structural changes, explicitly quantifying their dependence on network size, noise variance, and fading severity. Monte Carlo simulations validate these theoretical results, demonstrating linear increases in detection delay with network size, quadratic growth with noise variance, and inverse-square dependence on the magnitude of structural changes. Our findings provide rigorous theoretical insights and practical guidelines for designing robust online causal inference mechanisms to maintain network reliability under nonstationary wireless conditions.
Inferring causal relationships between variable pairs is crucial for understanding multivariate interactions in complex systems. Knowledge-based causal discovery -- which involves inferring causal relationships by reasoning over the metadata of variables (e.g., names or textual context) -- offers a compelling alternative to traditional methods that rely on observational data. However, existing methods using Large Language Models (LLMs) often produce unstable and inconsistent results, compromising their reliability for causal inference. To address this, we introduce a novel approach that integrates Knowledge Graphs (KGs) with LLMs to enhance knowledge-based causal discovery. Our approach identifies informative metapath-based subgraphs within KGs and further refines the selection of these subgraphs using Learning-to-Rank-based models. The top-ranked subgraphs are then incorporated into zero-shot prompts, improving the effectiveness of LLMs in inferring the causal relationship. Extensive experiments on biomedical and open-domain datasets demonstrate that our method outperforms most baselines by up to 44.4 points in F1 scores, evaluated across diverse LLMs and KGs. Our code and datasets are available on GitHub: https://github.com/susantiyuni/path-to-causality
Inferring cause-effect relationships from observational data has gained significant attention in recent years, but most methods are limited to scalar random variables. In many important domains, including neuroscience, psychology, social science, and industrial manufacturing, the causal units of interest are groups of variables rather than individual scalar measurements. Motivated by these applications, we extend nonlinear additive noise models to handle random vectors, establishing a two-step approach for causal graph learning: First, infer the causal order among random vectors. Second, perform model selection to identify the best graph consistent with this order. We introduce effective and novel solutions for both steps in the vector case, demonstrating strong performance in simulations. Finally, we apply our method to real-world assembly line data with partial knowledge of causal ordering among variable groups.
The importance of clinical variables in the prognosis of the disease is explained using statistical correlation or machine learning (ML). However, the predictive importance of these variables may not represent their causal relationships with diseases. This paper uses clinical variables from a heart failure (HF) patient cohort to investigate the causal explainability of important variables obtained in statistical and ML contexts. Due to inherent regression modeling, popular causal discovery methods strictly assume that the cause and effect variables are numerical and continuous. This paper proposes a new computational framework to enable causal structure discovery (CSD) and score the causal strength of mixed-type (categorical, numerical, binary) clinical variables for binary disease outcomes. In HF classification, we investigate the association between the importance rank order of three feature types: correlated features, features important for ML predictions, and causal features. Our results demonstrate that CSD modeling for nonlinear causal relationships is more meaningful than its linear counterparts. Feature importance obtained from nonlinear classifiers (e.g., gradient-boosting trees) strongly correlates with the causal strength of variables without differentiating cause and effect variables. Correlated variables can be causal for HF, but they are rarely identified as effect variables. These results can be used to add the causal explanation of variables important for ML-based prediction modeling.
Robust causal discovery in time series datasets depends on reliable benchmark datasets with known ground-truth causal relationships. However, such datasets remain scarce, and existing synthetic alternatives often overlook critical temporal properties inherent in real-world data, including nonstationarity driven by trends and seasonality, irregular sampling intervals, and the presence of unobserved confounders. To address these challenges, we introduce TimeGraph, a comprehensive suite of synthetic time-series benchmark datasets that systematically incorporates both linear and nonlinear dependencies while modeling key temporal characteristics such as trends, seasonal effects, and heterogeneous noise patterns. Each dataset is accompanied by a fully specified causal graph featuring varying densities and diverse noise distributions and is provided in two versions: one including unobserved confounders and one without, thereby offering extensive coverage of real-world complexity while preserving methodological neutrality. We further demonstrate the utility of TimeGraph through systematic evaluations of state-of-the-art causal discovery algorithms including PCMCI+, LPCMCI, and FGES across a diverse array of configurations and metrics. Our experiments reveal significant variations in algorithmic performance under realistic temporal conditions, underscoring the need for robust synthetic benchmarks in the fair and transparent assessment of causal discovery methods. The complete TimeGraph suite, including dataset generation scripts, evaluation metrics, and recommended experimental protocols, is freely available to facilitate reproducible research and foster community-driven advancements in time-series causal discovery.
The field of hypothesis generation promises to reduce costs in neuroscience by narrowing the range of interventional studies needed to study various phenomena. Existing machine learning methods can generate scientific hypotheses from complex datasets, but many approaches assume causal relationships are static over time, limiting their applicability to systems with dynamic, state-dependent behavior, such as the brain. While some techniques attempt dynamic causal discovery through factor models, they often restrict relationships to linear patterns or impose other simplifying assumptions. We propose a novel method that models dynamic graphs as a conditionally weighted superposition of static graphs, where each static graph can capture nonlinear relationships. This approach enables the detection of complex, time-varying interactions between variables beyond linear limitations. Our method improves f1-scores of predicted dynamic causal patterns by roughly 22-28% on average over baselines in some of our experiments, with some improvements reaching well over 60%. A case study on real brain data demonstrates our method's ability to uncover relationships linked to specific behavioral states, offering valuable insights into neural dynamics.
We hypothesize that optimal system responses emerge from adaptive strategies grounded in causal and counterfactual knowledge. Counterfactual inference allows us to create hypothetical scenarios to examine the effects of alternative system responses. We enhance this process through causal discovery, which identifies the strategies informed by the underlying causal structure that govern system behaviors. Moreover, we consider the psychological constructs and unobservable noises that might be influencing user-system interactions as latent factors. We show that these factors can be effectively estimated. We employ causal discovery to identify strategy-level causal relationships among user and system utterances, guiding the generation of personalized counterfactual dialogues. We model the user utterance strategies as causal factors, enabling system strategies to be treated as counterfactual actions. Furthermore, we optimize policies for selecting system responses based on counterfactual data. Our results using a real-world dataset on social good demonstrate significant improvements in persuasive system outcomes, with increased cumulative rewards validating the efficacy of causal discovery in guiding personalized counterfactual inference and optimizing dialogue policies for a persuasive dialogue system.
AI agents that leverage Large Language Models (LLMs) are increasingly becoming core building blocks of modern software systems. A wide range of frameworks is now available to support the specification of such applications. These frameworks enable the definition of agent setups using natural language prompting, which specifies the roles, goals, and tools assigned to the various agents involved. Within such setups, agent behavior is non-deterministic for any given input, highlighting the critical need for robust debugging and observability tools. In this work, we explore the use of process and causal discovery applied to agent execution trajectories as a means of enhancing developer observability. This approach aids in monitoring and understanding the emergent variability in agent behavior. Additionally, we complement this with LLM-based static analysis techniques to distinguish between intended and unintended behavioral variability. We argue that such instrumentation is essential for giving developers greater control over evolving specifications and for identifying aspects of functionality that may require more precise and explicit definitions.
Cross-Domain Recommendation (CDR) aims to leverage knowledge from a relatively data-richer source domain to address the data sparsity problem in a relatively data-sparser target domain. While CDR methods need to address the distribution shifts between different domains, i.e., cross-domain distribution shifts (CDDS), they typically assume independent and identical distribution (IID) between training and testing data within the target domain. However, this IID assumption rarely holds in real-world scenarios due to single-domain distribution shift (SDDS). The above two co-existing distribution shifts lead to out-of-distribution (OOD) environments that hinder effective knowledge transfer and generalization, ultimately degrading recommendation performance in CDR. To address these co-existing distribution shifts, we propose a novel Causal-Invariant Cross-Domain Out-of-distribution Recommendation framework, called CICDOR. In CICDOR, we first learn dual-level causal structures to infer domain-specific and domain-shared causal-invariant user preferences for tackling both CDDS and SDDS under OOD environments in CDR. Then, we propose an LLM-guided confounder discovery module that seamlessly integrates LLMs with a conventional causal discovery method to extract observed confounders for effective deconfounding, thereby enabling accurate causal-invariant preference inference. Extensive experiments on two real-world datasets demonstrate the superior recommendation accuracy of CICDOR over state-of-the-art methods across various OOD scenarios.
Deep learning models trained on extensive Electronic Health Records (EHR) data have achieved high accuracy in diagnosis prediction, offering the potential to assist clinicians in decision-making and treatment planning. However, these models lack two crucial features that clinicians highly value: interpretability and interactivity. The ``black-box'' nature of these models makes it difficult for clinicians to understand the reasoning behind predictions, limiting their ability to make informed decisions. Additionally, the absence of interactive mechanisms prevents clinicians from incorporating their own knowledge and experience into the decision-making process. To address these limitations, we propose II-KEA, a knowledge-enhanced agent-driven causal discovery framework that integrates personalized knowledge databases and agentic LLMs. II-KEA enhances interpretability through explicit reasoning and causal analysis, while also improving interactivity by allowing clinicians to inject their knowledge and experience through customized knowledge bases and prompts. II-KEA is evaluated on both MIMIC-III and MIMIC-IV, demonstrating superior performance along with enhanced interpretability and interactivity, as evidenced by its strong results from extensive case studies.
Causal discovery for dynamical systems poses a major challenge in fields where active interventions are infeasible. Most methods used to investigate these systems and their associated benchmarks are tailored to deterministic, low-dimensional and weakly nonlinear time-series data. To address these limitations, we present CausalDynamics, a large-scale benchmark and extensible data generation framework to advance the structural discovery of dynamical causal models. Our benchmark consists of true causal graphs derived from thousands of coupled ordinary and stochastic differential equations as well as two idealized climate models. We perform a comprehensive evaluation of state-of-the-art causal discovery algorithms for graph reconstruction on systems with noisy, confounded, and lagged dynamics. CausalDynamics consists of a plug-and-play, build-your-own coupling workflow that enables the construction of a hierarchy of physical systems. We anticipate that our framework will facilitate the development of robust causal discovery algorithms that are broadly applicable across domains while addressing their unique challenges. We provide a user-friendly implementation and documentation on https://kausable.github.io/CausalDynamics.
Causal discovery in multi-omic datasets is crucial for understanding the bigger picture of gene regulatory mechanisms, but remains challenging due to high dimensionality, differentiation of direct from indirect relationships, and hidden confounders. We introduce GENESIS (GEne Network inference from Expression SIgnals and SNPs), a constraint-based algorithm that leverages the natural causal precedence of genotypes to infer ancestral relationships in transcriptomic data. Unlike traditional causal discovery methods that start with a fully connected graph, GENESIS initialises an empty ancestrality matrix and iteratively populates it with direct, indirect or non-causal relationships using a series of provably sound marginal and conditional independence tests. By integrating genotypes as fixed causal anchors, GENESIS provides a principled ``head start'' to classical causal discovery algorithms, restricting the search space to biologically plausible edges. We test GENESIS on synthetic and real-world genomic datasets. This framework offers a powerful avenue for uncovering causal pathways in complex traits, with promising applications to functional genomics, drug discovery, and precision medicine.
We use a deep Koopman operator-theoretic formalism to develop a novel causal discovery algorithm, Kausal. Causal discovery aims to identify cause-effect mechanisms for better scientific understanding, explainable decision-making, and more accurate modeling. Standard statistical frameworks, such as Granger causality, lack the ability to quantify causal relationships in nonlinear dynamics due to the presence of complex feedback mechanisms, timescale mixing, and nonstationarity. This presents a challenge in studying many real-world systems, such as the Earth's climate. Meanwhile, Koopman operator methods have emerged as a promising tool for approximating nonlinear dynamics in a linear space of observables. In Kausal, we propose to leverage this powerful idea for causal analysis where optimal observables are inferred using deep learning. Causal estimates are then evaluated in a reproducing kernel Hilbert space, and defined as the distance between the marginal dynamics of the effect and the joint dynamics of the cause-effect observables. Our numerical experiments demonstrate Kausal's superior ability in discovering and characterizing causal signals compared to existing approaches of prescribed observables. Lastly, we extend our analysis to observations of El Ni\~no-Southern Oscillation highlighting our algorithm's applicability to real-world phenomena. Our code is available at https://github.com/juannat7/kausal.