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Causal learning from observational data is an important scientific endeavor, but the statistical and computational challenges posed by the high-dimensionality of many modern datasets are substantial. Peculiarities such as spurious correlations, endogeneity, noise accumulation, and deflated empirical covariance estimation complicate analysis. These issues may lead to confounding bias, which can be misleading when attempting to learn the true causal relationships and causal effects between variables. In this survey, we provide a comprehensive review of causal analysis and the theory behind high-dimensionality. We discuss the effects of high-dimensionality on causal estimation methods and their corresponding solutions. Finally, we present evaluation metrics and software tools for both causal effect estimation and causal discovery.

Causality, the science of cause and effect, has made it possible to create a new family of models. Such models are often referred to as causal models. Unlike those of mathematical, numerical, empirical, or machine learning (ML) nature, causal models hope to tie the cause(s) to the effect(s) pertaining to a phenomenon (i.e., data generating process) through causal principles. This paper presents one of the first works at creating causal models in the area of structural and construction engineering. To this end, this paper starts with a brief review of the principles of causality and then adopts four causal discovery algorithms, namely, PC (Peter-Clark), FCI (fast causal inference), GES (greedy equivalence search), and GRaSP (greedy relaxation of the sparsest permutation), have been used to examine four phenomena, including predicting the load-bearing capacity of axially loaded members, fire resistance of structural members, shear strength of beams, and resistance of walls against impulsive (blast) loading. Findings from this study reveal the possibility and merit of discovering complete and partial causal models. Finally, this study also proposes two simple metrics that can help assess the performance of causal discovery algorithms.

Abstract Causal relationships play an irreplaceable role in revealing the mechanisms of phenomena and guiding intervention actions. However, due to limitations in existing frameworks regarding model representations and learning algorithms, only a few studies have explored causal discovery on non-Euclidean data. In this paper, we address the issue by proposing a causal mapping process based on coordinate representations for heterogeneous non-Euclidean data. We propose a data generation mechanism between the parent nodes and the child nodes and create a causal mechanism based on multi-dimensional tensor regression. Furthermore, within the aforementioned theoretical framework, we propose a two-stage causal discovery approach based on regularized generalized canonical correlation analysis. Using the discrete representation in the shared projection direction, causal relationships between heterogeneous non-Euclidean variables can be discovered more accurately. Finally, empirical research is conducted on real-world industrial sensor data, which demonstrates the effectiveness of the proposed method for discovering causal relationships in heterogeneous non-Euclidean data.

Abstract Developing machine learning (ML) methods for healthcare predictive modeling requires absolute explainability and transparency to build trust and accountability. Graphical models (GM) are key tools for this but face challenges like small sample sizes, mixed variables, and latent confounders. This paper presents a novel learning framework addressing these challenges by integrating latent variables using fast causal inference (FCI), accommodating mixed variables with predictive permutation conditional independence tests (PPCIT), and employing a systematic graphical embedding approach leveraging expert knowledge. This method ensures a transparent model structure and an explainable feature selection and modeling approach, achieving competitive prediction performance. For real-world validation, data of hospital-acquired pressure injuries (HAPI) among individuals with spinal cord injury (SCI) were used, where the approach achieved a balanced accuracy of 0.941 and an AUC of 0.983, outperforming most benchmarks. The PPCIT method also demonstrated superior accuracy and scalability over other benchmarks in causal discovery validation on synthetic datasets that closely resemble our real dataset. This holistic framework effectively addresses the challenges of mixed variables and explainable predictive modeling for disease onset, which is crucial for enabling transparency and interpretability in ML-based healthcare.

Live-cell microscopy routinely provides massive amounts of time-lapse images of complex cellular systems under various physiological or therapeutic conditions. However, this wealth of data remains difficult to interpret in terms of causal effects. Here, we describe CausalXtract, a flexible computational pipeline that discovers causal and possibly time-lagged effects from morphodynamic features and cell–cell interactions in live-cell imaging data. CausalXtract methodology combines network-based and information-based frameworks, which is shown to discover causal effects overlooked by classical Granger and Schreiber causality approaches. We showcase the use of CausalXtract to uncover novel causal effects in a tumor-on-chip cellular ecosystem under therapeutically relevant conditions. In particular, we find that cancer-associated fibroblasts directly inhibit cancer cell apoptosis, independently from anticancer treatment. CausalXtract uncovers also multiple antagonistic effects at different time delays. Hence, CausalXtract provides a unique computational tool to interpret live-cell imaging data for a range of fundamental and translational research applications.

IntroductionCardiometabolic diseases, a major global health concern, stem from complex interactions of lifestyle, genetics, and biochemical markers. While extensive research has revealed strong associations between various risk factors and these diseases, latent confounding and limited causal discovery methods hinder understanding of their causal relationships, essential for mechanistic insights and developing effective prevention and intervention strategies.MethodsWe introduce anchorFCI, a novel adaptation of the conservative Really Fast Causal Inference (RFCI) algorithm, designed to enhance robustness and discovery power in causal learning by strategically selecting and integrating reliable anchor variables from a set of variables known not to be caused by the variables of interest. This approach is well-suited for studies of phenotypic, clinical, and sociodemographic data, using genetic variables that are recognized to be unaffected by these factors. We demonstrate the method’s effectiveness through simulation studies and a comprehensive causal analysis of the 2015 ISA-Nutrition dataset, featuring both anchorFCI for causal discovery and state-of-the-art effect size identification tools from Judea Pearl’s framework, showcasing a robust, fully data-driven causal inference pipeline.ResultsOur simulation studies reveal that anchorFCI effectively enhances robustness and discovery power while handles latent confounding by integrating reliable anchor variables and their non-ancestral relationships. The 2015 ISA-Nutrition dataset analysis not only supports many established causal relationships but also elucidates their interconnections, providing a clearer understanding of the complex dynamics and multifaceted nature of cardiometabolic risk.DiscussionAnchorFCI holds significant potential for reliable causal discovery in complex, multidimensional datasets. By effectively integrating non-ancestral knowledge and addressing latent confounding, it is well-suited for various applications requiring robust causal inference from observational studies, providing valuable insights in epidemiology, genetics, and public health.

Discovering causal relationships from observational data is a challenging task that relies on assumptions connecting statistical quantities to graphical or algebraic causal models. In this work, we focus on widely employed assumptions for causal discovery when objects of interest are (multivariate) groups of random variables rather than individual (univariate) random variables, as is the case in a variety of problems in scientific domains such as climate science or neuroscience. If the group level causal models are derived from partitioning a micro-level model into groups, we explore the relationship between micro- and group level causal discovery assumptions. We investigate the conditions under which assumptions like causal faithfulness hold or fail to hold. Our analysis encompasses graphical causal models that contain cycles and bidirected edges. We also discuss grouped time series causal graphs and variants thereof as special cases of our general theoretical framework. Thereby, we aim to provide researchers with a solid theoretical foundation for the development and application of causal discovery methods for variable groups.

Abstract Background Generating synthetic patient data is crucial for medical research, but common approaches build up on black-box models which do not allow for expert verification or intervention. We propose a highly available method which enables synthetic data generation from real patient records in a privacy preserving and compliant fashion, is interpretable and allows for expert intervention. Methods Our approach ties together two established tools in medical informatics, namely OMOP as a data standard for electronic health records and Synthea as a data synthetization method. For this study, data pipelines were built which extract data from OMOP, convert them into time series format, learn temporal rules by 2 statistical algorithms (Markov chain, TARM) and 3 algorithms of causal discovery (DYNOTEARS, J-PCMCI+, LiNGAM) and map the outputs into Synthea graphs. The graphs are evaluated quantitatively by their individual and relative complexity and qualitatively by medical experts. Results The algorithms were found to learn qualitatively and quantitatively different graph representations. Whereas the Markov chain results in extremely large graphs, TARM, DYNOTEARS, and J-PCMCI+ were found to reduce the data dimension during learning. The MultiGroupDirect LiNGAM algorithm was found to not be applicable to the problem statement at hand. Conclusion Only TARM and DYNOTEARS are practical algorithms for real-world data in this use case. As causal discovery is a method to debias purely statistical relationships, the gradient-based causal discovery algorithm DYNOTEARS was found to be most suitable.

Artificial intelligence plays an indispensable role in improving productivity and promoting social development, and causal discovery is one of the extremely important research directions in this field. Acyclic directed graphs (DAGs) are the most commonly used tool in causal modeling because of their excellent interpretability and structural properties. However, in the face of insufficient data, the accuracy and efficiency of DAGs learning are greatly reduced, resulting in a false perception of causality. As intuitive expert knowledge, structural constraints control DAG learning by limiting the causal relationship between variables, which is expected to solve the above-mentioned problem. However, it is often impossible to build a DAG by relying on expert knowledge alone. To solve this problem, we propose the use of expert knowledge as a hard constraint and the structural prior gained via data learning as a soft constraint. In this paper, we propose a fitness-rate-rank-based multiarmed bandit (FRRMAB) hyper-heuristic that integrates soft and hard constraints into the DAG learning process. For a linear structural equation model (SEM), soft constraints are obtained via partial correlation analysis. The experimental results on different networks show that the proposed method has higher scalability and accuracy.

Background/Objectives: Diabetes is a dangerous disease that is accompanied by various complications, including cardiovascular disease. As the global diabetes population continues to increase, it is crucial to identify its causes. Therefore, we predicted diabetes using an AI model and quantitatively examined causal relationships using a causal discovery and inference model. Methods: Kaggle’s dataset from the National Institute of Diabetes and Digestive and Kidney Diseases was analyzed using logistic regression, deep learning, gradient boosting, and decision trees. Causal discovery techniques, such as LiNGAM, were employed to infer relationships between variables. Results: The study achieved high accuracy across models using logistic regression (84.84%) and deep learning (84.83%). The causal model highlighted factors such as physical activity, difficulty in walking, and heavy drinking as direct contributors to diabetes. Conclusions: By combining AI with causal inference, this study provides both predictive performance and insight into the factors affecting diabetes, paving the way for tailored interventions.

Understanding the complex mechanisms of the brain can be unraveled by extracting the Dynamic Effective Connectome (DEC). Recently, score-based Directed Acyclic Graph (DAG) discovery methods have shown significant improvements in extracting the causal structure and inferring effective connectivity. However, learning DEC through these methods still faces two main challenges: one with the fundamental impotence of high-dimensional dynamic DAG discovery methods and the other with the low quality of fMRI data. In this paper, we introduce Bayesian Dynamic DAG learning with M-matrices Acyclicity characterization (BDyMA) method to address the challenges in discovering DEC. The presented dynamic DAG enables us to discover direct feedback loop edges as well. Leveraging an unconstrained framework in the BDyMA method leads to more accurate results in detecting high-dimensional networks, achieving sparser outcomes, making it particularly suitable for extracting DEC. Additionally, the score function of the BDyMA method allows the incorporation of prior knowledge into the process of dynamic causal discovery which further enhances the accuracy of results. Comprehensive simulations on synthetic data and experiments on Human Connectome Project (HCP) data demonstrate that our method can handle both of the two main challenges, yielding more accurate and reliable DEC compared to state-of-the-art and traditional methods. Additionally, we investigate the trustworthiness of DTI data as prior knowledge for DEC discovery and show the improvements in DEC discovery when the DTI data is incorporated into the process.

We introduce Dagma-DCE, an interpretable and model-agnostic scheme for differentiable causal discovery. Current non- or over-parametric methods in differentiable causal discovery use opaque proxies of “independence” to justify the inclusion or exclusion of a causal relationship. We show theoretically and empirically that these proxies may be arbitrarily different than the actual causal strength. Juxtaposed with existing differentiable causal discovery algorithms, Dagma-DCE uses an interpretable measure of causal strength to define weighted adjacency matrices. In a number of simulated datasets, we show our method achieves state-of-the-art level performance. We additionally show that Dagma-DCE allows for principled thresholding and sparsity penalties by domain-experts. The code for our method is available open-source at https://github.com/DanWaxman/DAGMA-DCE, and can easily be adapted to arbitrary differentiable models.

Causal discovery is the process of modeling cause and effect relationships among features. Unlike traditional model-based approaches, that rely on fitting data to the models, methods of causal discovery determine the causal structure from data. In clinical and EHR data analysis, causal discovery is used to identify dependencies among features that are difficult to estimate using model-based approaches. The resultant structures are represented as Directed Acyclic Graphs (DAG) consisting of nodes and arcs. Here, the direction of the arcs in a DAG indicates the influence of one feature over the other. These dependencies are fundamental to the discovery of novel insights obtained from data. However, causal discovery solely relies on establishing feature dependencies based on their conditional dependencies, that could lead to inaccurate inferences brought about by confounding bias. Our contribution in this work is ‘Non-Confounding Causal Discovery’ (NCCD), a framework aimed at overcoming confounding bias leveraging maximum relevancy and minimum redundancy between features using the concepts of information theory. The work presented uses threshold conditioned values on which the features in the graphical structure are connected to one another. Validation was carried out on three clinical trial benchmark datasets and compared the results against the previously known Naïve Bayes (NB) and Tree Augmented Naïve Bayes (TAN) algorithms. We observe a reduction in the complexity of the graph, evidenced by a decrease in the number of arcs. Notably, the graphs generated through NCCD exhibited a capacity to eliminate confounding dependencies while concurrently preserving the overall score of the network.

In causal learning, discovering the causal graph of the underlying generative mechanism from observed data is crucial. However, real-world data for causal discovery is scarce and expensive, leading researchers to rely on synthetic datasets, which may not accurately reflect real-world performance. To address this, we propose a novel method for evaluating causal discovery algorithms without needing real causal graphs. Specifically, our method employs deep learning evaluation strategies and ensemble learning techniques to robustly assess the performance of causal discovery methods. To elaborate, our approach emulates deep learning validation strategies by dividing the data into training and testing sets. We perform causal discovery on the training set and subsequently use the testing set to conduct Markov blanket tests on the node set and causal direction determination on the edge set. Moreover, we employ multiple ensemble strategies to ensure a comprehensive evaluation of the algorithms. Furthermore, experiments on both synthetic and real datasets demonstrate our method’s effectiveness in accurately and comprehensively validating causal discovery algorithms. Our results show that our proposed method can reflect the performance of causal discovery methods in practice with reasonable error.

Managing delivery risks is a critical challenge in modern supply chain management due to the increasing complexity and interdependencies of global supply networks. Existing methods often rely on correlation-based approaches, which fail to uncover the true causes behind delivery delays. This limitation makes it difficult for supply chain managers to identify actionable factors that can mitigate risks effectively. To address these challenges, we propose a novel method that integrates causal discovery with reinforcement learning to identify the root causes of delivery risks. Unlike traditional correlation-based methods, our approach uncovers both the direction and strength of causal relationships between variables, allowing for more accurate identification of the key drivers behind delivery delays. By applying causal strength quantification, we further measure the impact of each factor on delivery performance. Using real-world supply chain data, our results demonstrate that the proposed method reveals hidden causal relationships between factors such as shipping mode, order size, and delivery status. These insights enable supply chain managers to implement more targeted interventions, significantly improving risk mitigation strategies.

Variations in Marine Dissolved Oxygen Concentrations (MDOC) play a critical role in the study of marine ecosystems and global climate evolution. Although artificial intelligence methods, represented by deep learning, can enhance the precision of MDOC inversion, the uninterpretability of the operational mechanism involved in the “black-box” often make the process difficult to interpret. To address this issue, this paper proposes a high-precision interpretable framework (CDRP) for intelligent MDOC inversion, including Causal Discovery, Drift Detection, RuleFit Model, and Post Hoc Analysis. The entire process of the proposed framework is fully interpretable: (i) The causal relationships between various elements are further clarified. (ii) During the phase of concept drift analysis, the potential factors contributing to changes in marine data are extracted. (iii) The operational rules of RuleFit ensure computational transparency. (iv) Post hoc analysis provides a quantitative interpretation from both global and local perspectives. Furthermore, we have derived quantitative conclusions about the impacts of various marine elements, and our analysis maintains consistency with conclusions in marine literature on MDOC. Meanwhile, CDRP also ensures the precision of MDOC inversion: (i) PCMCI causal discovery eliminates the interference of weakly associated elements. (ii) Concept drift detection takes more representative key frames. (iii) RuleFit achieves higher precision than other models. Experiments demonstrate that CDRP has reached the optimal level in single point buoy data inversion task. Overall, CDRP can enhance the interpretability of the intelligent MDOC inversion process while ensuring high precision.

Abstract Existing studies have shown changes in the impact of atmospheric teleconnections on Indian Summer Monsoon (ISM) at interannual time scales due to the changing background state. However, the exploration of potential changes at subseasonal time scales remains limited. In this study, we use a causal discovery method to find the tropical atmospheric drivers of ISM subseasonal anomalies, and quantify the causal effects of the drivers on ISM, as well as the changes in causal effects over the past 40 years. We find the impact of tropical western Pacific on ISM subseasonal anomalies has strengthened, while the ISM self‐feedback has weakened. Wavenumber‐frequency analysis shows that the Rossby wave energy over 15°N–30°N at periods of 10–20 days has increased over the past four decades, which offers a plausible explanation for the enhanced tropical atmospheric teleconnection between western Pacific and ISM at subseasonal time scales.

BackgroundNon-suicidal self-injury (NSSI) has become a significant public health issue, especially prevalent among adolescents. The complexity and multifactorial nature of NSSI necessitate a comprehensive understanding of its underlying causal factors. This research leverages the causal discovery methodology to explore these causal associations in children.MethodsAn observational dataset was scrutinized using the causal discovery method, particularly employing the constraint-based approach. By integrating machine learning and causal inference techniques, the study aimed to determine direct causal relationships associated with NSSI. The robustness of the causal relationships was evaluated using three methods to construct and validate it: the PC (Peter and Clark) method, Fast Causal Inference (FCI) method, and the GAE (Graphical Autoencoder) method.ResultsAnalysis identified nine nodes with direct causal relationships to NSSI, including life satisfaction, depression, family dysfunction, sugary beverage consumption, PYD (positive youth development), internet addiction, COVID-19 related PTSD, academic anxiety, and sleep duration. Four principal causal pathways were identified, highlighting the roles of lockdown-induced lifestyle changes, screen time, positive adolescent development, and family dynamics in influencing NSSI risk.ConclusionsAn in-depth analysis of the factors leading to Non-Suicidal Self-Injury (NSSI), highlighting the intricate connections among individual, family, and pandemic-related influences. The results, derived from computational causal analysis, underscore the critical need for targeted interventions that tackle these diverse causative factors.

Causal discovery is central to human cognition, and learning directed acyclic graphs (DAGs) is its foundation. Recently, many nature-inspired meta-heuristic optimization algorithms have been proposed to serve as the basis for DAG learning. However, a single meta-heuristic algorithm requires specific domain knowledge and empirical parameter tuning and cannot guarantee good performance in all cases. Hyper-heuristics provide an alternative methodology to meta-heuristics, enabling multiple heuristic algorithms to be combined and optimized to achieve better generalization ability. In this paper, we propose a multi-population choice function hyper-heuristic to discover the causal relationships encoded in a DAG. This algorithm provides a reasonable solution for combining structural priors or possible expert knowledge with swarm intelligence. Under a linear structural equation model (SEM), we first identify the partial v-structures through partial correlation analysis as the structural priors of the next nature-inspired swarm intelligence approach. Then, through partial correlation analysis, we can limit the search space. Experimental results demonstrate the effectiveness of the proposed methods compared to the earlier state-of-the-art methods on six standard networks.

In a dynamic production processes, mechanical degradation poses a significant challenge, impacting product quality and process efficiency. This paper explores a novel approach for monitoring degradation in the context of viscose fiber production, a highly dynamic manufacturing process. Using causal discovery techniques, our method allows domain experts to incorporate background knowledge into the creation of causal graphs. Further, it enhances the interpretability and increases the ability to identify potential problems via changes in causal relations over time. The case study employs a comprehensive analysis of the viscose fiber production process within a prominent textile industry, emphasizing the advantages of causal discovery for monitoring degradation. The results are compared with state-of-the-art methods, which are not considered to be interpretable, specifically LSTM-based autoencoder, UnSupervised Anomaly Detection on Multivariate Time Series (USAD), and Deep Transformer Networks for Anomaly Detection in Multivariate Time Series Data (TranAD), showcasing the alignment and validation of our approach. This paper provides valuable information on degradation monitoring strategies, demonstrating the efficacy of causal discovery in dynamic manufacturing environments. The findings contribute to the evolving landscape of process optimization and quality control.

Semantic maps are used in lexical typology to summarize cross-linguistic implicational universals of co-expression between meanings in a domain. They are defined as networks which, using as few links as possible, connect the meanings so that every isolectic set (i.e., set of meanings that can be expressed by the same word in some language) forms a connected component. Due to the close connection between synchronic polysemies and semantic change, semantic maps are often interpreted diachronically as encoding potential pathways of semantic extension. While semantic maps are traditionally generated by hand, there have been attempts to automate this complex and non-deterministic process. I explore the problem from a new algorithmic angle by casting it in the framework of causal discovery, a field which explores the possibility of automatically inferring causal structures from observational data. I show that a standard causal inference algorithm can be used to reduce cross-linguistic polysemy data into minimal network structures which explain the observed polysemies. If the algorithm makes its link deletion decisions on the basis of the connected component criterion, the skeleton of the resulting causal structure is a synchronic semantic map. The arrows which are added to some links in the second stage can be interpreted as expressing the main tendencies of semantic extension. Much of the existing literature on semantic maps implicitly assumes that the data from the languages under analysis is correct and complete, whereas in reality, semantic map research is riddled by data quality and sparseness problems. To quantify the uncertainty inherent in the inferred diachronic semantic maps, I rely on bootstrapping on the language level to model the uncertainty caused by the given language sample, as well as on random link processing orders to explore the space of possible semantic maps for a given input. The maps inferred from the samples are then summarized into a consensus network where every link and arrow receives a confidence value. In experiments on cross-linguistic polysemy data of varying shapes, the resulting confidence values are found to mostly agree with previously published results, though challenges in directionality inference remain.

Perfect adaptation in a dynamical system is the phenomenon that one or more variables have an initial transient response to a persistent change in an external stimulus but revert to their original value as the system converges to equilibrium. With the help of the causal ordering algorithm, one can construct graphical representations of dynamical systems that represent the causal relations between the variables and the conditional independences in the equilibrium distribution. We apply these tools to formulate sufficient graphical conditions for identifying perfect adaptation from a set of first-order differential equations. Furthermore, we give sufficient conditions to test for the presence of perfect adaptation in experimental equilibrium data. We apply this method to a simple model for a protein signalling pathway and test its predictions in both simulations and using real-world protein expression data. We demonstrate that perfect adaptation can lead to misleading orientation of edges in the output of causal discovery algorithms.

Causal Reinforcement Learning (CRL) is an emerging field where two essential areas for the development of artificial intelligence are integrated. Existing works in the area have shown how causality can contribute to mitigate some of the limitations of reinforcement learning (RL), ranging from data-inefficiency, lack of interpretability, and long learning times, among others. However, how to use reinforcement learning to support causal discovery (CD) has so far been less explored. In this article, we introduce CARL, a Causality-Aware Reinforcement Learning framework for simultaneously learning and using causal models to speed-up the policy learning in online Markov decision process (MDP) settings. In a synergistic way, our method alternates between: (i) (RL for CD), where it promotes the selection of actions to obtain better causal models in fewer episodes than traditional methods of obtaining data in RL, (ii) (CD), where a score-based algorithm is used to learn causal models and (iii) (RL using CD), where the learned models are used to select actions that speed up the learning of the optimal policy by reducing the number of interactions with the environment. Experiments in simulated environments show that our method achieves better results in policy learning than traditional model-free and model-based algorithms while it is also able to learn the underlying causal models. We also demonstrate how the learned causal models can be directly transferred to a similar task of greater complexity, significantly reducing the number of episodes required to learn an optimal policy Finally, the method’s scalability to high-dimensional states, where the action-value function needs to be represented with deep neural networks, was verified.

Although gray matter atrophy is commonly observed with aging, it is highly variable, even among healthy people of the same age. This raises the question of what other factors may contribute to gray matter atrophy. Previous studies have reported that risk factors for cardiometabolic diseases are associated with accelerated brain aging. However, these studies were primarily based on standard correlation analyses, which do not unveil a causal relationship. While randomized controlled trials are typically required to investigate true causality, in this work, we investigated an alternative method by exploring data-driven causal discovery and inference techniques on observational data. Accordingly, this feasibility study used clinical and quantified gray matter volume data from 22,793 subjects from the UK biobank cohort without any known neurological disease. Our method identified that age, sex, body mass index (BMI), body fat percentage (BFP), and smoking exhibit a causal relationship with gray matter volume. Interventions on the causal network revealed that higher BMI and BFP values significantly increased the chance of gray matter atrophy in males, whereas this was not the case in females.

The causal structure of a system imposes constraints on the joint probability distribution of variables that can be generated by the system. Archetypal constraints consist of conditional independencies between variables. However, particularly in the presence of hidden variables, many causal structures are compatible with the same set of independencies inferred from the marginal distributions of observed variables. Additional constraints allow further testing for the compatibility of data with specific causal structures. An existing family of causally informative inequalities compares the information about a set of target variables contained in a collection of variables, with a sum of the information contained in different groups defined as subsets of that collection. While procedures to identify the form of these groups-decomposition inequalities have been previously derived, we substantially enlarge the applicability of the framework. We derive groups-decomposition inequalities subject to weaker independence conditions, with weaker requirements in the configuration of the groups, and additionally allowing for conditioning sets. Furthermore, we show how constraints with higher inferential power may be derived with collections that include hidden variables, and then converted into testable constraints using data processing inequalities. For this purpose, we apply the standard data processing inequality of conditional mutual information and derive an analogous property for a measure of conditional unique information recently introduced to separate redundant, synergistic, and unique contributions to the information that a set of variables has about a target.

Inferring causality from observed data is crucial in many scientific fields, but this process is often hindered by incomplete data. The incomplete data can lead to mistakes in understanding how variables affect each other, especially when some influencing factors are not directly observed. To tackle this problem, we’ve developed a new algorithm called Regression Loss-increased with Causal Intensity (RLCI). This approach uses regression and entropy analysis to uncover hidden variables. Through tests on various real-world datasets, RLCI has been proven to be effective. It can help spot hidden factors that may affect the relationship between variables and determine the direction of causal relationships.

The knowledge of the causal mechanisms underlying one single system may not be sufficient to answer certain questions. One can gain additional insights from comparing and contrasting the causal mechanisms underlying multiple systems and uncovering consistent and distinct causal relationships. For example, discovering common molecular mechanisms among different diseases can lead to drug repurposing. The problem of comparing causal mechanisms among multiple systems is non-trivial, since the causal mechanisms are usually unknown and need to be estimated from data. If we estimate the causal mechanisms from data generated from different systems and directly compare them (the naive method), the result can be sub-optimal. This is especially true if the data generated by the different systems differ substantially with respect to their sample sizes. In this case, the quality of the estimated causal mechanisms for the different systems will differ, which can in turn affect the accuracy of the estimated similarities and differences among the systems via the naive method. To mitigate this problem, we introduced the bootstrap estimation and the equal sample size resampling estimation method for estimating the difference between causal networks. Both of these methods use resampling to assess the confidence of the estimation. We compared these methods with the naive method in a set of systematically simulated experimental conditions with a variety of network structures and sample sizes, and using different performance metrics. We also evaluated these methods on various real-world biomedical datasets covering a wide range of data designs.

Storm ‘Daniel’ caused the most severe flood phenomenon that Greece has ever experienced, with thousands of hectares of farmland submerged for days. This led to sediment deposition in the inundated areas, which significantly altered the chemical properties of the soil, as revealed by extensive soil sampling and laboratory analysis. The causal relationships between the soil chemical properties and sediment deposition were extracted using the DirectLiNGAM algorithm. The results of the causality analysis showed that the sediment deposition affected the CaCO3 concentration in the soil. Also, causal relationships were identified between CaCO3 and the available phosphorus (P-Olsen), as well as those between the sediment deposit depth and available manganese. The quantified relationships between the soil variables were then used to generate data using a Multiple Linear Perceptron (MLP) regressor for various levels of deposit depth (0, 5, 10, 15, 20, 25, and 30 cm). Then, linear regression equations were fitted across the different levels of deposit depth to determine the effect of the deposit depth on CaCO3, P, and Mn. The results revealed quadratic equations for CaCO3, P, and Mn as follows: 0.001XCaCO32 + 0.08XCaCO3 + 6.42, 0.004XP2 − 0.26XP + 12.29, and 0.003XMn2 − 0.08XMn + 22.47, respectively. The statistical analysis indicated that corn growing in soils with a sediment over 10 cm requires a 31.8% increase in the P rate to prevent yield decline. Additional notifications regarding cropping strategies in the near future are also discussed.

Questionnaires on health-related quality of life (HRQoL) play a crucial role in managing patients by revealing insights into physical, psychological, lifestyle, and social factors affecting well-being. A methodological aspect that has not been adequately explored yet, and is of considerable potential, is causal discovery. This study explored causal discovery techniques within HRQoL, assessed various considerations for reliable estimation, and proposed means for interpreting outcomes. Five causal structure learning algorithms were employed to examine different aspects in structure estimation based on simulated data derived from HRQoL-related directed acyclic graphs. The performance of the algorithms was assessed based on various measures related to the differences between the true and estimated structures. Moreover, the Resource Description Framework was adopted to represent the responses to the HRQoL questionnaires and the detected cause–effect relationships among the questions, resulting in semantic knowledge graphs which are structured representations of interconnected information. It was found that the structure estimation was impacted negatively by the structure’s complexity and favorably by increasing the sample size. The performance of the algorithms over increasing sample size exhibited a similar pattern, with distinct differences being observed for small samples. This study illustrates the dynamics of causal discovery in HRQoL-related research, highlights aspects that should be addressed in estimation, and fosters the shareability and interoperability of the output based on globally established standards. Thus, it provides critical insights in this context, further promoting the critical role of HRQoL questionnaires in advancing patient-centered care and management.

Causal discovery from observational data is a fundamental problem in many disciplines.However,existing methods such as constraint-based methods and causal function-based methods have strong assumptions on the causal mechanism of data,and are only applicable to low-dimensional data,and cannot be applied to scenarios with hidden variables.To this end,we propose a causality discovery method using information bottlenecks,called causal information bottleneck.This method divides the causal mechanism into two stages:compression and extraction.In the compression stage,we assume that there is a compressed hidden variable in the middle,while in the extraction stage,we extract the correlated information from effect variable as much as possible.Based on the causal information bottleneck,by deriving its variational upper bound,a causality discovery method based on the variational autoencoder is designed.The experimental results shows that the information bottleneck based method improves the accuracy by 10% in synthetic data and 4% in real world data.

Abstract Background There has been a simultaneous increase in demand and accessibility across genomics, transcriptomics, proteomics and metabolomics data, known as omics data. This has encouraged widespread application of omics data in life sciences, from personalized medicine to the discovery of underlying pathophysiology of diseases. Causal analysis of omics data may provide important insight into the underlying biological mechanisms. Existing causal analysis methods yield promising results when identifying potential general causes of an observed outcome based on omics data. However, they may fail to discover the causes specific to a particular stratum of individuals and missing from others. Methods To fill this gap, we introduce the problem of stratified causal discovery and propose a method, Aristotle, for solving it. Aristotle addresses the two challenges intrinsic to omics data: high dimensionality and hidden stratification. It employs existing biological knowledge and a state-of-the-art patient stratification method to tackle the above challenges and applies a quasi-experimental design method to each stratum to find stratum-specific potential causes. Results Evaluation based on synthetic data shows better performance for Aristotle in discovering true causes under different conditions compared to existing causal discovery methods. Experiments on a real dataset on Anthracycline Cardiotoxicity indicate that Aristotle’s predictions are consistent with the existing literature. Moreover, Aristotle makes additional predictions that suggest further investigations.

Measurements of systems taken along a continuous functional dimension, such as time or space, are ubiquitous in many fields, from the physical and biological sciences to economics and engineering. Such measurements can be viewed as realisations of an underlying smooth process sampled over the continuum. However, traditional methods for independence testing and causal learning are not directly applicable to such data, as they do not take into account the dependence along the functional dimension. By using specifically designed kernels, we introduce statistical tests for bivariate, joint, and conditional independence for functional variables. Our method not only extends the applicability to functional data of the Hilbert–Schmidt independence criterion (hsic) and its d-variate version (d-hsic), but also allows us to introduce a test for conditional independence by defining a novel statistic for the conditional permutation test (cpt) based on the Hilbert–Schmidt conditional independence criterion (hscic), with optimised regularisation strength estimated through an evaluation rejection rate. Our empirical results of the size and power of these tests on synthetic functional data show good performance, and we then exemplify their application to several constraint- and regression-based causal structure learning problems, including both synthetic examples and real socioeconomic data.

As the Information Age brings people an amount of data, research on data prediction has been widely concerned. Time series data, a sequence of data points collected over an interval of time, are very common in many areas such as weather forecasting, stock markets, and so on. Thus, research on time series data prediction is of great significance. Traditional prediction methods are usually based on correlations between data points, but correlations do not always reflect the relationship exactly within the data. In this paper, we propose the LiNGAM Weight Adjust–LSTM (LWA-LSTM) algorithm, which combines a causality discovery algorithm, feature weight adjustment, and a deep neural network for time series data prediction. Several stocks in the Chinese stock market were selected and the algorithm was used to predict the stock price. Comparing the prediction effect of the model with that of the LSTM model alone, the results show that the LWA-LSTM model can find the stable relationship between the data better and has fewer prediction errors.

We examine the interactions between growth in CO2emissions, economic production, and energy use at the global and multi-regional levels over the period 1990–2014. Methodologically, we use causal discovery that relies on linear and nonlinear tests of conditional independence to study their relationships. At the global scale, we show that energy use is unambiguously a nonlinear causal factor of economic output, making energy central in the economic and decarbonization debate. At the multi-regional scale, causal discovery accurately identifies that three regions are driving global dynamics (East Asia and Pacific, Europe and Central Asia, and North America regions). Energy and climate policies in these regions will nonlinearly influence the degree of global CO2emission reduction rates and will impact the global economic dynamics. Our results further suggest that policy effectiveness could be gained if a country’s climate actions were coordinated with the other geographies most affected by their consequences, providing valuable information on the implementation of Article 6 of the Paris Agreement.

We applied a Bayesian Constraint-based Causal Discovery method (BCCD) to examine the hierarchical structure of the Minnesota Multiphasic Personality Inventory-2-Restructured Form (MMPI-2-RF) Restructured Clinical (RC) scales. Two different general psychopathology super spectra (p-factor) scales were extracted from (1) all RC scales and (2) all RC scales except the RCd (Demoralization) scale. These p-factor scales were included in separate models to investigate the structure of dimensions of psychopathology in a normative (n = 3,242) and clinical (n = 2,466) sample, as well as the combined normative/clinical sample (N = 5,708), by applying the BCCD algorithm to obtain a data-driven reconstruction of the internal hierarchical structure of the MMPI-2-RF. Research on the underlying structure of the MMPI-2-RF has clinical relevance as well as conceptual relevance in the context of the HiTOP model. Results demonstrated that the syndromes measured with the RC-scales—in presence of a p-factor—cluster into six spectra: internalizing, disinhibited-externalizing, antagonistic-externalizing, thought disorder, detachment, and somatoform. These results may support a super spectrum construct, as it was necessary for obtaining a bottom-up reconstruction of this six-spectrum structure. We found support for superiority of a broad super spectrum with additional variance over and above demoralization, as it resulted in the clearest structure (i.e., clustering of the RC scales). Furthermore, our results indicate independent support for the bifactor structure model of psychopathology.

A rolling bearing is a complex system consisting of the inner race, outer race, rolling element, etc. The interaction of components may lead to composite faults. Selecting the features that can accurately identify the fault type from the composite fault features with causality among components is key to composite fault diagnosis. To tackle this issue, we propose a feature selection approach for composite fault diagnosis based on the causal feature network. Based on the incremental association Markov blanket discovery, we first use the algorithm to mine the causal relationships between composite fault features and construct the causal feature network. Then, we draw upon the nodes’ centrality indicators in the complex network to quantify the importance of composite fault features. We also propose the criteria for threshold selection to determine the number of features in the optimal feature subset. Experimental results on the standard dataset for composite fault diagnosis show that our approach of using the causal relationship between features and the nodes’ centrality indicators of complex network can effectively identify the key features in composite fault signals and improve the accuracy of composite fault diagnosis. Experimental results thus verify our approach’s effectiveness.

We demonstrate a data-driven approach for calculating a “causal connectome” of directed connectivity from resting-state fMRI data using a greedy adjacency search and pairwise non-Gaussian edge orientations. We used this approach to construct n = 442 causal connectomes. These connectomes were very sparse in comparison to typical Pearson correlation-based graphs (roughly 2.25% edge density) yet were fully connected in nearly all cases. Prominent highly connected hubs of the causal connectome were situated in attentional (dorsal attention) and executive (frontoparietal and cingulo-opercular) networks. These hub networks had distinctly different connectivity profiles: attentional networks shared incoming connections with sensory regions and outgoing connections with higher cognitive networks, while executive networks primarily connected to other higher cognitive networks and had a high degree of bidirected connectivity. Virtual lesion analyses accentuated these findings, demonstrating that attentional and executive hub networks are points of critical vulnerability in the human causal connectome. These data highlight the central role of attention and executive control networks in the human cortical connectome and set the stage for future applications of data-driven causal connectivity analysis in psychiatry.

Scientists try to design experiments that will yield maximal information. For instance, given the available evidence and a limitation on the number of variables that can be observed simultaneously, it may be more informative to intervene on variable $X$ and observe the response of variable $Y$ than to intervene on $X$ and observe $Z$ ; in other situations, the opposite may be true. Scientists must often make these decisions without primary data. To address this problem, in previous work, we created software for annotating aggregate statistics in the literature and deriving consistent causal explanations, expressed as causal graphs. This meta-analytic pipeline is useful not only for synthesizing evidence but also for planning experiments: one can use it strategically to select experiments that could further eliminate causal graphs from consideration. In this paper, we introduce interpretable policies for selecting experiments in the context of piecemeal causal discovery, a common setting in biological sciences in which each experiment can measure not an entire system but rather a strict subset of its variables. The limits of this piecemeal approach are only beginning to be fully characterized, with crucial theoretical work published recently. With simulations, we show that our experiment-selection policies identify causal structures more efficiently than random experiment selection. Unlike methods that require primary data, our meta-analytic approach offers a flexible alternative for those seeking to incorporate qualitative domain knowledge into their search for causal mechanisms. We also present a method that categorizes hypotheses with respect to their utility for identifying a system’s causal structure. Although this categorization is usually infeasible to perform manually, it is critical for conducting research efficiently.

The North Atlantic Oscillation (NAO) is a major climatic phenomenon in the Northern Hemisphere, but the underlying air–sea interaction and physical mechanisms remain elusive. Despite successful short-term forecasts using physics-based numerical models, longer-term forecasts of NAO continue to pose a challenge. In this study, we employ advanced data-driven causal discovery techniques to explore the causality between multiple ocean–atmosphere processes and NAO. We identify the best NAO predictors based on this causality analysis and develop NAO-MCD, a multivariate air–sea coupled model that incorporates causal discovery to provide 1–6 month lead seasonal forecasts of NAO. Our results demonstrate that the selected predictors are strongly associated with NAO development, enabling accurate forecasts of NAO. NAO-MCD significantly outperforms conventional numerical models and provides reliable seasonal forecasts of NAO, particularly for winter events. Moreover, our model extends the range of accurate forecasts, surpassing state-of-the-art performance at 2- to 6-month lead-time NAO forecasts, substantially outperforming conventional numerical models.

Both imagery and execution of motor control consist of interactions within a neuronal network, including frontal motor-related and posterior parietal regions. To reveal neural representation in the frontoparietal motor network, two approaches have been proposed thus far: one is decoding of actions/modes related to motor control from the spatial pattern of brain activity; and the other is estimating directed functional connectivity (a directed association between two brain regions within motor areas). However, directed connectivity among multiple regions of the frontoparietal motor network during motor imagery (MI) or motor execution (ME) has not been investigated. Here, we attempted to characterize the directed functional connectivity representing the MI and ME conditions. We developed a delayed sequential movement and imagery task to evoke brain activity associated with ME and MI, which can be recorded by functional magnetic resonance imaging. We applied a causal discovery approach, a linear non-Gaussian acyclic causal model, to identify directed functional connectivity among the frontoparietal motor-related brain regions for each condition. We demonstrated higher directed functional connectivity from the contralateral dorsal premotor cortex (dPMC) to the primary motor cortex (M1) in ME than in MI. We further identified significant direct effects of the dPMC and ventral premotor cortex (vPMC) to the parietal regions. In particular, connectivity from the dPMC to the superior parietal lobule (SPL) in the same hemisphere showed significant positive effects across all conditions, while interlateral connectivities from the vPMC to the SPL showed significantly negative effects across all conditions. Finally, we found positive effects from A1 to M1, that is, the audio-motor pathway, in the same hemisphere. These results indicate that the sources of motor command originating in the d/vPMC influenced the M1 and parietal regions for achieving ME and MI. Additionally, sequential sounds may functionally facilitate temporal motor processes.

Knowledge of ecological responses to changes in the environment is vital to design appropriate measures for conserving biodiversity. Experimental studies are the standard to identify ecological cause-effect relationships, but their results do not necessarily translate to field situations. Deriving ecological cause-effect relationships from observational field data is, however, challenging due to potential confounding influences of unmeasured variables. Here, we present a causal discovery algorithm designed to reveal ecological relationships in rivers and streams from observational data. Our algorithm (a) takes into account the spatial structure of the river network, (b) reveals the complete network of ecological relationships, and (c) shows the directions of these relationships. We apply our algorithm to data collected in the US state of Ohio to better understand causes of reductions in fish and invertebrate community integrity. We found that nitrogen is a key variable underlying fish and invertebrate community integrity in Ohio, likely negatively impacting both. We also found that fish and community integrity are each linked to one physical habitat quality variable. Our algorithm further revealed a split between physical habitat quality and water quality variables, indicating that causal relations between these groups of variables are likely absent. Our approach is able to reveal networks of ecological relationships in rivers and streams based on observational data, without the need to formulate a priori hypotheses. This is an asset particularly for diagnostic assessments of the ecological state and potential causes of biodiversity impairment in rivers and streams.

Our goal was to understand the complex relationship between age, sex, midlife risk factors, and early white matter changes measured by diffusion tensor imaging (DTI) and their role in the evolution of longitudinal white matter hyperintensities (WMH). We identified 1564 participants (1396 cognitively unimpaired, 151 mild cognitive impairment and 17 dementia participants) with age ranges of 30–90 years from the population-based sample of Mayo Clinic Study of Aging. We used computational causal structure discovery and regression analyses to evaluate the predictors of WMH and DTI, and to ascertain the mediating effect of DTI on WMH. We further derived causal graphs to understand the complex interrelationships between midlife protective factors, vascular risk factors, diffusion changes, and WMH. Older age, female sex, and hypertension were associated with higher baseline and progression of WMH as well as DTI measures (P ≤ 0.003). The effects of hypertension and sex on WMH were partially mediated by microstructural changes measured on DTI. Higher midlife physical activity was predictive of lower WMH through a direct impact on better white matter tract integrity as well as an indirect effect through reducing the risk of hypertension by lowering BMI. This study identified key risks factors, early brain changes, and pathways that may lead to the evolution of WMH.

Teleconnections that link climate processes at widely separated spatial locations form a key component of the climate system. Their analysis has traditionally been based on means, climatologies, correlations, or spectral properties, which cannot always reveal the dynamical mechanisms between different climatological processes. More recently, causal discovery methods based either on time series at grid locations or on modes of variability, estimated through dimension-reduction methods, have been introduced. A major challenge in the development of such analysis methods is a lack of ground truth benchmark datasets that have facilitated improvements in many parts of machine learning. Here, we present a simplified stochastic climate model that outputs gridded data and represents climate modes and their teleconnections through a spatially aggregated vector-autoregressive model. The model is used to construct benchmarks and evaluate a range of analysis methods. The results highlight that the model can be successfully used to benchmark different causal discovery methods for spatiotemporal data and show their strengths and weaknesses. Furthermore, we introduce a novel causal discovery method at the grid level and demonstrate that it has orders of magnitude better performance than the current approaches. Improved causal analysis tools for spatiotemporal climate data are pivotal to advance process-based understanding and climate model evaluation.

Summer heatwaves repeatedly affect extended regions in Europe, resulting in adverse economic, social, and ecological impacts. Recent events, e.g. the 2022 heatwave, also attract interest regarding the spatial shifts of their impact centers. Evaluations so far either investigated heatwave passages at pre-defined locations or employed algorithms to spatio-temporally track their core regions. Usually, the latter focus on single events, and thus often fail to generalize spatial heatwave tracks or ignore track characteristics. Here, we use a data-driven approach employing causal discovery to robustly characterize European heatwave tracks in single-model initial condition large ensemble (SMILE) climate simulations to overcome sampling uncertainties of observational records. This enables us to identify specific recurrent heatwave tracks, evaluate their preferential seasonal occurrence, and associate them with moving high pressure centers. Additionally, the evaluation of heatwave track representation in the SMILE extends standard model evaluation, which is mostly based on static statistics. We provide the first comprehensive analysis on heatwave tracks considering internal climate variability conducted within a SMILE, promoting the latter as a methodological testbed in climate extremes research.

Causal discovery from observational data offers unique opportunities in many scientific disciplines: reconstructing causal drivers, testing causal hypotheses, and comparing and evaluating models for optimizing targeted interventions. Recent causal discovery methods focused on estimating the latent space of the data to get around a lack of causal sufficiency or additivity constraints. However, estimating the latent space significantly increases model complexity, compromising causal identifiability and making it hard to compare models that correspond to different causal hypotheses. We propose a kernel, non-parametric latent-space modelling approach and deal with the difficulty of comparing causal directions by measuring and controlling for the level of causal assumption fulfilment. We introduce a latent noise causal inference framework to estimate latent factors associated with the hypothesized causal direction by optimizing a loss function with kernel independence criteria. We extend the framework to work with time series using an additional time-dependent kernel regularizer. We discuss the additivity assumption and model complexity and give empirical evidence of performance in a wide range of synthetic and real causal discovery problems.

This paper builds on recent developments in Bayesian network (BN) structure learning under the controversial assumption that the input variables are dependent. This assumption can be viewed as a learning constraint geared towards cases where the input variables are known or assumed to be dependent. It addresses the problem of learning multiple disjoint subgraphs that do not enable full propagation of evidence. This problem is highly prevalent in cases where the sample size of the input data is low with respect to the dimensionality of the model, which is often the case when working with real data. The paper presents a novel hybrid structure learning algorithm, called SaiyanH, that addresses this issue. The results show that this constraint helps the algorithm to estimate the number of true edges with higher accuracy compared to the state-of-the-art. Out of the 13 algorithms investigated, the results rank SaiyanH 4th in reconstructing the true DAG, with accuracy scores lower by 8.1% (F1), 10.2% (BSF), and 19.5% (SHD) compared to the top ranked algorithm, and higher by 75.5% (F1), 118% (BSF), and 4.3% (SHD) compared to the bottom ranked algorithm. Overall, the results suggest that the proposed algorithm discovers satisfactorily accurate connected DAGs in cases where other algorithms produce multiple disjoint subgraphs that often underfit the true graph.

Constraint-based causal discovery (CCD) algorithms require fast and accurate conditional independence (CI) testing. The Kernel Conditional Independence Test (KCIT) is currently one of the most popular CI tests in the non-parametric setting, but many investigators cannot use KCIT with large datasets because the test scales at least quadratically with sample size. We therefore devise two relaxations called the Randomized Conditional Independence Test (RCIT) and the Randomized conditional Correlation Test (RCoT) which both approximate KCIT by utilizing random Fourier features. In practice, both of the proposed tests scale linearly with sample size and return accurate p-values much faster than KCIT in the large sample size context. CCD algorithms run with RCIT or RCoT also return graphs at least as accurate as the same algorithms run with KCIT but with large reductions in run time.

This study addresses the problem of learning a summary causal graph on time series with potentially different sampling rates. To do so, we first propose a new causal temporal mutual information measure for time series. We then show how this measure relates to an entropy reduction principle that can be seen as a special case of the probability raising principle. We finally combine these two ingredients in PC-like and FCI-like algorithms to construct the summary causal graph. There algorithm are evaluated on several datasets, which shows both their efficacy and efficiency.

This paper investigates the problem of selecting instrumental variables relative to a target causal influence X→Y from observational data generated by linear non-Gaussian acyclic causal models in the presence of unmeasured confounders. We propose a necessary condition for detecting variables that cannot serve as instrumental variables. Unlike many existing conditions for continuous variables, i.e., that at least two or more valid instrumental variables are present in the system, our condition is designed with a single instrumental variable. We then characterize the graphical implications of our condition in linear non-Gaussian acyclic causal models. Given that the existing graphical criteria for the instrument validity are not directly testable given observational data, we further show whether and how such graphical criteria can be checked by exploiting our condition. Finally, we develop a method to select the set of candidate instrumental variables given observational data. Experimental results on both synthetic and real-world data show the effectiveness of the proposed method.