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AbstractOne of the established approaches to causal discovery consists of combining directed acyclic graphs (DAGs) with structural causal models (SCMs) to describe the functional dependencies of effects on their causes. Possible identifiability of SCMs given data depends on assumptions made on the noise variables and the functional classes in the SCM. For instance, in the LiNGAM model, the functional class is restricted to linear functions and the disturbances have to be non-Gaussian. In this work, we propose TSLiNGAM, a new method for identifying the DAG of a causal model based on observational data. TSLiNGAM builds on DirectLiNGAM, a popular algorithm which uses simple OLS regression for identifying causal directions between variables. TSLiNGAM leverages the non-Gaussianity assumption of the error terms in the LiNGAM model to obtain more efficient and robust estimation of the causal structure. TSLiNGAM is justified theoretically and is studied empirically in an extensive simulation study. It performs significantly better on heavy-tailed and skewed data and demonstrates a high small-sample efficiency. In addition, TSLiNGAM also shows better robustness properties as it is more resilient to contamination. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

How do we construct our causal directed acyclic graphs (DAGs)—for example, for life-course modeling and analysis? In this commentary, I review how the data-driven construction of causal DAGs (causal discovery) has evolved, what promises it holds, and what limitations or caveats must be considered. I find that expert- or theory-driven model-building might benefit from some more checking against the data and that causal discovery could bring new ideas to old theories. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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.

Multivariate functional data arise in a wide range of applications. One fundamental task is to understand the causal relationships among these functional objects of interest. In this paper, we develop a novel Bayesian network (BN) model for multivariate functional data where conditional independencies and causal structure are encoded by a directed acyclic graph. Specifically, we allow the functional objects to deviate from Gaussian processes, which is the key to unique causal structure identification even when the functions are measured with noises. A fully Bayesian framework is designed to infer the functional BN model with natural uncertainty quantification through posterior summaries. Simulation studies and real data examples demonstrate the practical utility of the proposed model. [ABSTRACT FROM AUTHOR]

Life-course epidemiology relies on specifying complex (causal) models that describe how variables interplay over time. Traditionally, such models have been constructed by perusing existing theory and previous studies. By comparing data-driven and theory-driven models, we investigated whether data-driven causal discovery algorithms can help in this process. We focused on a longitudinal data set on a cohort of Danish men (the Metropolit Study, 1953–2017). The theory-driven models were constructed by 2 subject-field experts. The data-driven models were constructed by use of the temporal Peter-Clark (TPC) algorithm. The TPC algorithm utilizes the temporal information embedded in life-course data. We found that the data-driven models recovered some, but not all, causal relationships included in the theory-driven expert models. The data-driven method was especially good at identifying direct causal relationships that the experts had high confidence in. Moreover, in a post hoc assessment, we found that most of the direct causal relationships proposed by the data-driven model but not included in the theory-driven model were plausible. Thus, the data-driven model may propose additional meaningful causal hypotheses that are new or have been overlooked by the experts. In conclusion, data-driven methods can aid causal model construction in life-course epidemiology, and combining both data-driven and theory-driven methods can lead to even stronger models. [ABSTRACT FROM AUTHOR]

Causal Bayesian networks have become a powerful technology for reasoning under uncertainty in areas that require transparency and explainability, by relying on causal assumptions that enable us to simulate hypothetical interventions. The graphical structure of such models can be estimated by structure learning algorithms, domain knowledge, or a combination of both. Various knowledge approaches have been proposed in the literature that enables us to specify prior knowledge that constrains or guides these algorithms. This paper introduces some novel, and also describes some existing, knowledge-based approaches that enable us to combine structure learning with knowledge obtained from heterogeneous sources. We investigate the impact of these approaches on structure learning across different algorithms, case studies and settings that we might encounter in practice. Each approach is assessed in terms of effectiveness and efficiency, including graphical accuracy, model fitting, complexity, and runtime; making this the first paper that provides a comparative evaluation of a wide range of knowledge approaches for structure learning. Because the value of knowledge depends on what data are available, we illustrate the results both with limited and big data. While the overall results show that knowledge becomes less important with big data due to higher learning accuracy rendering knowledge less important, some of the knowledge approaches are found to be more important with big data. Amongst the main conclusions is the observation that reduced search space obtained from knowledge does not always imply reduced computational complexity, perhaps because the relationships implied by the data and knowledge are in tension. [ABSTRACT FROM AUTHOR]

Discovering causal relationships among observed variables is an important research focus in data mining. Existing causal discovery approaches are mainly based on constraint-based methods and functional causal models (FCMs). However, the constraint-based method cannot identify the Markov equivalence class and the functional causal models cannot identify the complex interrelationships when multiple variables affect one variable. To address the two aforementioned problems, we propose a new graph structure Causal Star Graph (CSG) and a corresponding framework Causal Discovery via Causal Star Graphs (CD-CSG) to divide a causal directed acyclic graph into multiple CSGs for causal discovery. In this framework, we also propose a generalized learning in CSGs based on a variational approach to learn the representative intermediate variable of CSG’s non-central variables. Through the generalized learning in CSGs, the asymmetry in the forward and backward model of CD-CSG can be found to identify the causal directions in the directed acyclic graphs. We further divide the CSGs into three categories and provide the causal identification principle under each category in our proposed framework. Experiments using synthetic data show that the causal relationships between variables can be effectively identified with CD-CSG and the accuracy of CD-CSG is higher than the best existing model. By applying CD-CSG to real-world data, our proposed method can greatly augment the applicability and effectiveness of causal discovery. [ABSTRACT FROM AUTHOR]

The article addresses a question posed by V. Didelez regarding the expert consensus meeting and provides additional topics for further research that is believed to aid both epidemiology and causal discovery research. Topics include expert discussions when creating the consensus model, usefulness of knowing more about the traditional approach, and a benchmarking question on whether causal discovery is a useful aid for actual scientific progress.

Causal reasoning is a crucial part of science and human intelligence. In order to discover causal relationships from data, we need structure discovery methods. We provide a review of background theory and a survey of methods for structure discovery. We primarily focus on modern, continuous optimization methods, and provide reference to further resources such as benchmark datasets and software packages. Finally, we discuss the assumptive leap required to take us from structure to causality. [ABSTRACT FROM AUTHOR]

Finding a directed acyclic graph (DAG) that best encodes the conditional independence statements observable from data is a central question within causality. Algorithms that greedily transform one candidate DAG into another given a fixed set of moves have been particularly successful, for example, the greedy equivalence search, greedy interventional equivalence search, and max-min hill climbing algorithms. In 2010, Studeny\', Hemmecke, and Lindner introduced the characteristic imset (CIM) polytope, CIMp, whose vertices correspond to Markov equivalence classes, as a way of transforming causal discovery into a linear optimization problem. We show that the moves of the aforementioned algorithms are included within classes of edges of CIMp and that restrictions placed on the skeleton of the candidate DAGs correspond to faces of CIMp. Thus, we observe that greedy equivalence search, greedy interventional equivalence search, and max-min hill climbing all have geometric realizations as greedy edge-walks along CIMp. Furthermore, the identified edges of CIMp strictly generalize the moves of these algorithms. Exploiting this generalization, we introduce a greedy simplex-type algorithm called greedy CIM, and a hybrid variant, skeletal greedy CIM, that outperforms current competitors among hybrid and constraint-based algorithms. [ABSTRACT FROM AUTHOR]

Reduction of graphs is a class of procedures used to decrease the dimensionality of a given graph in which the properties of the reduced graph are to be induced from the properties of the larger original graph. This paper introduces both a new method for reducing chain graphs to simpler directed acyclic graphs (DAGs), that we call power chain graphs (PCG), as well as a procedure for structure learning of this new type of graph from correlational data of a Gaussian graphical model. A definition for PCGs is given, directly followed by the reduction method. The structure learning procedure is a two-step approach: first, the correlation matrix is used to cluster the variables; and then, the averaged correlation matrix is used to discover the DAGs using the PC-stable algorithm. The results of simulations are provided to illustrate the theoretical proposal, which demonstrate initial evidence for the validity of our procedure to recover the structure of power chain graphs. The paper ends with a discussion regarding suggestions for future studies as well as some practical implications. [ABSTRACT FROM AUTHOR]

This paper presents a computational framework that generates ensemble predictive mechanics models with uncertainty quantification (UQ). We first develop a causal discovery algorithm to infer causal relations among time-history data measured during each representative volume element (RVE) simulation through a directed acyclic graph. With multiple plausible sets of causal relationships estimated from multiple RVE simulations, the predictions are propagated in the derived causal graph while using a deep neural network equipped with dropout layers as a Bayesian approximation for UQ. We select two representative numerical examples (traction-separation laws for frictional interfaces, elastoplasticity models for granular assembles) to examine the accuracy and robustness of the proposed causal discovery method for the common material law predictions in civil engineering applications. [ABSTRACT FROM AUTHOR]

• Existing algorithms for LiNGAM do not use sparseness and non-Gaussianity sufficiently. • Penalized likelihood-based approach enables us to estimate the model efficiently. • Solutions can be obtained by ADMM-based algorithm with some devices. • Our method exceeds the existing methods in numerical experiments and real data analysis. We consider the problem of inferring the causal structure from observational data, especially when the structure is sparse. This type of problem is usually formulated as an inference of a Directed Acyclic Graph (DAG) model. The Linear Non-Gaussian Acyclic Model (LiNGAM) is one of the most successful DAG models, and various estimation methods have been developed. However, existing methods are not efficient for some reasons: (i) the sparse structure is not always incorporated in causal order estimation, and (ii) the information of higher-order moments of the data is not used in parameter estimation. To address these issues, we propose a new estimation method for a linear DAG model with non-Gaussian noises. The proposed method is based on a single statistical criterion that includes the log-likelihood of independent component analysis (ICA) and two penalty terms. The two penalties are related to the sparsity and the consistency condition, respectively. This criterion enables us to leverage the sparse structure and the information of higher-order moments throughout the estimation. For stable and efficient optimization, we propose some devices, such as a modified natural gradient. Numerical experiments show that the proposed method outperforms the existing methods. [ABSTRACT FROM AUTHOR]

Directed Acyclic Graphs (DAGs) provide an efficient framework to describe the causal relations in actual applications, and it appears more and more important to learn a DAG from training data in causal discovery. Recently, a novel methodology, which projects the acyclic constraints by an algebraic characterization and employs continuous optimization to carry the causal discovery, gradually became the mainstream. However, such methods focus on a best-fitting to the training data and cannot utilize the prior knowledge in an efficient way. To resolve this problem, we suggest incorporating structural constraints into continuous optimization. For edge constraints, we regard the activation value of the difference between the constraint matrix after thresholding and the weight matrix as the optimization goal. For path constraints, we use the deviation concluded from the power matrix on k th path graphs to design the penalty functions. For ordering constraints, we exploit the representation based on the negative edge/path constraints. The mathematical derivations prove that equality constraint program (ECP), in which proposed equality constraints powerfully embody the required structural restrictions, are solvable. Furthermore, the experimental evaluations indicate that the proposed method develops higher scalability and accuracy against state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

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 BDyMA to discover dynamic causal structure of high-dimensional networks. • We demonstrate the effectiveness of the BDyMA in comparison to both existing method. • We show that our method enhances the intrasubject and intersubject reliability. • We examine the trustworthiness of DTI data as prior knowledge of DEC discovery. [ABSTRACT FROM AUTHOR]

Learning the causal structure of high-dimensional non-stationary time series can help in understanding the data generation mechanism, which is a crucial task in machine learning. However, current causal discovery methods for high-dimensional non-stationary time series face several challenges, including the inability to effectively capture non-stationarity, failure to ensure acyclicity of causal graphs, and reliance on subjective threshold definitions, leading to suboptimal algorithm performance. To address these challenges, we introduce a novel Causal Structure Learning model for High-dimensional Non-stationary Time Series (CSL-HNTS). Firstly, this model presents a graph neural network to model the non-stationarity of time series. Secondly, it introduces a novel Directed Acyclic Graph (DAG) sampling method that transforms the space of DAGs into a continuous space, enabling the search for causal graphs within this continuous space to ensure acyclicity. Finally, the model proposes an automatic threshold definition method, without prior knowledge, to convert the weighted adjacency matrix into the Boolean adjacency matrix of the causal graph, thereby avoiding time-consuming postprocessing steps. The proposed approach is validated using simulation datasets and two real datasets, and is benchmarked against current state-of-the-art methods and ablation experiments. The results demonstrate a significant improvement over existing methods, highlighting the efficacy of the proposed model. • A Graph Neural Network (GNN) to model the non-stationarity of high-dimensional time series is proposed. • A novel method to transform the discrete space of directed acyclic graphs into a continuous space is introduced. • An automatic threshold definition method that does not rely on any prior knowledge to transform the weighted adjacency matrix into the Boolean adjacency matrix of a causal graph is presented. [ABSTRACT FROM AUTHOR]

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.

We consider the task of estimating a high-dimensional directed acyclic graph, given observations from a linear structural equation model with arbitrary noise distribution. By exploiting properties of common random graphs, we develop a new algorithm that requires conditioning only on small sets of variables. The proposed algorithm, which is essentially a modified version of the PC-Algorithm, offers significant gains in both computational complexity and estimation accuracy. In particular, it results in more efficient and accurate estimation in large networks containing hub nodes, which are common in biological systems. We prove the consistency of the proposed algorithm, and show that it also requires a less stringent faithfulness assumption than the PC-Algorithm. Simulations in low and high-dimensional settings are used to illustrate these findings. An application to gene expression data suggests that the proposed algorithm can identify a greater number of clinically relevant genes than current methods. [ABSTRACT FROM AUTHOR]

Causal discovery plays a vital role in the human understanding of the world. Searching a directed acyclic graph (DAG) from observed data is one of the most widely used methods. However, in most existing approaches, the global search has poor scalability, and the local search is often insufficient to discover a reliable causal graph. In this paper, we propose a generic metaheuristic method to discover the causal relationship in the DAG itself instead in of any equivalent but indirect substitutes. We first propose several novel heuristic factors to expand the search space and maintain acyclicity. Second, using these factors, we propose a metaheuristic algorithm to further search for the optimal solution closer to real causality in the DAG space. Theoretical studies show the correctness of our proposed method. Extensive experiments are conducted to verify its generalization ability, scalability, and effectiveness on real-world and simulated structures for both discrete and continuous models by comparing it with other state-of-the-art causal solvers. We also compare the performance of our method with that of a state-of-the-art approach on well-known medical data. [ABSTRACT FROM AUTHOR]

• A Causal-GAT is proposed with adaptive attention on cause variables. • Node representations are disentangled to improve feature extraction efficiency. • Expertise and data are combined for charactering the high-dimensional data structure. • A real dataset concerning HST braking systems fault detection is conducted. • Interpretability of the proposed method is investigated. Considering the importance of complex systems fault detection, much efforts have been dedicated to fault feature extraction with monitoring data. The graph-based approach has become a trending topic, which exploits the non-Euclidean structure and generates representation based on spatial information. However, most graph-based models are built based on correlation assumption, and disregards the causality which are intrinsic in system and its failure process. In this paper, a causal graph attention network with disentangled representations (Causal-GAT) is proposed for fault detection. High-dimensional variables are first characterized into directed acyclic graphs using data-driven causal discovery combining expertise. The causal graph, which represents variables' cause-effect relations, is fed into the Causal-GAT. Disentangled Causal Attention (DC-Attention) is proposed to adaptively aggregate cause variables for embedding the effect variables. To improve feature extraction efficiency in the multi-head attention, the DC-Attention enforces disentangled node representation by regularizing it with a specified causal condition. To verify the effectiveness of the proposed method, a real case study concerning the high-speed train braking systems is considered. Experimental results with the benchmark methods demonstrate the advantages of the proposed method. Validities of causal graph construction, representation disentanglement, as well as interpretability of the model are also discussed in this work. [ABSTRACT FROM AUTHOR]

Several algorithms have been proposed towards discovering the graphical structure of Bayesian networks. Most of these algorithms are restricted to observational data and some enable us to incorporate knowledge as constraints in terms of what can and cannot be discovered by an algorithm. A common type of such knowledge involves the temporal order of the variables in the data. For example, knowledge that event B occurs after observing A and hence, the constraint that B cannot cause A. This paper investigates real-world case studies that incorporate interesting properties of objective temporal variable order, and the impact these temporal constraints have on the learnt graph. The results show that most of the learnt graphs are subject to major modifications after incorporating incomplete temporal objective information. Because temporal information is widely viewed as a form of knowledge that is subjective, rather than as a form of data that tends to be objective, it is generally disregarded and reduced to an optional piece of information that only few of the structure learning algorithms may consider. The paper argues that objective temporal information should form part of observational data, to reduce the risk of disregarding such information when available and to encourage its reusability across related studies. [ABSTRACT FROM AUTHOR]