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Bayesian network is currently one of the most effective theoretical models in the field of uncertain knowledge expression and inference. Before utilizing Bayesian networks for analysis and inference, it is first necessary to obtain their network models through structural and parametric learning, and structure learning is the basis for parameter learning. Aiming at the existing firefly algorithm that does not conform to biological rules as well as learning the Bayesian network structure that has low efficiency and is easy to fall into local optimization, MGM-FA (firefly algorithm based on mutual information and gender mechanism) was designed. Firstly, the Bayesian network skeleton graph was obtained by calculating the mutual information of nodes, and the MGM-FA algorithm was driven to generate the initial population based on the skeleton graph. Secondly, a personalized Bayesian network population updating strategy based on the gender mechanism was introduced to safeguard the diversity of the Bayesian network individuals. Lastly, the local optimizer and perturbation operator were introduced to enhance the algorithm's ability of optimality seeking. Simulation experiments were carried out on standard networks of different sizes respectively, and the accuracy and efficiency of the algorithm are improved compared with existing algorithms of the same type. [ABSTRACT FROM AUTHOR]

Network analysis is an emerging field for the study of psychopathology that considers constructs as arising from the interactions among their constituents. Pairwise effects among psychological components are often investigated by using this framework. Few studies have applied Bayesian networks, models that include directed interactions to perform causal inference on psychological constructs. Directed graphical models may be less straightforward to interpret in case the construct at hand does not contain symptoms but instead psychometric items from self-report measures. However, they may be useful in validating specific research questions that arise while using standard pairwise network models. In this study, we use Bayesian networks to investigate a well-known psychological construct, empathy from the Interpersonal Reactivity Index, in large two samples of 1973 university students from Belgium. Overall, our results support the hypotheses emphasizing empathic concern (i.e., sympathy) as causally important in the construct of empathy, and overall attribute the primacy of emotional components of empathy over their intellectual counterparts. Bayesian networks help researchers identify the plausible causal relationships in psychometric data, to gain new insight on the psychological construct under examination, help generate new hypotheses and provide evidence relevant to old ones. [ABSTRACT FROM AUTHOR]

Bayesian networks (BNs) are highly effective in handling uncertain problems, which can assist in decision-making by reasoning with limited and incomplete information. Learning a faithful directed acyclic graph (DAG) from a large number of complex samples of a joint distribution is currently a challenging combinatorial problem. Due to the growing volume and complexity of data, some Bayesian structure learning algorithms are ineffective and lack the necessary precision to meet the required needs. In this paper, we propose a new PCCL-CC algorithm. To ensure the accuracy of the network structure, we introduce the new ensemble weights and edge constraints setting mechanism. In this mechanism, we employ a method that estimates the interaction between network nodes from multiple perspectives and divides the learning process into multiple stages. We utilize an asymmetric weighted ensemble method and adaptively adjust the network structure. Additionally, we propose a causal discovery method that effectively utilizes the causal relationships among data samples to correct the network structure and mitigate the influence of Markov equivalence classes (MEC). Experimental results on real datasets demonstrate that our approach outperforms state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Abstract Bayesian networks (BNs) are highly effective in handling uncertain problems, which can assist in decision-making by reasoning with limited and incomplete information. Learning a faithful directed acyclic graph (DAG) from a large number of complex samples of a joint distribution is currently a challenging combinatorial problem. Due to the growing volume and complexity of data, some Bayesian structure learning algorithms are ineffective and lack the necessary precision to meet the required needs. In this paper, we propose a new PCCL-CC algorithm. To ensure the accuracy of the network structure, we introduce the new ensemble weights and edge constraints setting mechanism. In this mechanism, we employ a method that estimates the interaction between network nodes from multiple perspectives and divides the learning process into multiple stages. We utilize an asymmetric weighted ensemble method and adaptively adjust the network structure. Additionally, we propose a causal discovery method that effectively utilizes the causal relationships among data samples to correct the network structure and mitigate the influence of Markov equivalence classes (MEC). Experimental results on real datasets demonstrate that our approach outperforms state-of-the-art methods.

Federated learning makes it possible to train a machine learning model on decentralized data. Bayesian networks are widely used probabilistic graphical models. While some research has been published on the federated learning of Bayesian networks, publications on Bayesian networks in a vertically partitioned data setting are limited, with important omissions, such as handling missing data. We propose a novel method called VertiBayes to train Bayesian networks (structure and parameters) on vertically partitioned data, which can handle missing values as well as an arbitrary number of parties. For structure learning we adapted the K2 algorithm with a privacy-preserving scalar product protocol. For parameter learning, we use a two-step approach: first, we learn an intermediate model using maximum likelihood, treating missing values as a special value, then we train a model on synthetic data generated by the intermediate model using the EM algorithm. The privacy guarantees of VertiBayes are equivalent to those provided by the privacy preserving scalar product protocol used. We experimentally show VertiBayes produces models comparable to those learnt using traditional algorithms. Finally, we propose two alternative approaches to estimate the performance of the model using vertically partitioned data and we show in experiments that these give accurate estimates. [ABSTRACT FROM AUTHOR]

When learning the structure of a Bayesian network, the search space expands significantly as the network size and the number of nodes increase, leading to a noticeable decrease in algorithm efficiency. Traditional constraint-based methods typically rely on the results of conditional independence tests. However, excessive reliance on these test results can lead to a series of problems, including increased computational complexity and inaccurate results, especially when dealing with large-scale networks where performance bottlenecks are particularly evident. To overcome these challenges, we propose a Markov blanket discovery algorithm based on constrained local neighborhoods for constructing undirected independence graphs. This method uses the Markov blanket discovery algorithm to refine the constraints in the initial search space, sets an appropriate constraint radius, thereby reducing the initial computational cost of the algorithm and effectively narrowing the initial solution range. Specifically, the method first determines the local neighborhood space to limit the search range, thereby reducing the number of possible graph structures that need to be considered. This process not only improves the accuracy of the search space constraints but also significantly reduces the number of conditional independence tests. By performing conditional independence tests within the local neighborhood of each node, the method avoids comprehensive tests across the entire network, greatly reducing computational complexity. At the same time, the setting of the constraint radius further improves computational efficiency while ensuring accuracy. Compared to other algorithms, this method can quickly and efficiently construct undirected independence graphs while maintaining high accuracy. Experimental simulation results show that, this method has significant advantages in obtaining the structure of undirected independence graphs, not only maintaining an accuracy of over 96% but also reducing the number of conditional independence tests by at least 50%. This significant performance improvement is due to the effective constraint on the search space and the fine control of computational costs. [ABSTRACT FROM AUTHOR]

Understanding consumers' intention of using contactless logistics technology is necessary for logistics service providers to make value-added business strategies in the COVID-19 pandemic. Previous studies have suggested that multiple factors shall be considered when investigating the intention, but few have attempted to comprehensively explain the causality of the intention. To bridge this gap, this study develops a Genetic Algorithm (GA)-based structure learning method and constructs a Copula-Bayesian Network (Copula-BN) upon questionnaire survey data to explore the causation of the intention. Based on the derived Copula-BN, we identify the key factors that contribute to the intention and reveal the causal relations along the main branch composed of those factors. Several findings provide theoretical and practical insights into the consumer-technology interaction under the pandemic context. Besides, this study demonstrates that the structure of the Copula-BN is rational and reasonable, which provides a solid basis for investigating the causality of the intention. [ABSTRACT FROM AUTHOR]

Causal Bayesian Networks (CBNs) provide an important tool for reasoning under uncertainty with potential application to many complex causal systems. Structure learning algorithms that can tell us something about the causal structure of these systems are becoming increasingly important. In the literature, the validity of these algorithms is often tested for sensitivity over varying sample sizes, hyper-parameters, and occasionally objective functions, but the effect of the order in which the variables are read from data is rarely quantified. We show that many commonly-used algorithms, both established and state-of-the-art, are more sensitive to variable ordering than these other factors when learning CBNs from discrete variables. This effect is strongest in hill-climbing and its variants where we explain how it arises, but extends to hybrid, and to a lesser-extent, constraint-based algorithms. Because the variable ordering is arbitrary, any significant effect it has on learnt graph accuracy is concerning, and raises questions about the validity of both many older and more recent results produced by these algorithms in practical applications and their rankings in performance evaluations. [ABSTRACT FROM AUTHOR]

Graphical models are used to capture complex multivariate relationships and have applications in diverse disciplines such as biology, physics, and economics. Within this field, Gaussian graphical models aim to identify the pairs of variables whose dependence is maintained even after conditioning on the remaining variables in the data, known as the conditional dependence structure of the data. There are many existing software packages for Gaussian graphical modeling, however, they often make restrictive assumptions that reduce their flexibility for modeling data that are not identically distributed. Conversely, covdepGE is an R implementation of a variational weighted pseudo-likelihood algorithm for modeling the conditional dependence structure as a continuous function of an extraneous covariate. To build on the efficiency of this algorithm, covdepGE leverages parallelism and C++ integration with R. Additionally, covdepGE provides fully-automated and data-driven hyperparameter specification while maintaining flexibility for the user to decide key components of the estimation procedure. Through an extensive simulation study spanning diverse settings, covdepGE is demonstrated to be top of its class in recovering the ground truth conditional dependence structure while efficiently managing computational overhead. [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]

Patch foraging presents a sequential decision-making problem widely studied across organisms-stay with a current option or leave it in search of a better alternative? Behavioral ecology has identified an optimal strategy for these decisions, but, across species, foragers systematically deviate from it, staying too long with an option or overharvesting relative to this optimum. Despite the ubiquity of this behavior, the mechanism underlying it remains unclear and an object of extensive investigation. Here, we address this gap by approaching foraging as both a decision-making and learning problem. Specifically, we propose a model in which foragers 1) rationally infer the structure of their environment and 2) use their uncertainty over the inferred structure representation to adaptively discount future rewards. We find that overharvesting can emerge from this rational statistical inference and uncertainty adaptation process. In a patch-leaving task, we show that human participants adapt their foraging to the richness and dynamics of the environment in ways consistent with our model. These findings suggest that definitions of optimal foraging could be extended by considering how foragers reduce and adapt to uncertainty over representations of their environment.

Abstract Federated learning makes it possible to train a machine learning model on decentralized data. Bayesian networks are widely used probabilistic graphical models. While some research has been published on the federated learning of Bayesian networks, publications on Bayesian networks in a vertically partitioned data setting are limited, with important omissions, such as handling missing data. We propose a novel method called VertiBayes to train Bayesian networks (structure and parameters) on vertically partitioned data, which can handle missing values as well as an arbitrary number of parties. For structure learning we adapted the K2 algorithm with a privacy-preserving scalar product protocol. For parameter learning, we use a two-step approach: first, we learn an intermediate model using maximum likelihood, treating missing values as a special value, then we train a model on synthetic data generated by the intermediate model using the EM algorithm. The privacy guarantees of VertiBayes are equivalent to those provided by the privacy preserving scalar product protocol used. We experimentally show VertiBayes produces models comparable to those learnt using traditional algorithms. Finally, we propose two alternative approaches to estimate the performance of the model using vertically partitioned data and we show in experiments that these give accurate estimates.

In view of the low accuracy of transformer fault diagnosis, a transformer fault diagnosis method based on ISMA(Improved Slime Mold optimization Algorithm) and optimized BN(Bayesian Network) is proposed. The hill-climbing algorithm searches the oriented maximum support tree to obtain the initial structure of the Bayesian network, that is, the initial population. The reverse learning strategy and SCA(Sine Cosine Algorithm) are introduced into the improved slime mold optimization algorithm to increase population diversity, update population location, and avoid the population falling into local optimal. The characteristics of transformer fault state are selected by the improved code-free ratio method, and the structure of Bayesian network is optimized by the improved slime mold optimization algorithm to improve the accuracy of transformer fault diagnosis based on Bayesian network. Different kinds of test functions are used to verify that the improved slime mold optimization algorithm has the excellent performance of fast convergence speed and high convergence accuracy. The simulation results show that the accuracy of the training set and the test set of the ISMA-BN diagnostic model is up to 98.2% and 97.14%, respectively, which has certain research value. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The Bayesian network provides a useful way to deal with uncertain information, which helps researchers to better understand the human cognitive process. The foundation of the Bayesian network focuses on identifying the qualitative relations between variables, which is also called structure learning. Local search in the ordering space is an effective method for learning the structure of large-scale Bayesian networks. However, the existing algorithms tend to the local optimum and stop searching for superior solutions. To tackle the problem, random perturbations are applied to the local optimum without specific strategies, resulting in many meaningless restarts that sacrifice much time but still fail to improve the results. As an extension of the local search, simulated annealing stochastically searches the solution spaces and selects relatively poor solutions with a certain probability. This paper proposes a method based on simulated annealing to learn Bayesian network structure in the ordering space, which expands the search scope by probabilistically accepting poorer solutions. Moreover, we improve simulated annealing by adding a memory module and modifying the termination condition. The memory module records the optimal solution before accepting a worse solution, which avoids losing the possible global optimal solution. The new termination condition is related to the quality of the search results, which reduces many redundant searches. Besides, we design a new restart strategy based on ensemble learning. When the search traps in the local optimum, a new ordering is obtained to restart the search by perturbing the current ordering with constraints. The constraints are generated by the results of ensemble learning on multiple structures, which help the algorithm approach the global optimum solution. Experimental results show that our proposed methods improve the accuracy and efficiency in learning the optimal structure over the benchmarks compared to the state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

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Causal structure learning is one of the major fields in causal inference. Only the Markov equivalence class (MEC) can be learned from observational data; to fully orient unoriented edges, experimental data need to be introduced from external intervention experiments to improve the identifiability of causal graphs. Finding suitable intervention targets is key to intervention experiments. We propose a causal structure active learning strategy based on graph structures. In the context of randomized experiments, the central nodes of the directed acyclic graph (DAG) are considered as the alternative intervention targets. In each stage of the experiment, we decompose the chain graph by removing the existing directed edges; then, each connected component is oriented separately through intervention experiments. Finally, all connected components are merged to obtain a complete causal graph. We compare our algorithm with previous work in terms of the number of intervention variables, convergence rate and model accuracy. The experimental results show that the performance of the proposed method in restoring the causal structure is comparable to that of previous works. The strategy of finding the optimal intervention target is simplified, which improves the speed of the algorithm while maintaining the accuracy. [ABSTRACT FROM AUTHOR]

Directed acyclic graphs provide an effective framework for learning causal relationships among variables given multivariate observations. Under pure observational data, directed acyclic graphs encoding the same conditional independencies cannot be distinguished and are collected into Markov equivalence classes. In many contexts, however, observational measurements are supplemented by interventional data that improve directed acyclic graph identifiability and enhance causal effect estimation. We propose a Bayesian framework for multivariate data partially generated after stochastic interventions. To this end, we introduce an effective prior elicitation procedure leading to a closed-form expression for the directed acyclic graph marginal likelihood and guaranteeing score equivalence among directed acyclic graphs that are Markov equivalent post intervention. Under the Gaussian setting, we show, in terms of posterior ratio consistency, that the true network will be asymptotically recovered, regardless of the specific distribution of the intervened variables and of the relative asymptotic dominance between observational and interventional measurements. We validate our theoretical results via simulation and we implement a Markov chain Monte Carlo sampler for posterior inference on the space of directed acyclic graphs on both synthetic and biological protein expression data. [ABSTRACT FROM AUTHOR]

The article introduces SLED, a Structure Learning based Denoising framework for recommendation systems. It addresses the challenge of denoising implicit feedback in recommender systems without relying on additional behavior signals. It is reported that SLED consists of two phases, center-aware graph structure learning and denoised recommendation.

Structure learning is the core of graph model Bayesian Network learning, and the current mainstream single search algorithm has problems such as poor learning effect, fuzzy initial network, and easy falling into local optimum. In this paper, we propose a heuristic learning algorithm HC-PSO combining the HC (Hill Climbing) algorithm and PSO (Particle Swarm Optimization) algorithm, which firstly uses HC algorithm to search for locally optimal network structures, takes these networks as the initial networks, then introduces mutation operator and crossover operator, and uses PSO algorithm for global search. Meanwhile, we use the DE (Differential Evolution) strategy to select the mutation operator and crossover operator. Finally, experiments are conducted in four different datasets to calculate BIC (Bayesian Information Criterion) and HD (Hamming Distance), and comparative analysis is made with other algorithms, the structure shows that the HC-PSO algorithm is superior in feasibility and accuracy. [ABSTRACT FROM AUTHOR]

Understanding how the human body works during sleep and how this varies in the population is a task with significant implications for medicine. Polysomnographic studies, or sleep studies, are a common diagnostic method that produces a significant quantity of time-series sensor data. This study seeks to learn the causal structure from data from polysomnographic studies carried out on 600 adult volunteers in the United States. Two methods are used to learn the causal structure of these data: the well-established Granger causality and "DYNOTEARS", a modern approach that uses continuous optimisation to learn dynamic Bayesian networks (DBNs). The results from the two methods are then compared. Both methods produce graphs that have a number of similarities, including the mutual causation between electrooculogram (EOG) and electroencephelogram (EEG) signals and between sleeping position and SpO2 (blood oxygen level). However, DYNOTEARS, unlike Granger causality, frequently finds a causal link to sleeping position from the other variables. Following the creation of these causal graphs, the relationship between the discovered causal structure and the characteristics of the participants is explored. It is found that there is an association between the waist size of a participant and whether a causal link is found between the electrocardiogram (ECG) measurement and the EOG and EEG measurements. It is concluded that a person's body shape appears to impact the relationship between their heart and brain during sleep and that Granger causality and DYNOTEARS can produce differing results on real-world data. [ABSTRACT FROM AUTHOR]

The reconstruction of 3D shapes from a single view has been a longstanding challenge. Previous methods have primarily focused on learning either geometric features that depict overall shape contours but are insufficient for occluded regions, local features that capture details but cannot represent the complete structure, or structural features that encode part relationships but require predefined semantics. However, the fusion of geometric, local, and structural features has been lacking, leading to inaccurate reconstruction of shapes with occlusions or novel compositions. To address this issue, we propose a two-stage approach for achieving 3D shape reconstruction. In the first stage, we encode the hierarchical structure features of the 3D shape using an encoder-decoder network. In the second stage, we enhance the hierarchical structure features by fusing them with global and point features and feed the enhanced features into a signed distance function (SDF) prediction network to obtain rough SDF values. Using the camera pose, we project arbitrary 3D points in space onto different depth feature maps of the CNN and obtain their corresponding positions. Then, we concatenate the features of these corresponding positions together to form local features. These local features are also fed into the SDF prediction network to obtain fine-grained SDF values. By fusing the two sets of SDF values, we improve the accuracy of the model and enable it to reconstruct other object types with higher quality. Comparative experiments demonstrate that the proposed method outperforms state-of-the-art approaches in terms of accuracy. [ABSTRACT FROM AUTHOR]

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]

Bayesian networks have been widely used to generate causal hypotheses from multivariate data. Despite their popularity, the vast majority of existing causal discovery approaches make the strong assumption of a (partially) homogeneous sampling scheme. However, such assumption can be seriously violated, causing significant biases when the underlying population is inherently heterogeneous. To this end, we propose a novel causal Bayesian network model, termed BN‐LTE, that embeds heterogeneous samples onto a low‐dimensional manifold and builds Bayesian networks conditional on the embedding. This new framework allows for more precise network inference by improving the estimation resolution from the population level to the observation level. Moreover, while causal Bayesian networks are in general not identifiable with purely observational, cross‐sectional data due to Markov equivalence, with the blessing of causal effect heterogeneity, we prove that the proposed BN‐LTE is uniquely identifiable under relatively mild assumptions. Through extensive experiments, we demonstrate the superior performance of BN‐LTE in causal structure learning as well as inferring observation‐specific gene regulatory networks from observational data. [ABSTRACT FROM AUTHOR]

Joint modeling of a large number of variables often requires dimension reduction strategies that lead to structural assumptions of the underlying correlation matrix, such as equal pair-wise correlations within subsets of variables. The underlying correlation matrix is thus of interest for both model specification and model validation. In this article, we develop tests of the hypothesis that the entries of the Kendall rank correlation matrix are linear combinations of a smaller number of parameters. The asymptotic behavior of the proposed test statistics is investigated both when the dimension is fixed and when it grows with the sample size. We pay special attention to the restricted hypothesis of partial exchangeability, which contains full exchangeability as a special case. We show that under partial exchangeability, the test statistics and their large-sample distributions simplify, which leads to computational advantages and better performance of the tests. We propose various scalable numerical strategies for implementation of the proposed procedures, investigate their behavior through simulations and power calculations under local alternatives, and demonstrate their use on a real dataset of mean sea levels at various geographical locations. for this article are available online. [ABSTRACT FROM AUTHOR]

Bayesian network is a popular approach to uncertainty knowledge representation and reasoning. Structure learning is the first step to learn a Bayesian network. Score-based methods are one of the most popular ways of learning the structure. In most cases, the score of Bayesian network is defined as adding the log-likelihood score and complexity score by using the penalty function. If the penalty function is set unreasonably, it may hurt the performance of structure search. Thus, Bayesian network structure learning is essentially a bi-objective optimization problem. However, the existing bi-objective structure learning algorithms can only be applied to small-scale networks. To this end, this paper proposes a bi-objective evolutionary Bayesian network structure learning algorithm via skeleton constraint (BBS) for the medium-scale networks. To boost the performance of searching, BBS introduces the random order prior (ROP) initial operator. ROP generates a skeleton to constrain the searching space, which is the key to expanding the scale of structure learning problems. Then, the acyclic structures are guaranteed by adding the orders of variables in the initial skeleton. After that, BBS designs the Pareto rank based crossover and skeleton guided mutation operators. The operators operate on the skeleton obtained in ROP to make the search more targeted. Finally, BBS provides a strategy to choose the final solution. The experimental results show that BBS can always find the structure which is closer to the ground truth compared with the single-objective structure learning methods. Furthermore, compared with the existing bi-objective structure learning methods, BBS is scalable and can be applied to medium-scale Bayesian network datasets. On the educational problem of discovering the influencing factors of students’ academic performance, BBS provides higher quality solutions and is featured with the flexibility of solution selection compared with the widely-used Bayesian network structure learning methods. [ABSTRACT FROM AUTHOR]

Abstract Background Cognitive flexibility refers to the capacity to shift between conceptual representations particularly in response to changes in instruction and feedback. It enables individuals to swiftly adapt to changes in their environment and has significant implications for learning. The present study focuses on investigating changes in cognitive flexibility following an intervention programme—Structure Learning training. Methods Participants are pseudo-randomised to either the Training or Control group, while matched on age, sex, intelligence and cognitive flexibility performance. In the Training group, participants undergo around 2 weeks of training (at least 13 sessions) on Structure Learning. In the Control group, participants do not have to undergo any training and are never exposed to the Structure Learning task. The effects of Structure Learning training are investigated at both the behavioural and neural level. We measured covariates that can influence an individual’s training performance before the training phase and outcome measures that can potentially show training benefits after the training phase. At the behavioural level, we investigated outcomes in both cognitive and social aspects with a primary focus on executive functions. At the neural level, we employed a multimodality approach and investigated potential changes to functional connectivity patterns, neurometabolite concentration in the frontal brain regions, and brain microstructure and myelination. Discussion We reported the development of a novel training programme based on Structure Learning that aims to hone a general learning ability to potentially achieve extensive transfer benefits across various cognitive constructs. Potential transfer benefits can be exhibited through better performance in outcome measures between Training and Control participants, and positive associations between training performance and outcomes after the training in Training participants. Moreover, we attempt to substantiate behavioural findings with evidence of neural changes across different imaging modalities by the Structure Learning training. Trial registration National Institutes of Health U.S. National Library of Medicine ClinicalTrials.gov NCT05611788. Registered on 7 November 2022. Protocol version: 11 May 2023.

Bayesian networks are analytical models that may represent probabilistic dependent connections among variables and are useful in machine learning for generating knowledge structure. Due to the vastness of the solution space, learning Bayesian network (BN) structures from data is an NP-hard problem. The score and search technique is one Bayesian Network structure learning strategy. In Bayesian network structure learning the Falcon Optimization Algorithm (FOA) is presented and evaluated by the authors. Inserting, Reversing, Moving, and Deleting, are used in the method to create the FOA for finding the best structural solution. The FOA algorithm is based on the falcon's searching technique during drought conditions. The suggested technique is compared to the score metric function of Pigeon Inspired search algorithm, Greedy Search, and Antlion optimization search algorithm. The performance of these techniques in terms of confusion matrices was further evaluated by the authors using a variety of benchmark data sets. The Falcon optimization algorithm outperforms the previous algorithms and generates higher scores and accuracy values, as evidenced by the results of our experiments.

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]

The computational complexity of Bayesian Networks(BN) increases with the increase of the number of nodes, and the optimal structure of BN is still a NP(Non-deterministic Polynomial Time)-hard problem. To optimize the BN structure and improve the computing power of the complex BN structure, the BN structure is optimized through the hybrid learning method of constraints and scores. In the constrained learning, PC (Peter-Clark) algorithm is used to generate the initial network structure to improve the initial score of the network. Score-based learning uses the sparrow search algorithm to find the optimal structure of BN to enhance its scoring search ability in BN. The sparrow search algorithm and PC algorithm are applied to BN to optimize its structure, and the standard BN is used to conduct experiments, which proves the feasibility and effectiveness of the proposed algorithm in BN structure learning. Experiments on networks with different complexities show that the proposed method obtains better BIC scores than other algorithms, and in the test of 2 000 samples on the ASIA network, the error from the standard score is only 0.2. [ABSTRACT FROM AUTHOR]

Constructing Bayesian network structures from data is an NP-hard problem. This paper presents a novel method for Bayesian network structure learning using a discrete Harris hawks optimization algorithm, named BNC-HHO. It uses the max-min parents and children algorithm, V-structure & log-likelihood function, and neighborhood structures to limit the search space during the initialization phase. Then, the Harris hawk optimization algorithm is extended from the continuous to the discrete domain by redefining the movement strategies of hawks using genetic operators in genetic algorithm. The crossover and mutation operations in the proposed method are controlled by an adaptive crossover and mutation rate based on the X-conditional cloud. To balance the exploration and exploitation phases, a nonlinear escaping energy curve is also designed. Finally, the quality of the solution is further improved using a local optimizer. Experiments on various standard networks demonstrate that the proposed algorithm can quickly get higher structure scores and better convergence accuracy in most cases compared to other state-of-the-art algorithms. It indicates that the proposed algorithm can be used as an effective and feasible method for learning Bayesian network structures. [ABSTRACT FROM AUTHOR]

Bayesian networks play a vital role in human understanding of the world. Finding a precise equivalence class of a Bayesian network is an effective way to represent causality. However, as one of the most widely used methods of searching for equivalence classes, greedy equivalence search (GES), can easily fall into a local optimum. To address this problem, we explore the reasons why GES becomes stuck in a local optimum by analyzing its operators and search strategies in detail. Moreover, we demonstrate that converting the search space into another space can address the drawbacks of local search in the space of the equivalence class. Accordingly, two novel frameworks based on switching spaces are proposed to improve GES. Finally, the effectiveness, scalability, and stability of the proposed methods are verified by extensive experiments through which our frameworks are compared with state-of-the-art methods on different benchmarks. The results show that our methods significantly strengthen the performance of GES. [ABSTRACT FROM AUTHOR]

To obtain the optimal Bayesian network (BN) structure, researchers often use the hybrid learning algorithm that combines the constraint-based (CB) method and the score-and-search (SS) method. This hybrid method has the problem that the search efficiency could be improved due to the ample search space. The search process quickly falls into the local optimal solution, unable to obtain the global optimal. Based on this, the Particle SwarmOptimization (PSO) algorithm based on the search space constraint process is proposed. In the first stage, the method uses dynamic adjustment factors to constrain the structure search space and enrich the diversity of the initial particles. In the second stage, the update mechanism is redefined, so that each step of the update process is consistent with the current structure which forms a one-to-one correspondence. At the same time, the "self-awakened" mechanism is added to prevent precocious particles frombeing part of the best. After the fitness value of the particle converges prematurely, the activation operation makes the particles jump out of the local optimal values to prevent the algorithm from converging too quickly into the local optimum. Finally, the standard network dataset was compared with other algorithms. The experimental results showed that the algorithmcould find the optimal solution at a small number of iterations and a more accurate network structure to verify the algorithm's effectiveness. [ABSTRACT FROM AUTHOR]

Probabilistic graphical models enjoy great popularity in a wide range of domains due to their ability to model the conditional dependency relationships among random variables. This paper explores the structure learning for the exponential family graphical model with false discovery rate (FDR) control. Most existing FDR-controlled structure learning procedures have been designed for the Gaussian graphical model (GGM). A systematic approach for more general exponential family graphical models is still lacking. In this paper, we introduce a unified procedure to learn the structure of the exponential family graphical model with FDR control utilizing the symmetrized data aggregation (SDA) technique via sample splitting, data screening, and information pooling. We show that our method controls FDR asymptotically under some mild conditions. Extensive simulation results and two real-data examples validate the effectiveness of our method. [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.

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.

Causal structure learning is one of the major fields in causal inference. Only the Markov equivalence class (MEC) can be learned from observational data; to fully orient unoriented edges, experimental data need to be introduced from external intervention experiments to improve the identifiability of causal graphs. Finding suitable intervention targets is key to intervention experiments. We propose a causal structure active learning strategy based on graph structures. In the context of randomized experiments, the central nodes of the directed acyclic graph (DAG) are considered as the alternative intervention targets. In each stage of the experiment, we decompose the chain graph by removing the existing directed edges; then, each connected component is oriented separately through intervention experiments. Finally, all connected components are merged to obtain a complete causal graph. We compare our algorithm with previous work in terms of the number of intervention variables, convergence rate and model accuracy. The experimental results show that the performance of the proposed method in restoring the causal structure is comparable to that of previous works. The strategy of finding the optimal intervention target is simplified, which improves the speed of the algorithm while maintaining the accuracy.

Experience is known to facilitate our ability to interpret sequences of events and make predictions about the future by extracting temporal regularities in our environments. Here, we ask whether uncertainty in dynamic environments affects our ability to learn predictive structures. We exposed participants to sequences of symbols determined by first-order Markov models and asked them to indicate which symbol they expected to follow each sequence. We introduced uncertainty in this prediction task by manipulating the: (a) probability of symbol co-occurrence, (b) stimulus presentation rate. Further, we manipulated feedback, as it is known to play a key role in resolving uncertainty. Our results demonstrate that increasing the similarity in the probabilities of symbol cooccurrence impaired performance on the prediction task. In contrast, increasing uncertainty in stimulus presentation rate by introducing temporal jitter resulted in participants adopting a strategy closer to probability maximization than matching and improving in the prediction tasks. Next, we show that feedback plays a key role in learning predictive statistics. Trial-by-trial feedback yielded stronger improvement than block feedback or no feedback; that is, participants adopted a strategy closer to probability maximization and showed stronger improvement when trained with trial-by-trial feedback. Further, correlating individual strategy with learning performance showed better performance in structure learning for observers who adopted a strategy closer to maximization. Our results indicate that executive cognitive functions (i.e., selective attention) may account for this individual variability in strategy and structure learning ability. Taken together, our results provide evidence for flexible structure learning; individuals adapt their decision strategy closer to probability maximization, reducing uncertainty in temporal sequences and improving their ability to learn predictive statistics in variable environments. [ABSTRACT FROM AUTHOR]

Background: Cognitive flexibility refers to the capacity to shift between conceptual representations particularly in response to changes in instruction and feedback. It enables individuals to swiftly adapt to changes in their environment and has significant implications for learning. The present study focuses on investigating changes in cognitive flexibility following an intervention programme—Structure Learning training. Methods: Participants are pseudo-randomised to either the Training or Control group, while matched on age, sex, intelligence and cognitive flexibility performance. In the Training group, participants undergo around 2 weeks of training (at least 13 sessions) on Structure Learning. In the Control group, participants do not have to undergo any training and are never exposed to the Structure Learning task. The effects of Structure Learning training are investigated at both the behavioural and neural level. We measured covariates that can influence an individual's training performance before the training phase and outcome measures that can potentially show training benefits after the training phase. At the behavioural level, we investigated outcomes in both cognitive and social aspects with a primary focus on executive functions. At the neural level, we employed a multimodality approach and investigated potential changes to functional connectivity patterns, neurometabolite concentration in the frontal brain regions, and brain microstructure and myelination. Discussion: We reported the development of a novel training programme based on Structure Learning that aims to hone a general learning ability to potentially achieve extensive transfer benefits across various cognitive constructs. Potential transfer benefits can be exhibited through better performance in outcome measures between Training and Control participants, and positive associations between training performance and outcomes after the training in Training participants. Moreover, we attempt to substantiate behavioural findings with evidence of neural changes across different imaging modalities by the Structure Learning training. Trial registration: National Institutes of Health U.S. National Library of Medicine ClinicalTrials.gov NCT05611788. Registered on 7 November 2022. Protocol version: 11 May 2023. [ABSTRACT FROM AUTHOR]

Learning causal structure from observed data has important applications. An existing method for learning causal structure is to learn causal structure by testing the independence between noise and causal variables under the functional causal model assumption. However, such methods often involve highly computationally complex in process of testing independence, which affects the practicability and robustness of the structure learning algorithm. To this end, this paper proposed a causal structure learning algorithm that used higher-order cumulants as independence scores under a linear non-Gaussian model. The algorithm was mainly divided into two steps. The first step was to use the method based on conditional independence constraints to learn the Markov equivalence class of the causal structure. The second step was to define a score based on high-order cumulants, the score could determine the independence of two random variables so that the causal structure of the best independence score could be searched from the Markov equivalence class as the output of the algorithm. The advantages of this algorithm were: a)Compared with the independence test based on the kernel method, the method had lower computational complexity. b)The method based on score search could always obtain a model that best matches the data generation process, which improved the robustness of the learning method. Experimental results show that the high-order cumulant-based causal structure learning method improves the F1 score by 5% in synthetic data and learns more causal directions in real data. [ABSTRACT FROM AUTHOR]

Bayesian networks are analytical models that may represent probabilistic dependent connections among variables and are useful in machine learning for generating knowledge structure. Due to the vastness of the solution space, learning Bayesian network (BN) structures from data is an NP-hard problem. The score and search technique is one Bayesian Network structure learning strategy. In Bayesian network structure learning the Falcon Optimization Algorithm (FOA) is presented and evaluated by the authors. Inserting, Reversing, Moving, and Deleting, are used in the method to create the FOA for finding the best structural solution. The FOA algorithm is based on the falcon's searching technique during drought conditions. The suggested technique is compared to the score metric function of Pigeon Inspired search algorithm, Greedy Search, and Antlion optimization search algorithm. The performance of these techniques in terms of confusion matrices was further evaluated by the authors using a variety of benchmark data sets. The Falcon optimization algorithm outperforms the previous algorithms and generates higher scores and accuracy values, as evidenced by the results of our experiments. [ABSTRACT FROM AUTHOR]