Bayesian Network Structure Learning Research Articles

Parallel structural learning of Bayesian networks: Iterative divide and conquer algorithm based on structural fusion

Learning Bayesian Networks (BNs) from high-dimensional data is a complex and time-consuming task. Although the literature includes approaches based on horizontal (instances) or vertical (variables) partitioning, none can guarantee the same theoretical properties as the Greedy Equivalence Search (GES) algorithm, except those based on the GES algorithm itself. This paper proposes a distributed BN learning algorithm that uses GES as the local learning algorithm, ensuring the same theoretical properties as GES but requiring less CPU time. The two main novelties in our proposed method are (1) the distribution of the set of possible edges among local learning processes, which are constrained to only use its local edge set; and (2) the use of BN fusion to aggregate the networks learned constrained to local edge sets. The algorithm is iterative, and at each step, the last aggregated network is used as the starting point by each local BN process. After a comprehensive experimental evaluation, the results show that the proposed algorithm (pGES) obtains networks of equal or better quality than GES in less computational time. This improvement is especially noticeable in high-dimensional BNs.

Dynamic Bayesian network structure learning based on an improved bacterial foraging optimization algorithm

With the rapid development of artificial intelligence and data science, Dynamic Bayesian Network (DBN), as an effective probabilistic graphical model, has been widely used in many engineering fields. And swarm intelligence algorithm is an optimization algorithm based on natural selection with the characteristics of distributed, self-organization and robustness. By applying the high-performance swarm intelligence algorithm to DBN structure learning, we can fully utilize the algorithm's global search capability to effectively process time-based data, improve the efficiency of network generation and the accuracy of network structure. This study proposes an improved bacterial foraging optimization algorithm (IBFO-A) to solve the problems of random step size, limited group communication, and the inability to maintain a balance between global and local searching. The IBFO-A algorithm framework comprises four layers. First, population initialization is achieved using a logistics-sine chaotic mapping strategy as the basis for global optimization. Second, the activity strategy of a colony foraging trend is constructed by combining the exploration phase of the Osprey optimization algorithm. Subsequently, the strategy of bacterial colony propagation is improved using a "genetic" approach and the Multi-point crossover operator. Finally, the elimination-dispersal activity strategy is employed to escape the local optimal solution. To solve the problem of complex DBN learning structures due to the introduction of time information, a DBN structure learning method called IBFO-D, which is based on the IBFO-A algorithm framework, is proposed. IBFO-D determines the edge direction of the structure by combining the dynamic K2 scoring function, the designed V-structure orientation rule, and the trend activity strategy. Then, according to the improved reproductive activity strategy, the concept of "survival of the fittest" is applied to the network candidate solution while maintaining species diversity. Finally, the global optimal network structure with the highest score is obtained based on the elimination-dispersal activity strategy. Multiple tests and comparison experiments were conducted on 10 sets of benchmark test functions, two non-temporal and temporal data types, and six data samples of two benchmark 2T-BN networks to evaluate and analyze the optimization performance and structure learning ability of the proposed algorithm under various data types. The experimental results demonstrated that IBFO-A exhibits good convergence, stability, and accuracy, whereas IBFO-D is an effective approach for learning DBN structures from data and has practical value for engineering applications.

Finding community structure in Bayesian networks by heuristic K-standard deviation method

When constructing a Bayesian network for high-dimensional data, due to the complex relationships among distinct nodes, the difficulty in detecting the community structure will directly restrict the feasibility of the divide-and-conquer learning algorithm. This study attempts to solve this problem from the shortest path perspective and proposes the heuristic K-standard deviation algorithm. Firstly, we design a novel heuristic function and drive the A* algorithm to find the shortest paths between nodes in the Bayesian network. In addition, the new heuristic function is theoretically proved to be admissible and consistent. Experiments on different synthetic datasets and benchmark Bayesian networks verify that the proposed heuristic K-standard deviation algorithm generally gets better clustering performance than other representative algorithms and improves the efficiency and accuracy of the conventional Bayesian network structure learning algorithms, especially for high-dimensional data.

Parallel and Distributed Bayesian Network Structure Learning

Parallel and Distributed Bayesian Network Structure Learning

Assessment of the organizational factors in incident management practices in healthcare: A tree augmented Naive Bayes model.

Despite the exponential transformation occurring in the healthcare industry, operational failures pose significant challenges in the delivery of safe and efficient care. Incident management plays a crucial role in mitigating these challenges; however, it encounters limitations due to organizational factors within complex and dynamic healthcare systems. Further, there are limited studies examining the interdependencies and relative importance of these factors in the context of incident management practices. To address this gap, this study utilized aggregate-level hospital data to explore the influence of organizational factors on incident management practices. Employing a Bayesian Belief Network (BBN) structural learning algorithm, Tree Augmented Naive (TAN), this study assessed the probabilistic relationships, represented graphically, between organizational factors and incident management. Significantly, the model highlighted the critical roles of morale and staff engagement in influencing incident management practices within organizations. This study enhances our understanding of the importance of organizational factors in incident management, providing valuable insights for healthcare managers to effectively prioritize and allocate resources for continuous quality improvement efforts.

Abstract A015: Predicting efficacious drugs and drug-biomarker relationships for targeted glioblastoma treatment

Abstract Glioblastoma multiforme (GBM) is the deadliest, most heterogeneous, and common brain cancer in adults. Despite major advancements in neurosurgery as well as chemotherapy and radiotherapy techniques, overall prognosis has changed little over the decades. Not only is there an urgent need to identify efficacious therapeutics but there is also a great need to pair these therapeutics with biomarkers that can help tailor treatment to the right patient populations given the heterogeneous nature of the disease. Here, we implement several machine learning and statistical based pipelines for drug and biomarker discovery, leveraging previous work building patient drug response models using high-throughput cell line drug screening data as well as Bayesian network structure learning. Through these discovery pipelines, we identified multiple agents of interest for GBM, including MEK inhibitors (MEKis). MEKis were consistently predicted to be effective against GBM in multiple cross platform (microarray and RNA-sequencing) patient and patient derived xenograft (PDX) datasets. Additionally, they were experimentally shown to be more efficacious in tumor samples than standard of care agents (Temozolomide and Carmustine). We also predicted PHGDH gene expression levels to be causally associated with MEKi efficacy, which increased tumor sensitivity to a MEKi (Trametinib) during experimental testing in GBM cell lines with knockdown. These findings support our drug and biomarker discovery pipelines as an effective strategy to unite multiple cross platform and cross species datasets to help achieve GBM precision medicine. They also demonstrate that patient PHGDH levels can help inform Trametinib response in the fight against GBM. Citation Format: Danielle Maeser, Robert Gruener, Robert Galvin, Stephanie Huang, Tomo Koga, Florina Grigore. Predicting efficacious drugs and drug-biomarker relationships for targeted glioblastoma treatment [abstract]. In: Proceedings of the AACR Special Conference on Brain Cancer; 2023 Oct 19-22; Minneapolis, Minnesota. Philadelphia (PA): AACR; Cancer Res 2024;84(5 Suppl_1):Abstract nr A015.

Conditional probability table limit-based quantization for Bayesian networks: model quality, data fidelity and structure score

Bayesian Networks (BN) are robust probabilistic graphical models mainly used with discrete random variables requiring discretization and quantization of continuous data. Quantization is known to affect model accuracy, speed and interpretability, and there are various quantization methods and performance comparisons proposed in literature. Therefore, this paper introduces a novel approach called CPT limit-based quantization (CLBQ) aimed to address the trade-off among model quality, data fidelity and structure score. CLBQ sets CPT size limitation based on how large the dataset is so as to optimize the balance between the structure score of BNs and mean squared error. For such a purpose, a range of quantization values for each variable was evaluated and a Pareto set was designed considering structure score and mean squared error (MSE). A quantization value was selected from the Pareto set in order to balance MSE and structure score, and the method’s effectiveness was tested using different datasets, such as discrete variables with added noise, continuous variables and real continuous data. In all tests, CLBQ was compared to another quantization method known as Dynamic Discretization. Moreover, this study assesses the suitability of CLBQ for the search and score of BN structure learning, in addition to examining the landscape of BN structures while varying dataset sizes and confirming its consistency. It was sought to find the expected structure location through a landscape analysis and optimal BNs on it so as to confirm whether the expected results were actually achieved in the search and score of BN structure learning. Results demonstrate that CLBQ is quite capable of striking a balance between model quality, data fidelity and structure score, in addition to evidencing its potential application in the search and score of BN structure learning, thus further research should explore different structure scores and quantization methods through CLBQ. Furthermore, its code and used datasets have all been made available.

Bayesian network-based Mendelian randomization for variant prioritization and phenotypic causal inference.

Mendelian randomization is a powerful method for inferring causal relationships. However, obtaining suitable genetic instrumental variables is often challenging due to gene interaction, linkage, and pleiotropy. We propose Bayesian network-based Mendelian randomization (BNMR), a Bayesian causal learning and inference framework using individual-level data. BNMR employs the random graph forest, an ensemble Bayesian network structural learning process, to prioritize candidate genetic variants and select appropriate instrumental variables, and then obtains a pleiotropy-robust estimate by incorporating a shrinkage prior in the Bayesian framework. Simulations demonstrate BNMR can efficiently reduce the false-positive discoveries in variant selection, and outperforms existing MR methods in terms of accuracy and statistical power in effect estimation. With application to the UK Biobank, BNMR exhibits its capacity in handling modern genomic data, and reveals the causal relationships from hematological traits to blood pressures and psychiatric disorders. Its effectiveness in handling complex genetic structures and modern genomic data highlights the potential to facilitate real-world evidence studies, making it a promising tool for advancing our understanding of causal mechanisms.

Bayesian network structure learning based on HC-PSO algorithm

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.

Model-Driven Bayesian Network Learning for Factory-Level Fault Diagnostics and Resilience

We propose to use engineering models for Bayesian Network (BN) learning for fault diagnostics at the factory-level using key performance indicators (KPIs) such as overall equipment effectiveness (OEE). OEE is widely used in industry and it measures sustainability by capturing product quality (e.g., less scrap) and measures resilience by capturing availability. A major advantage of the proposed approach is that the engineering models are likely to be available long before the corresponding digitalized smart factory becomes fully operational. Specifically, for BN structure learning, we propose to use analytical queueing theory models of the factory to elicit the structure, and to carry out intervention we propose to use designed experiments based on discrete-event simulation models of the factory. For parameter learning, we apply a qualitative maximum a posteriori (QMAP) method and propose additional expert constraints based on the law of propagation of uncertainty from queueing theory. Furthermore, the proposed approach overcomes the challenge of obtaining balanced-class data in BN learning for fault diagnostics. We apply the proposed BN learning approach to (i) a 4-robot cell in our laboratory and (ii) a robotic machining cell in a commercial vehicle factory. In both cases, the proposed method is found to be efficacious in accurately learning the BN structure and parameter, as measured using structural-hamming distance and Kullback–Leibler divergence score, respectively. The proposed approach can pave the way for a new class of resilient and sustainable smart manufacturing systems.

Learning and Optimization of Patient–Physician Matching Index in Specialty Care

It is challenging for a patient without medical knowledge to select a ‘capable’ physician based on nontransparent medical information. The situation becomes pervasive in specialty care. Motivated by this existing patient-physician matching problem, we propose a novel physician matching index (PMI) obtained by an analytical framework integrated with an improved multi-disease pre-diagnosing Bayesian network (BN) model. The pre-diagnosis BN structure learning is critical since it provides the causal map among diseases and symptoms, but it has been proved to be NP-hard. To improve the computational tractability of the BN structure learning, we propose a dynamic programming based cache calculation algorithm integrated with expert knowledge. The optimal BN structure is obtained through an improved branch-and-bound algorithm. Given patients’ symptoms and physicians’ specialty information, we apply the trained pre-diagnosis BN model to obtain PMI, which can be extended to the weighted matching index by considering patient preferences. A case study of the patient-physician matching problem in the ear, nose, and throat (ENT) department is conducted. The branch-and-bound algorithm with the proposed cache calculation algorithm learns the optimal BN structure with high pre-diagnosing accuracy and time efficiency. We disclose that the proposed PMI can rectify the misdiagnosis since the highly related diseases usually belong to one specialty. Moreover, we demonstrate the significance of the consistency between the physicians’ specialty and the patients’ disease distribution. We also highlight that the proposed PMI guides the patients in choosing physicians more appropriately under independent patient preferences. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This research is motivated by a potential healthcare quality issue caused by the mismatch between patient and physician in specialty care, which is critical for both referral and non-referral systems. We propose a novel physician matching index (PMI) according to patients’ symptoms and physicians’ specialties based on potential disease(s) pre-diagnosed by a Bayesian network model. In the case study of the ear, nose, and throat (ENT) department, we show that PMI can rectify a large portion of misdiagnosed cases. Under the consideration of independent patient preferences, we also find that PMI improves the matching performance. To improve the systematic matching outcome, we suggest that physicians’ specialty cross-training programs be consistent with the patient’s disease distribution. However, we assume that patients’ symptoms are known and physicians’ specialties are clearly described, which might need to be further investigated. The framework proposed in this research can be extended to other specialty care departments, e.g., neurology and orthopedics.

Analysis of factors influencing the degree of accidental injury of bicycle riders considering data heterogeneity and imbalance.

Bicycle safety has emerged as a pressing concern within the vulnerable transportation community. Numerous studies have been conducted to identify the significant factors that contribute to the severity of cyclist injuries, yet the findings have been subject to uncertainty due to unobserved heterogeneity and class imbalance. This research aims to address these issues by developing a model to examine the impact of key factors on cyclist injury severity, accounting for data heterogeneity and imbalance. To incorporate unobserved heterogeneity, a total of 3,895 bicycle accidents were categorized into three homogeneous sub-accident clusters using Latent Class Cluster Analysis (LCA). Additionally, five over-sampling techniques were employed to mitigate the effects of data imbalance in each accident cluster category. Subsequently, Bayesian Network (BN) structure learning algorithms were utilized to construct 32 BN models after pairing the accident data from the four accident cluster types before and after sampling. The optimal BN models for each accident cluster type provided insights into the key factors associated with cyclist injury severity. The results indicate that the key factors influencing serious cyclist injuries vary heterogeneously across different accident clusters. Female cyclists, adverse weather conditions such as rain and snow, and off-peak periods were identified as key factors in several subclasses of accident clusters. Conversely, factors such as the week of the accident, characteristics of the trafficway, the season, drivers failing to yield to the right-of-way, distracted cyclists, and years of driving experience were found to be key factors in only one subcluster of accident clusters. Additionally, factors such as the time of the crash, gender of the cyclist, and weather conditions exhibit varying levels of heterogeneity across different accident clusters, and in some cases, exhibit opposing effects.

Analysis of the Impact of Curriculum Civics on Students’ Quality Cultivation Based on Bayesian Networks

Abstract This paper first analyzes the Bayesian network model based on probabilistic reasoning to study and explore the random phenomenon law of curriculum thinking. Secondly, probability theory and graph theory are utilized to deal with uncertain information and reduce the meta-multiplicity of the analysis of uncertain knowledge. Then, the Bayesian network structure learning problem is analyzed, and a constraint-based structure learning method is proposed to score students’ qualities by a given scoring function, and using a search algorithm, the best scoring network structure is searched. Finally, in order to analyze the influence of the Civics curriculum on the quality of students in college A, we should analyze the impact of the curriculum. The results show that from the innovative quality of students, the distribution density of innovative habit and innovative ability scores in the interval of 70~75 is (0.02, 0.035), and the distribution density of innovative consciousness scores in the interval of 70~86.25 is (0.005, 0.07). The data show that curriculum Civics can effectively promote the cultivation of innovative talents and the construction of an innovative country by internalizing the quality of innovation in the heart and externalizing it in the form of cultivating students’ innovative habits, improving their innovative consciousness and enhancing their innovative ability.

Bayesian Network Structural Learning Using Adaptive Genetic Algorithm with Varying Population Size

A Bayesian network (BN) is a probabilistic graphical model that can model complex and nonlinear relationships. Its structural learning from data is an NP-hard problem because of its search-space size. One method to perform structural learning is a search and score approach, which uses a search algorithm and structural score. A study comparing 15 algorithms showed that hill climbing (HC) and tabu search (TABU) performed the best overall on the tests. This work performs a deeper analysis of the application of the adaptive genetic algorithm with varying population size (AGAVaPS) on the BN structural learning problem, which a preliminary test showed that it had the potential to perform well on. AGAVaPS is a genetic algorithm that uses the concept of life, where each solution is in the population for a number of iterations. Each individual also has its own mutation rate, and there is a small probability of undergoing mutation twice. Parameter analysis of AGAVaPS in BN structural leaning was performed. Also, AGAVaPS was compared to HC and TABU for six literature datasets considering F1 score, structural Hamming distance (SHD), balanced scoring function (BSF), Bayesian information criterion (BIC), and execution time. HC and TABU performed basically the same for all the tests made. AGAVaPS performed better than the other algorithms for F1 score, SHD, and BIC, showing that it can perform well and is a good choice for BN structural learning.

Multi-source multi-modal markers for Bayesian Networks: Application to the extremely preterm born brain

The preterm phenotype results from the interplay of multiple disorders affecting the brain and cognitive outcomes. Accurately characterising these interactions can reveal prematurity markers. Bayesian Networks (BNs) are powerful tools to disentangle these relationships, as they inherently measure associations between variables while mitigating confounding factors. We present Modified PC-HC (MPC-HC), a Bayesian Network (BN) structural learning algorithm. MPC-HC employs statistical testing and search-and-score techniques to explore equivalent classes. We employ MPC-HC to estimate BNs for extremely preterm (EP) young adults and full-term controls. Using MRI measurements and cognitive performance markers, we investigate predictive relationships and mutual influences through predictions and sensitivity analysis. We assess the confidence in the estimated BN structures using bootstrapping. Furthermore, MPC-HC’s validation involves assessing its ability to recover benchmark BN structures. MPC-HC achieves an average prediction accuracy of 72.5% compared to 62.5% of PC, 64.5% of MMHC, and 71.5% of HC, while it outperforms PC, MMHC, and HC algorithms in reconstructing the true structure of benchmark BNs. The sensitivity analysis shows that MRI measurements mainly affect EP cognitive scores. Our work has two key contributions: first, the introduction and validation of a new BN structure learning method. Second, demonstrating the potential of BNs in modelling variable relationships, predicting variables of interest, modelling uncertainty, and evaluating how variables impact each other. Finally, we demonstrate this by characterising complex phenotypes, such as preterm birth, and discovering results consistent with literature findings.

Bayesian Network structure learning algorithm for highly missing and non imputable data: Application to breast cancer radiotherapy data

It is not uncommon for real-life data produced in healthcare to have a higher proportion of missing data than in other scopes. To take into account these missing data, imputation is not always desired by healthcare experts, and complete case analysis can lead to a significant loss of data. The algorithm proposed here, allows the learning of Bayesian Network graphs when both imputation and complete case analysis are not possible. The learning process is based on a set of local bootstrap learnings performed on complete sub-datasets which are then aggregated and locally optimized. This learning method presents competitive results compared to other structure learning algorithms, whatever the mechanism of missing data.

Feature Selection for Efficient Local-to-global Bayesian Network Structure Learning

Local-to-global learning approach plays an essential role in Bayesian network (BN) structure learning. Existing local-to-global learning algorithms first construct the skeleton of a DAG (directed acyclic graph) by learning the MB (Markov blanket) or PC (parents and children) of each variable in a dataset, then orient edges in the skeleton. However, existing MB or PC learning methods are often computationally expensive especially with a large-sized BN, resulting in inefficient local-to-global learning algorithms. To tackle the problem, in this article, we link feature selection with local BN structure learning and develop an efficient local-to-global learning approach using filtering feature selection. Specifically, we first analyze the rationale of the well-known Minimum-Redundancy and Maximum-Relevance (MRMR) feature selection approach for learning a PC set of a variable. Based on the analysis, we propose an efficient F2SL (feature selection-based structure learning) approach to local-to-global BN structure learning. The F2SL approach first employs the MRMR approach to learn the skeleton of a DAG, then orients edges in the skeleton. Employing independence tests or score functions for orienting edges, we instantiate the F2SL approach into two new algorithms, F2SL-c (using independence tests) and F2SL-s (using score functions). Compared to the state-of-the-art local-to-global BN learning algorithms, the experiments validated that the proposed algorithms in this article are more efficient and provide competitive structure learning quality than the compared algorithms.

Innovative Path of Civic Education Management Mode in Colleges and Universities Based on Bayesian Networks

Abstract This paper constructs a Bayesian network structure learning model using both the Bayesian network and the Notears algorithm. Combined with acyclic graph and conditional probability table, the structure and parameters of BN are described respectively. Focusing on the basic methods of Bayesian network structure, the hybrid algorithm based on Notears is chosen as the basic method of structure learning by analyzing the application of the evaluation search method, constraint method and hybrid search algorithm. The results show that the ideal education management method should focus on the integration with real life, so much so that it has a low rate of detachment from reality as well as a low rate of theory, accounting for 0.35 and 0.4, respectively. The traditional way of management of ideology and political education in colleges and universities is more theoretical and detached from the actual situation of education and management, with theoretical management accounting for 0.75, and management is inefficient, with a percentage of 0.6. The research in this paper promotes, to a certain extent, the innovation of the management of the ideological education in colleges and universities, for the management of ideological education in colleges and universities.

Advocating the Use of Bayesian Network in Analyzing the Modes of Occurrence of Elements in Coal.

Modes of occurrence of elements in coal are important because they can be used not only to understand the origin of inorganic components in coal but also to determine the impact on the environment and human health and the deposition process of coal seams as well. Statistical analysis is one of the commonly used indirect methods used to analyze the modes of occurrence of elements in coal, among which hierarchical clustering is widely used. However, hierarchical clustering may lead to misleading results due to its limitation that it focuses on the clusters of elements rather than a single element. To tackle this issue, we use the first part of a well-known Bayesian network structure learning algorithm, i.e., Peter-Clark (PC) algorithm, to explore the relationships of the coal elemental data and then infer modes of occurrence of elements in coal. A data set containing 95 Late Paleozoic coal samples from the Datanhao and Adaohai mines in Inner Mongolia, China, is used for the performance evaluation. Analytical results show that many instructive and surprising insights can be concluded from the first part of the PC algorithm. Compared with the hierarchical clustering algorithm, the first part of the PC algorithm demonstrates superiority in analyzing the modes of occurrence of elements in coal.

Bayesian network based probabilistic weighted high-order fuzzy time series forecasting

The present article proposes a probabilistic weighted high-order fuzzy time series (FTS) forecasting model employing Bayesian network (BN) to address complex relationships and uncertainty hidden in time series. As considerable FTS forecasting models considers the fuzzy relationships between precedent moments and the consequent moment as the complex relationships in time series, BN structure learning is utilized to discover and model dependence relationships between each moment in time series. The combination of the fuzzy relationships modeled by fuzzy logical relationships and the dependence relationships modeled by the BN provides a comprehensive establishment and representation of the complex relationships inherent in time series data. The proposed FTS forecasting method calculates the fuzzy-probabilistic weights of each fuzzy logical relationship group using the improved fuzzy empirical probabilities to model both aleatoric and epistemic uncertainty in time series. To this end, the improved fuzzy empirical probabilities are formulated by integrating fuzzy empirical probabilities with the BN to incorporate dependence relationships from the original time series into the FTS forecasting procedure. The efficiency of the proposed forecasting model is validated on fourteen publicly available time series. Experimental results confirm the better performance of the proposed method comparing with nine existing FTS models and six numeric models. Hypothesis tests also validate the robustness and reliability of the proposed method.