Bayesian Network Structure Learning Algorithm Research Articles

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.

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.

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.

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.

Estimating Treatment Effect of Adjuvant Chemotherapy in Elderly Patients With Stage III Colon Cancer Using Bayesian Networks.

While adjuvant therapy with capecitabine and oxaliplatin (CAPOX) has been proven to be effective in stage III colon cancer, capecitabine monotherapy (CapMono) might be equally effective in elderly patients. Unfortunately, the elderly are under-represented in clinical trials and patients included may not be representative of the routine care population. Observational data might alleviate this problem but is sensitive to biases such as confounding by indication. Here, we build causal models using Bayesian Networks (BNs), identify confounders, and estimate the effect of adjuvant chemotherapy using survival analyses. Patients 70 years and older were selected from the Netherlands Cancer Registry (N = 982). We developed several BNs using constraint-based, score-based, and hybrid algorithms while precluding noncausal relations. In addition, we created models using a limited set of recurrence and survival nodes. Potential confounders were identified through the resulting graphs. Several Cox models were fitted correcting for confounders and for propensity scores. When comparing adjuvant treatment with surgery only, pathological lymph node classification, physical status, and age were identified as potential confounders. Adjuvant treatment was significantly associated with survival in all Cox models, with hazard ratios between 0.39 and 0.45; CIs overlapped. BNs investigating CAPOX versus CapMono did not find any association between the treatment choice and survival and thus no confounders. Analyses using Cox models did not identify significant association either. We were able to successfully leverage BN structure learning algorithms in conjunction with clinical knowledge to create causal models. While confounders differed depending on the algorithm and included nodes, results were not contradictory. We found a strong effect of adjuvant therapy on survival in our cohort. Additional oxaliplatin did not have a marked effect and should be avoided in elderly patients.

An improved hybrid structure learning strategy for Bayesian networks based on ensemble learning

In the application of Bayesian networks to solve practical problems, it is likely to encounter the situation that the data set is expensive and difficult to obtain in large quantities and the small data set is easy to cause the inaccuracy of Bayesian network (BN) scoring functions, which affects the BN optimization results. Therefore, how to better learn Bayesian network structures under a small data set is an important problem we need to pay attention to and solve. This paper introduces the idea of parallel ensemble learning and proposes a new hybrid Bayesian network structure learning algorithm. The algorithm adopts the elite-based structure learner using genetic algorithm (ESL-GA) as the base learner. Firstly, the adjacency matrices of the network structures learned by ESL-GA are weighted and averaged. Then, according to the preset threshold, the edges between variables with weak dependence are filtered to obtain a fusion matrix. Finally, the fusion matrix is modified as the adjacency matrix of the integrated Bayesian network so as to obtain the final Bayesian network structure. Comparative experiments on the standard Bayesian network data sets show that the accuracy and reliability of the proposed algorithm are significantly better than other algorithms.

Automated detection of causal relationships among diseases and imaging findings in textual radiology reports.

Textual radiology reports contain a wealth of information that may help understand associations among diseases and imaging observations. This study evaluated the ability to detect causal associations among diseases and imaging findings from their co-occurrence in radiology reports. This IRB-approved and HIPAA-compliant study analyzed 1702462 consecutive reports of 1396293 patients; patient consent was waived. Reports were analyzed for positive mention of 16839 entities (disorders and imaging findings) of the Radiology Gamuts Ontology (RGO). Entities that occurred in fewer than 25 patients were excluded. A Bayesian network structure-learning algorithm was applied at P < 0.05 threshold: edges were evaluated as possible causal relationships. RGO and/or physician consensus served as ground truth. 2742 of 16839 RGO entities were included, 53849 patients (3.9%) had at least one included entity. The algorithm identified 725 pairs of entities as causally related; 634 were confirmed by reference to RGO or physician review (87% precision). As shown by its positive likelihood ratio, the algorithm increased detection of causally associated entities 6876-fold. Causal relationships among diseases and imaging findings can be detected with high precision from textual radiology reports. This approach finds causal relationships among diseases and imaging findings with high precision from textual radiology reports, despite the fact that causally related entities represent only 0.039% of all pairs of entities. Applying this approach to larger report text corpora may help detect unspecified or heretofore unrecognized associations.

A Parallel Framework for Constraint-Based Bayesian Network Learning via Markov Blanket Discovery

Bayesian networks (BNs) are a widely used graphical model in machine learning. As learning the structure of BNs is NP-hard, high-performance computing methods are necessary for constructing large-scale networks. In this paper, we present a parallel framework to scale BN structure learning algorithms to tens of thousands of variables. Our framework is applicable to learning algorithms that rely on the discovery of Markov blankets (MBs) as an intermediate step. We demonstrate the applicability of our framework by parallelizing three different algorithms: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Grow-Shrink</i> ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GS</i> ), <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Incremental Association MB</i> ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">IAMB</i> ), and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Interleaved IAMB</i> ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Inter-IAMB</i> ). Our implementations are available as part of an open-source software called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ramBLe</i> , and are able to construct BNs from real data sets with tens of thousands of variables and thousands of observations in less than a minute on 1024 cores, with a speedup of up to 845X and 82.5% efficiency. Furthermore, we demonstrate using simulated data sets that our proposed parallel framework can scale to BNs of even higher dimensionality. Our implementations were selected for the reproducibility challenge component of the 2021 student cluster competition (SCC'21), which tasked undergraduate teams from around the world with reproducing the results that we obtained using the implementations. We discuss details of the challenge and the results of the experiments conducted by the top teams in the competition. The results of these experiments indicate that our key results are reproducible, despite the use of completely different data sets and experiment infrastructure, and validate the scalability of our implementations.

A Bayesian network structure learning method for optimizing ordering search operator

Local search algorithm in ordering space is a good method which can effectively improve the efficiency of bayesian network structure learning. However, the existing algorithms usually have problems such as insufficient order optimization, low learning accuracy, and easy stop at a local optimal. In order to solve these problems, the local search algorithm in ordering space is studied, and a new method to improve the accuracy of bayesian network structure learning by optimizing order search operator is proposed. Combining the iterative local search algorithm with the window operator to search the neighborhood of a given order in the ordering space, the probability of the algorithm falling into the local optimal value is reduced, and the network structure with higher quality is obtained. Experimental results show that comparing with the bayesian network structure learning algorithm in network structure space, the learning efficiency of the present algorithm is improved by 54.12%. Comparing with the bayesian network structure learning algorithm in ordering space, the learning accuracy of the present algorithm is improved by 2.33%.

Score-based Bayesian network structure learning algorithms for modeling radioisotope levels in nuclear power plant reactors

Radioactive corrosion products released into the primary coolant loop dominate the final shutdown radiation fields of pressurized water reactors. Thus, reducing the concentration of these corrosion products is a paramount duty in the optimization process of the reactor performance. However, the complexity and uncertainty present in this process make it difficult to predict their evolution in a theoretical way. We propose the application of structural learning of Bayesian networks to discover the complex relations between the corrosion products and the most relevant variables in the primary loop, giving rise to probabilistic models that obtain accurate and reliable predictions of the corrosion products. Our analysis of 5 power plants demonstrates that our approach results in simpler and more reliable models. Additionally, we conclude that the learned structures may represent an interpretable tool for power plant technicians since they reveal useful information that can be directly employed to improve the reactor operation.

Data poisoning attacks detection based on the convergence of the Peter and Clark algorithm and Bayesian adversarial federated learning

Effective Bayesian network structure learning algorithms, such as the Peter and Clark (PC) algorithm, must be designed and used with data integrity as a top priority. Deep learning models can be jointly built by thousands of participants; thanks to the innovative distributed learning technology known as federated learning. This research proposes a technique for the detection of data poisoning attacks along with enhancing secure data transmission and routing by utilizing the integration of the PC algorithm and federated learning. Data integrity of the network is likewise enhanced using the Convergence of the PC algorithm. Detection of attacks in established secure data transmission is carried out using Bayesian adversarial federated learning. We provided an optimization-based model poisoning approach and introduced adversarial neurons into the redundant area of a neural network by assessing model capacity. It should be highlighted that while those redundant neurons have little relevance to the primary goal of federated learning, they are crucial for poisoning attacks. Numerical tests show that the suggested approach can get beyond defense mechanisms and have a high attack success rate.

An efficient Bayesian network structure learning algorithm based on structural information

An efficient Bayesian network structure learning algorithm based on structural information

Bayesian Network Structure Learning Algorithm Combining Improved Dragonfly Optimization

Bayesian Network Structure Learning Algorithm Combining Improved Dragonfly Optimization

Hybrid Bayesian network discovery with latent variables by scoring multiple interventions

In Bayesian Networks (BNs), the direction of edges is crucial for causal reasoning and inference. However, Markov equivalence class considerations mean it is not always possible to establish edge orientations, which is why many BN structure learning algorithms cannot orientate all edges from purely observational data. Moreover, latent confounders can lead to false positive edges. Relatively few methods have been proposed to address these issues. In this work, we present the hybrid mFGS-BS (majority rule and Fast Greedy equivalence Search with Bayesian Scoring) algorithm for structure learning from discrete data that involves an observational data set and one or more interventional data sets. The algorithm assumes causal insufficiency in the presence of latent variables and produces a Partial Ancestral Graph (PAG). Structure learning relies on a hybrid approach and a novel Bayesian scoring paradigm that calculates the posterior probability of each directed edge being added to the learnt graph. Experimental results based on well-known networks of up to 109 variables and 10 k sample size show that mFGS-BS improves structure learning accuracy relative to the state-of-the-art and it is computationally efficient.

Decomposition-Based Bayesian Network Structure Learning Algorithm for Abnormity Diagnosis Model for Coal Mill Process

In the structure learning of the large-scale Bayesian network (BN) model for the coal mill process, taking the view of the problem that the decomposition-based method cannot guarantee the sufficient learning of abnormal state node neighborhood in the diagnosis model, this paper proposes a new BN structure learning method based on decomposition. Firstly, a sketch is constructed based on an improved Markov blanket discovery algorithm and edge thickening and thinning. Second, the node centrality of k-path is used to search the important nodes, and the subgraph decomposition is realized by extracting these important nodes and their neighborhoods from the sketch. Then, through the targeted design of subgraph de-duplication, subgraph learning, and subgraph reorganization methods, the learning of large-scale BN is realized. This method is applied to public data sets, and its advantages and disadvantages are analyzed by comparing them with other methods. The advantage of the BN structure learning method of the abnormal condition diagnosis model is further verified by applying the method to the coal mill process, which is consistent with the original design intention.

Effective and efficient structure learning with pruning and model averaging strategies

Learning the structure of a Bayesian Network (BN) with score-based solutions involves exploring the search space of possible graphs and moving towards the graph that maximises a given objective function. Some algorithms offer exact solutions that guarantee to return the graph with the highest objective score, while others offer approximate solutions in exchange for reduced computational complexity. This paper describes an approximate BN structure learning algorithm, which we call Model Averaging Hill-Climbing (MAHC), that combines two novel strategies with hill-climbing search. The algorithm starts by pruning the search space of graphs, where the pruning strategy can be viewed as an aggressive version of the pruning strategies that are typically applied to combinatorial optimisation structure learning problems. It then performs model averaging in the hill-climbing search process and moves to the neighbouring graph that maximises the objective function, on average, for that neighbouring graph and over all its valid neighbouring graphs. Comparisons with other algorithms spanning different classes of learning suggest that the combination of aggressive pruning with model averaging is both effective and efficient, particularly in the presence of data noise.

Dynamic Programming BN Structure Learning Algorithm Integrating Double Constraints under Small Sample Condition

The Bayesian Network (BN) structure learning algorithm based on dynamic programming can obtain global optimal solutions. However, when the sample cannot fully contain the information of the real structure, especially when the sample size is small, the obtained structure is inaccurate. Therefore, this paper studies the planning mode and connotation of dynamic programming, restricts its process with edge and path constraints, and proposes a dynamic programming BN structure learning algorithm with double constraints under small sample conditions. The algorithm uses double constraints to limit the planning process of dynamic programming and reduces the planning space. Then, it uses double constraints to limit the selection of the optimal parent node to ensure that the optimal structure conforms to prior knowledge. Finally, the integrating prior-knowledge method and the non-integrating prior-knowledge method are simulated and compared. The simulation results verify the effectiveness of the method proposed and prove that the integrating prior knowledge can significantly improve the efficiency and accuracy of BN structure learning.

Greedy structure learning from data that contain systematic missing values

Learning from data that contain missing values represents a common phenomenon in many domains. Relatively few Bayesian Network structure learning algorithms account for missing data, and those that do tend to rely on standard approaches that assume missing data are missing at random, such as the Expectation-Maximisation algorithm. Because missing data are often systematic, there is a need for more pragmatic methods that can effectively deal with data sets containing missing values not missing at random. The absence of approaches that deal with systematic missing data impedes the application of BN structure learning methods to real-world problems where missingness are not random. This paper describes three variants of greedy search structure learning that utilise pairwise deletion and inverse probability weighting to maximally leverage the observed data and to limit potential bias caused by missing values. The first two of the variants can be viewed as sub-versions of the third and best performing variant, but are important in their own in illustrating the successive improvements in learning accuracy. The empirical investigations show that the proposed approach outperforms the commonly used and state-of-the-art Structural EM algorithm, both in terms of learning accuracy and efficiency, as well as both when data are missing at random and not at random.

PSL: An Algorithm for Partial Bayesian Network Structure Learning

Learning partial Bayesian network (BN) structure is an interesting and challenging problem. In this challenge, it is computationally expensive to use global BN structure learning algorithms, while only one part of a BN structure is interesting, local BN structure learning algorithms are not a favourable solution either due to the issue of false edge orientation. To address the problem, this article first presents a detailed analysis of the false edge orientation issue with local BN structure learning algorithms and then proposes PSL, an efficient and accurate P artial BN S tructure L earning (PSL) algorithm. Specifically, PSL divides V-structures in a Markov blanket (MB) into two types: Type-C V-structures and Type-NC V-structures, then it starts from the given node of interest and recursively finds both types of V-structures in the MB of the current node until all edges in the partial BN structure are oriented. To further improve the efficiency of PSL, the PSL-FS algorithm is designed by incorporating F eature S election (FS) into PSL. Extensive experiments with six benchmark BNs validate the efficiency and accuracy of the proposed algorithms.

A Bayesian Network Structure Learning Algorithm Based on Probabilistic Incremental Analysis and Constraint

To address the problem of low efficiency of the existing hill-climbing algorithm in Bayesian network structure learning, this paper proposes a Bayesian network structure learning algorithm based on probabilistic incremental analysis and constraints. The algorithm constructs a suitable measure for representing the degree of node association in Bayesian networks based on the principle of random forest feature extraction; then uses the method to construct the initial Bayesian network structure and constrains the search space by setting a corresponding threshold for the probability increment centered on each node; finally takes the initial Bayesian network as the starting point and learns it by the forbidden hill-climbing search and BIC scoring method to obtain the optimal Bayesian network structure. Experimental results show that the correlation degree measure and mutual information proposed in this paper have an approximate correlation expression effect; compared with other Bayesian network structure learning algorithms of the same type, the method in this paper has a faster operation speed while ensuring the quality of the learned network. The experimental results show that the Bayesian network structure learning algorithm based on probabilistic incremental analysis and constraints is an effective and efficient Bayesian network structure learning algorithm.