Max-Min Hill-Climbing Research Articles

Improving Causal Bayesian Networks Using Expertise in Authoritative Medical Ontologies

Discovering causal relationships among symptoms is a topical issue in the analysis of observational patient datasets. A Causal Bayesian Network (CBN) is a popular analytical framework for causal inference. While there are many methods and algorithms capable of learning a Bayesian network, they are reliant on the complexity and thoroughness of the algorithm and do not consider prior expertise from authoritative sources. This article proposes a novel method of extracting prior causal knowledge contained in Authoritative Medical Ontologies (AMOs) and using this prior knowledge to orient arcs in a CBN learned from observational patient data. Since AMOs are robust biomedical ontologies containing the collective knowledge of the experts who created them, utilizing the ordering information contained within them produces improved CBNs that provide additional insight into the disease domain. To demonstrate our method, we obtained prior causal ordering information among symptoms from three AMOs: (1) the Medical Dictionary for Regulatory Activities Terminology (MedDRA), (2) the International Classification of Diseases Version 10 Clinical Modification (ICD-10-CM), and (3) Systematized Nomenclature of Medicine Clinical Terms (SNOMED CT). The prior ontological knowledge from these three AMOs is then used to orient arcs in a series of CBNs learned from the National Institutes of Mental Health study on Sequenced Treatment Alternatives to Relieve Depression (STAR*D) patient dataset using the Max-Min Hill-Climbing (MMHC) algorithm. Six distinct CBNs are generated using MMHC: an unmodified baseline model using only the algorithm, three CBNs oriented with ordered-variable pairs from MedDRA, ICD-10-CM, and SNOMED CT, and two more with ordered pairs from a combination of these AMOs. The resulting CBNs modified using ordered-variable pairs significantly change the structure of the network. The agreement between the Modified networks and the Baseline ranges from 50% to 90%. A modified network using ordering information from all ontologies obtained an agreement of 50% (10 out of 20 arcs exist in both the Baseline and Modified models) while maintaining comparable predictive accuracy. This indicates that the Modified CBN reflects the causal claims in the AMOs and agrees with both the AMOs and the observational STAR*D dataset. Furthermore, the Modified models discovered new potentially causal relationships among symptoms in the model, while eliminating weaker edges in a qualitative analysis of the significance of these relationships in existing epidemiological research.

Bayesian Network Structure Learning Using Improved A* with Constraints from Potential Optimal Parent Sets

Learning the structure of a Bayesian network and considering the efficiency and accuracy of learning has always been a hot topic for researchers. This paper proposes two constraints to solve the problem that the A* algorithm, an exact learning algorithm, is not efficient enough to search larger networks. On the one hand, the parent–child set constraints reduce the number of potential optimal parent sets. On the other hand, the path constraints are obtained from the potential optimal parent sets to constrain the search process of the A* algorithm. Both constraints are proposed based on the potential optimal parent sets. Experiments show that the time efficiency of the A* algorithm can be significantly improved, and the ability of the A* algorithm to search larger Bayesian networks can be improved by the two constraints. In addition, compared with the globally optimal Bayesian network learning using integer linear programming (GOBNILP) algorithm and the max–min hill-climbing (MMHC) algorithm, which are state of the art, the A* algorithm enhanced by constraints still performs well in most cases.

Scalable Causal Structure Learning: Scoping Review of Traditional and Deep Learning Algorithms and New Opportunities in Biomedicine.

Causal structure learning refers to a process of identifying causal structures from observational data, and it can have multiple applications in biomedicine and health care. This paper provides a practical review and tutorial on scalable causal structure learning models with examples of real-world data to help health care audiences understand and apply them. We reviewed traditional (combinatorial and score-based) methods for causal structure discovery and machine learning-based schemes. Various traditional approaches have been studied to tackle this problem, the most important among these being the Peter Spirtes and Clark Glymour algorithms. This was followed by analyzing the literature on score-based methods, which are computationally faster. Owing to the continuous constraint on acyclicity, there are new deep learning approaches to the problem in addition to traditional and score-based methods. Such methods can also offer scalability, particularly when there is a large amount of data involving multiple variables. Using our own evaluation metrics and experiments on linear, nonlinear, and benchmark Sachs data, we aimed to highlight the various advantages and disadvantages associated with these methods for the health care community. We also highlighted recent developments in biomedicine where causal structure learning can be applied to discover structures such as gene networks, brain connectivity networks, and those in cancer epidemiology. We also compared the performance of traditional and machine learning-based algorithms for causal discovery over some benchmark data sets. Directed Acyclic Graph-Graph Neural Network has the lowest structural hamming distance (19) and false positive rate (0.13) based on the Sachs data set, whereas Greedy Equivalence Search and Max-Min Hill Climbing have the best false discovery rate (0.68) and true positive rate (0.56), respectively. Machine learning-based approaches, including deep learning, have many advantages over traditional approaches, such as scalability, including a greater number of variables, and potentially being applied in a wide range of biomedical applications, such as genetics, if sufficient data are available. Furthermore, these models are more flexible than traditional models and are poised to positively affect many applications in the future.

The identification and prediction of frailty based on Bayesian network analysis in a community-dwelling older population

BackgroundWe have witnessed frailty, which characterized by a decline in physiological reserves, become a major public health issue in older adults. Understanding the influential factors associated with frailty may help prevent or if possible reverse frailty. The present study aimed to investigate factors associated with frailty status and frailty transition in a community-dwelling older population.MethodsA prospective cohort study on community-dwelling subjects aged ≥ 60 years was conducted, which was registered beforehand (ChiCTR 2,000,032,949). Participants who had completed two visits during 2020–2021 were included. Frailty status was evaluated using the Fried frailty phenotype. The least absolute shrinkage and selection operator (LASSO) regression was applied for variable selection. Bayesian network analysis with the max-min hill-climbing (MMHC) algorithm was used to identify factors related to frailty status and frailty transition.ResultsOf 1,981 subjects at baseline, 1,040 (52.5%) and 165 (8.33%) were classified as prefrailty and frailty. After one year, improved, stable, and worsening frailty status was observed in 460 (35.6%), 526 (40.7%), and 306 (23.7%) subjects, respectively. Based on the variables screened by LASSO regression, the Bayesian network structure suggested that age, nutritional status, instrumental activities of daily living (IADL), balance capacity, and social support were directly related to frailty status. The probability of developing frailty is 14.4% in an individual aged ≥ 71 years, which increases to 20.2% and 53.2% if the individual has balance impairment alone, or combined with IADL disability and malnutrition. At a longitudinal level, ADL/IADL decline was a direct predictor of worsening in frailty state, which further increased the risk of hospitalization. Low high-density lipoprotein cholesterol (HDL-C) and diastolic blood pressure (DBP) levels were related to malnutrition, and further had impacts on ADL/IADL decline, and ultimately led to the worsening of the frailty state. Knowing the status of any one or more of these factors can be used to infer the risk of frailty based on conditional probabilities.ConclusionOlder age, malnutrition, IADL disability, and balance impairment are important factors for identifying frailty. Malnutrition and ADL/IADL decline further predict worsening of the frailty state.

Development and application of a Bayesian network-based model for systematically reducing safety risks in the commercial air transportation system

Aiming to explore the nature of incidents in the commercial air transportation system, multiple causal factor events and result events, and their cause and effect relationships were retrieved from 7,265 incident cases in the Aviation Safety Reporting System (ASRS). The Bayesian network of commercial air transportation system safety risk (CATSSR-BN) was constructed on the basis of the hybrid algorithm of max–min hill-climbing (MMHC). The k-fold cross-validation of structure learning verified the accuracy and effectiveness of the CATSSR-BN. The measure of mutual information between causal factor event and result event was evaluated for determining its importance on safety performance of commercial air transportation system. Ten causal factor events with the highest values of mutual information across different result events were identified. A decision-making model was developed for optimizing resource investment in commercial aviation safety management. As a result, resource investment combination was determined on the combination of five causal factor events, which provided a systematic approach for reducing safety risk in commercial air transportation system and avoiding the occurrence of commercial aviation incidents with a high level of risk.

Transfer Learning-based Hybrid Approach for Bayesian Network Structure Learning

Bayesian network is a graphical model that is widely used to perform probabilistic reasoning. However, learning the structure of Bayesian network is a complex task. In this paper, we propose a hybrid structure learning algorithm that has two phases: a constraint-based phase to reduce the search space and a score-and-search phase that employs case-injected genetic algorithms for determining the optimal structure from the reduced space of structures. We use a case-injected genetic algorithm-based hybrid approach for the structure learning in order to improve the learning accuracy over similar problems. A case-injected genetic algorithm is the augmentation of a case-based memory with the Genetic Algorithm (GA). Thereby, it finds near-optimal solutions in fewer generations compared to GA. Our method stores relevant or partial solutions in a case-base while solving the problems and utilizes those stored solutions on new similar problems. We use small-to-very large networks for assessing our viability of our approach. In this paper, a series of experiments are conducted on datasets generated from four benchmark Bayesian networks. We compare our method against GA-based hybrid approach and a state-of-the-art algorithm, Max-Min Hill Climbing (MMHC). Presented results indicate an enhanced improvement of our approach over GA and MMHC in learning the Bayesian network structures.

Exploring influencing factors of chronic obstructive pulmonary disease based on elastic net and Bayesian network

This study aimed to construct Bayesian networks (BNs) to analyze the network relationships between COPD and its influencing factors, and the strength of each factor's influence on COPD was reflected through network reasoning. Elastic Net and Max-Min Hill-Climbing (MMHC) algorithm were adopted to screen the variables on the surveillance data of COPD among residents in Shanxi Province, China from 2014 to 2015, and construct BNs respectively. 10 variables finally entered the model after screening by Elastic Net. The BNs constructed by MMHC showed that smoking status, household air pollution, family history, cough, air hunger or dyspnea were directly related to COPD, and Gender was indirectly linked to COPD through smoking status. Moreover, smoking status, household air pollution and family history were the parent nodes of COPD, and cough, air hunger or dyspnea represented the child nodes of COPD. In other words, smoking status, household air pollution and family history were related to the occurrence of COPD, and COPD would make patients’ cough, air hunger or dyspnea worse. Generally speaking, BNs could reveal the complex network linkages between COPD and its relevant factors well, making it more convenient to carry out targeted prevention and control of COPD.

Prognosis Model of Advanced Non-Small-Cell Lung Cancer Based on Max-Min Hill-Climbing Algorithm.

A safer and more effective treatment is need for the comprehensive treatment based on chemotherapy in patients with advanced non-small-cell lung cancer (NSCLC). The max-min hill-climbing (MMHC) is a common algorithm for disease prediction. This study is aimed at analyzing the efficacy of the MMHC algorithm in prognosis evaluation of advanced NSCLC. In this study, the prognosis model of lung cancer was first established by the MMHC algorithm. Then, according to the MMHC algorithm results, 40 patients with advanced NSCLC were divided into the research group and control group before anlotinib hydrochloride capsule combined with pemetrexed disodium chemotherapy. The diameter of solid tumor lesions, objective response rate (ORR), disease control rate (DCR), and progression-free survival (PFS) was compared between the two groups. The results showed that the MMHC model has a higher prediction accuracy of survival status of lung cancer patients. Under the guidance of the model, the research group has a smaller diameter of primary foci and metastatic foci, a higher ORR, DCR, and a longer PFS than the control group (P < 0.05). We can conclude that the MMHC algorithm can guide the maintenance treatment of advanced NSCLC, which is conducive to the prognosis judgment and treatment cost control.

A Bayesian network structural learning algorithm for calculating the failure probabilities of complex engineering systems with limited data

The failure of complex engineering systems is easy to lead to disastrous consequences. To prevent the failure, it is necessary to model complex engineering systems using probabilistic techniques with limited data which is a major feature of complex engineering systems. It is a good choice to perform such modeling using Bayesian network because of its advantages in probabilistic modeling. However, few Bayesian network structural learning algorithms are designed for complex engineering systems with limited data. Therefore, an algorithm for learning the Bayesian network structure of them should be developed. Based on the process of self-purification of water, a complex engineering system is segmented into three components according to the degree of difficulty in solving them. And then a Bayesian network learning algorithm with three components (TC), including PC algorithm, MIK algorithm which is originated by the paper through combining Mutual Information and K2 algorithm, and the Hill-Climbing method, is developed, i.e. TC algorithm. To verify its effectiveness, TC algorithm, K2 algorithm, and Max-Min Hill-Climbing are respectively used to learn Alarm network with different sizes of samples. The results imply that TC algorithm has the best performance. Finally, TC algorithm is applied to study tank spill accidents with 220 samples.

Learning Bayesian Network for Rainfall Prediction Modeling in Urban Area using Remote Sensing Satellite Data (Case Study: Jakarta, Indonesia)

Rainfall modeling is one of the most critical factors in agricultural monitoring and statistics, transportation schedules, and urban flood prevention. Weather anomaly during the dry season in urban coastal areas of tropical countries such as Jakarta, Indonesia has become a challenging issue that causes unexpected changes in rain patterns. In this paper, we propose the Bayesian Network (BN) approach to model the probabilistic nature of rain patterns in urban areas and causal relationships among its predictor variables. Rain occurrences are predicted using temperature, relative humidity, mean-sea level (MSL) pressure, cloud cover, and precipitation variables. Data are obtained from the remote sensing sources of the National Oceanic and Atmospheric Administration (NOAA) satellite in Jakarta 2020-2021. We compare both of the score-based, i.e., Hill Climbing (HC), and hybrid structure learning algorithms of Bayesian Network including the techniques of Max-Min Hill Climbing (MMHC), General 2-Phase Restricted Maximization (RSMAX2), and Hybrid-Hybrid Parents &amp; Children (H2PC). Further, we also compare the performance of score-based model (Hill Climbing) under five different popular scorings: Bayesian Information Criterion (BIC), K2, Log-Likelihood, Bayesian Dirichlet Equivalent (BDE), and Akaike Information Criterion (AIC) methods. The main contributions of this study are as follows: (1) insights that the hybrid structure learning algorithms of Bayesian Network models are either superior in performance or at least comparable to its score-based counterparts (2) our proposed best performed Bayesian Network model that is able to predict the rain occurrences in Jakarta with a promising overall accuracy of more than 81 percent.

Using Bayesian network model with MMHC algorithm to detect risk factors for stroke.

Stroke is a major chronic non-communicable disease with high incidence, high mortality, and high recurrence. To comprehensively digest its risk factors and take some relevant measures to lower its prevalence is of great significance. This study aimed to employ Bayesian Network (BN) model with Max-Min Hill-Climbing (MMHC) algorithm to explore the risk factors for stroke. From April 2019 to November 2019, Shanxi Provincial People's Hospital conducted opportunistic screening for stroke in ten rural areas in Shanxi Province. First, we employed propensity score matching (PSM) for class balancing for stroke. Afterwards, we used Chi-square testing and Logistic regression model to conduct a preliminary analysis of risk factors for stroke. Statistically significant variables were incorporated into BN model construction. BN structure learning was achieved using MMHC algorithm, and its parameter learning was achieved with Maximum Likelihood Estimation. After PSM, 748 non-stroke cases and 748 stroke cases were included in this study. BN was built with 10 nodes and 12 directed edges. The results suggested that age, fasting plasma glucose, systolic blood pressure, and family history of stroke constitute direct risk factors for stroke, whereas sex, educational levels, high density lipoprotein cholesterol, diastolic blood pressure, and urinary albumin-to-creatinine ratio represent indirect risk factors for stroke. BN model with MMHC algorithm not only allows for a complicated network relationship between risk factors and stroke, but also could achieve stroke risk prediction through Bayesian reasoning, outshining traditional Logistic regression model. This study suggests that BN model boasts great prospects in risk factor detection for stroke.

A theoretical framework for data-driven artificial intelligence decision making for enhancing the asset integrity management system in the oil & gas sector

Asset integrity and reliability is one of the 20 elements of Process Safety Management (PSM) as defined by the Center for Chemical Process Safety (CCPS). We combine expert knowledge and data analytics (Artificial Intelligence, Machine Learning, and Keyword Analysis) to create a reaction network for Asset Integrity Management (AIM) and provide a theoretical and practical basis for handling uncertainty in large data sets such as company incident databases. The purpose of the current study is to control and minimize the total number of incidents that occur within an oil and gas operation by applying a multidisciplinary approach to explore and develop AIM. This systematic approach can improve AIM to better understand PSM as a whole and the underlying dynamics ever-present in the system. In this study, AIM is divided into 2 major groups – asset and human factors – and then, in order to get more detailed results, each group is divided into 9 and 5 subcategories, respectively. To analyze the relationships between the different factors of AIM, two score-based (Tabu and Hill Climbing) and one hybrid (Max-Min Hill-Climbing) Bayesian networks are used to develop one final viable solution. The findings of these techniques point towards the same results for reducing incident rates. Four factors related to assets, including construction, testing, inspection, and maintenance, account for more than half the incidents (54.78%). Additionally, there must be a greater emphasis placed on the impact of human factors as they are directly (23.58%) and indirectly (11.10%) responsible for accidents as well as other technological malfunctions. By focusing on AIM which is a key element of PSM, it will be possible to gain a better understanding of one of the most significant and problematic sources of risk in process safety.

Application of a novel hybrid algorithm of Bayesian network in the study of hyperlipidemia related factors: a cross-sectional study

BackgroundThis article aims to understand the prevalence of hyperlipidemia and its related factors in Shanxi Province. On the basis of multivariate Logistic regression analysis to find out the influencing factors closely related to hyperlipidemia, the complex network connection between various variables was presented through Bayesian networks(BNs).MethodsLogistic regression was used to screen for hyperlipidemia-related variables, and then the complex network connection between various variables was presented through BNs. Since some drawbacks stand out in the Max-Min Hill-Climbing (MMHC) hybrid algorithm, extra hybrid algorithms are proposed to construct the BN structure: MMPC-Tabu, Fast.iamb-Tabu and Inter.iamb-Tabu. To assess their performance, we made a comparison between these three hybrid algorithms with the widely used MMHC hybrid algorithm on randomly generated datasets. Afterwards, the optimized BN was determined to explore to study related factors for hyperlipidemia. We also make a comparison between the BN model with logistic regression model.ResultsThe BN constructed by Inter.iamb-Tabu hybrid algorithm had the best fitting degree to the benchmark networks, and was used to construct the BN model of hyperlipidemia. Multivariate logistic regression analysis suggested that gender, smoking, central obesity, daily average salt intake, daily average oil intake, diabetes mellitus, hypertension and physical activity were associated with hyperlipidemia. BNs model of hyperlipidemia further showed that gender, BMI, and physical activity were directly related to the occurrence of hyperlipidemia, hyperlipidemia was directly related to the occurrence of diabetes mellitus and hypertension; the average daily salt intake, daily average oil consumption, smoking, and central obesity were indirectly related to hyperlipidemia.ConclusionsThe BN of hyperlipidemia constructed by the Inter.iamb-Tabu hybrid algorithm is more reasonable, and allows for the overall linking effect between factors and diseases, revealing the direct and indirect factors associated with hyperlipidemia and correlation between related variables, which can provide a new approach to the study of chronic diseases and their associated factors.

Structural equation modeling for unraveling the multivariate genomic architecture of milk proteins in dairy cattle

The aims of this study were to investigate potential functional relationships among milk protein fractions in dairy cattle and to carry out a structural equation model (SEM) GWAS to provide a decomposition of total SNP effects into direct effects and effects mediated by traits that are upstream in a phenotypic network. To achieve these aims, we first fitted a mixed Bayesian multitrait genomic model to infer the genomic correlations among 6 milk nitrogen fractions [4 caseins (CN), namely κ-, β-, αS1-, and αS2-CN, and 2 whey proteins, namely β-lactoglobulin (β-LG) and α-lactalbumin (α-LA)], in a population of 989 Italian Brown Swiss cows. Animals were genotyped with the Illumina BovineSNP50 Bead Chip v.2 (Illumina Inc.). A Bayesian network approach using the max-min hill-climbing (MMHC) algorithm was implemented to model the dependencies or independence among traits. Strong and negative genomic correlations were found between β-CN and αS1-CN (-0.706) and between β-CN and κ-CN (-0.735). The application of the MMHC algorithm revealed that κ-CN and β-CN seemed to directly or indirectly influence all other milk protein fractions. By integrating multitrait model GWAS and SEM-GWAS, we identified a total of 127 significant SNP for κ-CN, 89 SNP for β-CN, 30 SNP for αS1-CN, and 14 SNP for αS2-CN (mostly shared among CN and located on Bos taurus autosome 6) and 15 SNP for β-LG (mostly located on Bos taurus autosome 11), whereas no SNP passed the significance threshold for α-LA. For the significant SNP, we assessed and quantified the contribution of direct and indirect paths to total marker effect. Pathway analyses confirmed that common regulatory mechanisms (e.g., energy metabolism and hormonal and neural signals) are involved in the control of milk protein synthesis and metabolism. The information acquired might be leveraged for setting up optimal management and selection strategies aimed at improving milk quality and technological characteristics in dairy cattle.

Genomic Bayesian Confirmatory Factor Analysis and Bayesian Network To Characterize a Wide Spectrum of Rice Phenotypes.

With the advent of high-throughput phenotyping platforms, plant breeders have a means to assess many traits for large breeding populations. However, understanding the genetic interdependencies among high-dimensional traits in a statistically robust manner remains a major challenge. Since multiple phenotypes likely share mutual relationships, elucidating the interdependencies among economically important traits can better inform breeding decisions and accelerate the genetic improvement of plants. The objective of this study was to leverage confirmatory factor analysis and graphical modeling to elucidate the genetic interdependencies among a diverse agronomic traits in rice. We used a Bayesian network to depict conditional dependencies among phenotypes, which can not be obtained by standard multi-trait analysis. We utilized Bayesian confirmatory factor analysis which hypothesized that 48 observed phenotypes resulted from six latent variables including grain morphology, morphology, flowering time, physiology, yield, and morphological salt response. This was followed by studying the genetics of each latent variable, which is also known as factor, using single nucleotide polymorphisms. Bayesian network structures involving the genomic component of six latent variables were established by fitting four algorithms (i.e., Hill Climbing, Tabu, Max-Min Hill Climbing, and General 2-Phase Restricted Maximization algorithms). Physiological components influenced the flowering time and grain morphology, and morphology and grain morphology influenced yield. In summary, we show the Bayesian network coupled with factor analysis can provide an effective approach to understand the interdependence patterns among phenotypes and to predict the potential influence of external interventions or selection related to target traits in the interrelated complex traits systems.

Learning Moral Graphs in Construction of High-Dimensional Bayesian Networks for Mixed Data.

Bayesian networks have been widely used in many scientific fields for describing the conditional independence relationships for a large set of random variables. This letter proposes a novel algorithm, the so-called p-learning algorithm, for learning moral graphs for high-dimensional Bayesian networks. The moral graph is a Markov network representation of the Bayesian network and also the key to construction of the Bayesian network for constraint-based algorithms. The consistency of the p-learning algorithm is justified under the small-n, large-p scenario. The numerical results indicate that the p-learning algorithm significantly outperforms the existing ones, such as the PC, grow-shrink, incremental association, semi-interleaved hiton, hill-climbing, and max-min hill-climbing. Under the sparsity assumption, the p-learning algorithm has a computational complexity of O(p2) even in the worst case, while the existing algorithms have a computational complexity of O(p3) in the worst case.

On scoring Maximal Ancestral Graphs with the Max–Min Hill Climbing algorithm

We consider the problem of causal structure learning in presence of latent confounders. We propose a hybrid method, MAG Max–Min Hill-Climbing (M3HC) that takes as input a data set of continuous variables, assumed to follow a multivariate Gaussian distribution, and outputs the best fitting maximal ancestral graph. M3HC builds upon a previously proposed method, namely GSMAG, by introducing a constraint-based first phase that greatly reduces the space of structures to investigate. On a large scale experimentation we show that the proposed algorithm greatly improves on GSMAG in all comparisons, and over a set of known networks from the literature it compares positively against FCI and cFCI as well as competitively against GFCI, three well known constraint-based approaches for causal-network reconstruction in presence of latent confounders.

Gene Regulatory Networks Reconstruction Using the Flooding-Pruning Hill-Climbing Algorithm.

The explosion of genomic data provides new opportunities to improve the task of gene regulatory network reconstruction. Because of its inherent probability character, the Bayesian network is one of the most promising methods. However, excessive computation time and the requirements of a large number of biological samples reduce its effectiveness and application to gene regulatory network reconstruction. In this paper, Flooding-Pruning Hill-Climbing algorithm (FPHC) is proposed as a novel hybrid method based on Bayesian networks for gene regulatory networks reconstruction. On the basis of our previous work, we propose the concept of DPI Level based on data processing inequality (DPI) to better identify neighbors of each gene on the lack of enough biological samples. Then, we use the search-and-score approach to learn the final network structure in the restricted search space. We first analyze and validate the effectiveness of FPHC in theory. Then, extensive comparison experiments are carried out on known Bayesian networks and biological networks from the DREAM (Dialogue on Reverse Engineering Assessment and Methods) challenge. The results show that the FPHC algorithm, under recommended parameters, outperforms, on average, the original hill climbing and Max-Min Hill-Climbing (MMHC) methods with respect to the network structure and running time. In addition, our results show that FPHC is more suitable for gene regulatory network reconstruction with limited data.

A hybrid algorithm for Bayesian network structure learning with application to multi-label learning

We present a novel hybrid algorithm for Bayesian network structure learning, called H2PC. It first reconstructs the skeleton of a Bayesian network and then performs a Bayesian-scoring greedy hill-climbing search to orient the edges. The algorithm is based on divide-and-conquer constraint-based subroutines to learn the local structure around a target variable. We conduct two series of experimental comparisons of H2PC against Max–Min Hill-Climbing (MMHC), which is currently the most powerful state-of-the-art algorithm for Bayesian network structure learning. First, we use eight well-known Bayesian network benchmarks with various data sizes to assess the quality of the learned structure returned by the algorithms. Our extensive experiments show that H2PC outperforms MMHC in terms of goodness of fit to new data and quality of the network structure with respect to the true dependence structure of the data. Second, we investigate H2PC’s ability to solve the multi-label learning problem. We provide theoretical results to characterize and identify graphically the so-called minimal label powersets that appear as irreducible factors in the joint distribution under the faithfulness condition. The multi-label learning problem is then decomposed into a series of multi-class classification problems, where each multi-class variable encodes a label powerset. H2PC is shown to compare favorably to MMHC in terms of global classification accuracy over ten multi-label data sets covering different application domains. Overall, our experiments support the conclusions that local structural learning with H2PC in the form of local neighborhood induction is a theoretically well-motivated and empirically effective learning framework that is well suited to multi-label learning. The source code (in R) of H2PC as well as all data sets used for the empirical tests are publicly available.

Bayesian belief network learning algorithms for modeling contextual relationships in natural imagery: a comparative study

This paper presents a comparative study of Bayesian belief network structure learning algorithms with a view to identify a suitable algorithm for modeling the contextual relations among objects typically found in natural imagery. Four popular structure learning algorithms are compared: two constraint-based algorithms (PC proposed by Spirtes and Glymour and Fast Incremental Association Markov Blanket proposed by Yaramakala and Margaritis), a score-based algorithm (Hill Climbing as implemented by Daly), and a hybrid algorithm (Max-Min Hill Climbing proposed by Tsamardinos et al.). Contrary to the belief regarding the superiority of constraint-based approaches, our empirical results show that a score-based approach performs better on our context dataset in terms of prediction power and learning time. The hybrid algorithm could achieve similar prediction performance as the score-based approach, but requires longer time to learn the desired network. Another interesting fact the study has revealed is the existence of strong correspondence between the linear correlation pattern within the dataset and the edges found in the learned networks.