Conditional Gaussian Bayesian Network Research Articles

A novel fault diagnosis method for Bayesian networks fusing models and data

Data-driven methods are the mainstream methods applied in current fault diagnosis research; however, in natural mechanical systems, fault samples are difficult or even impossible to obtain, and physical model-based methods cannot easily model the faults of complex systems. To address the respective limitations of data-driven and model diagnosis methods in fault diagnosis, in this paper, a Bayesian network fault diagnosis method based on a joint model and data modelling is proposed. Conditional Gaussian Bayesian networks are used to fuse discrete and continuous information, and the discrete information in the residuals is used to compensate for the insufficient feature information problem caused by small amounts of data. To address the exponential modeling complexity growth in the case of multiple fault types cases, a single classification method is chosen for fault classification. Meanwhile, the T2 statistics distance suppression method is introduced into the Bayesian network to improve the diagnostic capabilities for new types of faults. By comparing the mainstream methods that address small sample diagnosis and the existing fusion methods, the experimental results show that in cases with small numbers of samples, the method in this paper has good fault diagnosis capabilities by effectively utilizing the model’s diagnostic results to compensate for the diagnostic errors caused by a lack of data, and it has an improved ability to recognize unknown faults.

Bayesian network analysis of BIN1 risk allele and other risk factors and biomarkers of Alzheimer’s disease

AbstractBackgroundThe Bridging Integrator I (BIN1) is a significant genetic risk gene, second only to the established risk gene apolipoprotein E (APOE4), for late‐onset Alzheimer’s disease (LOAD, AD) (Carrasquillo, 2011). BIN1 rs744733 risk allele was shown to affect tau pathology and cognitive decline (Franzmeier, 2021).In this study, we compared BIN1 risk allele rs6733839 with APOE4 on interdependency among AD risk factors and biomarkers by applying Bayesian Network (BN) modeling (Scutari, 2017) to data from Lilly AD clinical trials.MethodData from A05C (n = 142, NCT01565382), A05E (n = 217, NCT02016560), and untreated arms of AZES (n = 206, NCT02245737), LLCF (n = 229, NCT02791191), and LZAX (n = 194, NCT01900665) trial participants were used for the analysis (table 1). We constructed graphs representing the dependencies among the variables, including demographics, genetic risk genes, brain amyloid and tau measured by 18F‐Florbetapir or 18F‐Flortaucipir positron emission tomography (PET) imaging quantified globally and regionally as a standardized uptake value ratio. Longitudinal tau changes from baseline were computed for a sub cohort (n = 234). Conditional Gaussian Bayesian Network (CGBN) was used to model discrete (gender, genotype) and continuous (age, PET quantifications) variables. Directed Acyclic Graphs (DAG) structure was learned using constraint‐based Incremental Association (iamb) algorithm and score‐based Hill‐Climbing (hc) algorithm with one‐sided type I error rate at 10%. The connection strength was estimated by bootstrap resampling and computing the probability of any variable influencing another variable. Model parameters were estimated using the maximum likelihood estimation method.ResultThe result shows that age influences baseline amyloid (Strength s = 1.0) and parietal tau (s = 0.83). APOE4 influences baseline amyloid (s = 0.75) and tau at four lopes with strength ranging from 0.84 to 0.31 in the order of frontal, parietal, occipital, and temporal lobes. BIN1 influences baseline tau at the parietal lobe (s = 0.42) and other lobes with strength below 0.3. We have not observed consistent dependency between variables and change in tau, likely due to the small sample size (n = 234).ConclusionOur study result is consistent with current knowledge of APOE4 influencing amyloid and tau. The finding that BIN1 influences tau supports the observation of BIN1 rs744373, in linkage disequilibrium with rs6733839, in ADNI and BioFINDER studies (Franzmeier, 2021).

Healthcare Cost Prediction Based on Hybrid Machine Learning Algorithms

Healthcare cost is an issue of concern right now. While many complex machine learning algorithms have been proposed to analyze healthcare cost and address the shortcomings of linear regression and reliance on expert analyses, these algorithms do not take into account whether each characteristic variable contained in the healthcare data has a positive effect on predicting healthcare cost. This paper uses hybrid machine learning algorithms to predict healthcare cost. First, network structure learning algorithms (a score-based algorithm, constraint-based algorithm, and hybrid algorithm) for a Conditional Gaussian Bayesian Network (CGBN) are used to learn the isolated characteristic variables in healthcare data without changing the data properties (i.e., discrete or continuous). Then, the isolated characteristic variables are removed from the original data and the remaining data used to train regression algorithms. Two public healthcare datasets are used to test the performance of the proposed hybrid machine learning algorithm model. Experiments show that when compared to popular single machine learning algorithms (Long Short Term Memory, Random Forest, etc.) the proposed scheme can obtain similar or higher prediction accuracy with a reduced amount of data.

Survivability Prognosis for Lung Cancer Patients at Different Severity Stages by a Risk Factor-Based Bayesian Network Modeling

Lung cancer is a major reason of mortalities. Estimating the survivability for this disease has become a key issue to families, hospitals, and countries. A conditional Gaussian Bayesian network model was presented in this study. This model considered 15 risk factors to predict the survivability of a lung cancer patient at 4 severity stages. We surveyed 1075 patients. The presented model is constructed by using the demographic, diagnosed-based, and prior-utilization variables. The proposed model for the survivability prognosis at different four stages performed R2 of 93.57%, 86.83%, 67.22%, and 52.94%, respectively. The model predicted the lung cancer survivability with high accuracy compared with the reported models. Our model also shows that it reached the ceiling of an ideal Bayesian network.

Maize Carotenoid Gene Locus Mining Based on Conditional Gaussian Bayesian Network

How to mine the gene locus for maize carotenoid components is an important research problem in biology study. Along with the rapid development of high-throughput biotechnologies, we have produced a large number of maize multi-omics data, including genome, transcriptome, metabolome, phenotype, etc. How to conjointly analyze these continuous and discrete data, and thus to mine the genetic loci that control the maize carotenoid components have a very important biological significance. In this work, we use the conditional Gaussian Bayesian network learning method to construct the network of maize gene, SNP locus and carotenoid components, aim to get the possible significant loci about four reported genes for the carotenoid component traits. The method is validated using the multi-omics data of maize global germplasm collection with 368 elite inbred lines. Four algorithms are used to do the comparison, and experiment results show the method can mine the effective locus for the phenotype traits. It is concluded that the conditional Gaussian Bayesian network learning method is an effective way of analyzing multi-omics data conjointly, mining the possible gene locus for maize carotenoid component traits, and thus to provide genetic resources and useful information for molecular breeding of maize.

Medical expenditure estimation by Bayesian network for lung cancer patients at different severity stages

Lung cancer is one of the leading causes of mortality, and its medical expenditure has increased dramatically. Estimating the expenditure for this disease has become an urgent concern of the supporting families, medial institutes, and government. In this study, a conditional Gaussian Bayesian network (CGBN) model was developed to incorporate the comprehensive risk factors to estimate the medical expenditure of a lung cancer patient at different stages. A total of 961 patients were surveyed by the four severity stages of lung cancer. The proposed CGBN model identified the correlation and association of 15 risk factors to the medical expenditure of different severity stages of lung cancer patients. The relationships among the demographic, diagnosed-based, and prior-utilization variables are constructed. The model predicted the lung cancer-related medical expenditure with high accuracy of 32.63%, 50.30%, 50.36%, and 66.58%, respectively for stages 1–4, as compared with the reported models. A greedy search was also applied to find the upper threshold of R2, while our model also shows that it approached the upper threshold.

Short‐term traffic flow prediction with linear conditional Gaussian Bayesian network

SummaryTraffic flow prediction is an essential part of intelligent transportation systems (ITS). Most of the previous traffic flow prediction work treated traffic flow as a time series process only, ignoring the spatial relationship from the upstream flows or the correlation with other traffic attributes like speed and density. In this paper, we utilize a linear conditional Gaussian (LCG) Bayesian network (BN) model to consider both spatial and temporal dimensions of traffic as well as speed information for short‐term traffic flow prediction. The LCG BN allows both continuous and discrete variables, which enables the consideration of categorical variables in traffic flow prediction. A microscopic traffic simulation dataset is used to test the performance of the proposed model compared to other popular approaches under different predicting time intervals. In addition, the authors investigate the importance of spatial data and speed data in flow prediction by comparing models with different levels of information. The results indicate that the prediction accuracy will increase significantly when both spatial data and speed data are included. Copyright © 2016 John Wiley & Sons, Ltd.

Belief propagation in genotype-phenotype networks.

Graphical models have proven to be a valuable tool for connecting genotypes and phenotypes. Structural learning of phenotype-genotype networks has received considerable attention in the post-genome era. In recent years, a dozen different methods have emerged for network inference, which leverage natural variation that arises in certain genetic populations. The structure of the network itself can be used to form hypotheses based on the inferred direct and indirect network relationships, but represents a premature endpoint to the graphical analyses. In this work, we extend this endpoint. We examine the unexplored problem of perturbing a given network structure, and quantifying the system-wide effects on the network in a node-wise manner. The perturbation is achieved through the setting of values of phenotype node(s), which may reflect an inhibition or activation, and propagating this information through the entire network. We leverage belief propagation methods in Conditional Gaussian Bayesian Networks (CG-BNs), in order to absorb and propagate phenotypic evidence through the network. We show that the modeling assumptions adopted for genotype-phenotype networks represent an important sub-class of CG-BNs, which possess properties that ensure exact inference in the propagation scheme. The system-wide effects of the perturbation are quantified in a node-wise manner through the comparison of perturbed and unperturbed marginal distributions using a symmetric Kullback-Leibler divergence. Applications to kidney and skin cancer expression quantitative trait loci (eQTL) data from different mus musculus populations are presented. System-wide effects in the network were predicted and visualized across a spectrum of evidence. Sub-pathways and regions of the network responded in concert, suggesting co-regulation and coordination throughout the network in response to phenotypic changes. We demonstrate how these predicted system-wide effects can be examined in connection with estimated class probabilities for covariates of interest, e.g. cancer status. Despite the uncertainty in the network structure, we demonstrate the system-wide predictions are stable across an ensemble of highly likely networks. A software package, geneNetBP, which implements our approach, was developed in the R programming language.

The metabolomics of asthma control: a promising link between genetics and disease.

Short-acting β agonists (e.g., albuterol) are the most commonly used medications for asthma, a disease that affects over 300 million people in the world. Metabolomic profiling of asthmatics taking β agonists presents a new and promising resource for identifying the molecular determinants of asthma control. The objective is to identify novel genetic and biochemical predictors of asthma control using an integrative “omics” approach. We generated lipidomic data by liquid chromatography tandem mass spectrometry (LC-MS), ­ using plasma samples from 20 individuals with asthma. The outcome of interest was a binary indicator of asthma control defined by the use of albuterol inhalers in the preceding week. We integrated metabolomic data with genome-wide genotype, gene expression, and methylation data of this cohort to identify genomic and molecular indicators of asthma control. A Conditional Gaussian Bayesian Network (CGBN) was generated using the strongest predictors from each of these analyses. Integrative and metabolic pathway over-representation analyses (ORA) identified enrichment of known biological pathways within the strongest molecular determinants. Of the 64 metabolites measured, 32 had known identities. The CGBN model based on four SNPs (rs9522789, rs7147228, rs2701423, rs759582) and two metabolites—monoHETE_0863 and sphingosine-1-phosphate (S1P) could predict asthma control with an AUC of 95%. Integrative ORA identified 17 significantly enriched pathways related to cellular immune response, interferon signaling, and cytokine-related signaling, for which arachidonic acid, PGE2 and S1P, in addition to six genes (CHN1, PRKCE, GNA12, OASL, OAS1, and IFIT3) appeared to drive the pathway results. Of these predictors, S1P, GNA12, and PRKCE were enriched in the results from integrative and metabolic ORAs. Through an integrative analysis of metabolomic, genomic, and methylation data from a small cohort of asthmatics, we implicate altered metabolic pathways, related to sphingolipid metabolism, in asthma control. These results provide insight into the pathophysiology of asthma control.

CGBayesNets: conditional Gaussian Bayesian network learning and inference with mixed discrete and continuous data.

Bayesian Networks (BN) have been a popular predictive modeling formalism in bioinformatics, but their application in modern genomics has been slowed by an inability to cleanly handle domains with mixed discrete and continuous variables. Existing free BN software packages either discretize continuous variables, which can lead to information loss, or do not include inference routines, which makes prediction with the BN impossible. We present CGBayesNets, a BN package focused around prediction of a clinical phenotype from mixed discrete and continuous variables, which fills these gaps. CGBayesNets implements Bayesian likelihood and inference algorithms for the conditional Gaussian Bayesian network (CGBNs) formalism, one appropriate for predicting an outcome of interest from, e.g., multimodal genomic data. We provide four different network learning algorithms, each making a different tradeoff between computational cost and network likelihood. CGBayesNets provides a full suite of functions for model exploration and verification, including cross validation, bootstrapping, and AUC manipulation. We highlight several results obtained previously with CGBayesNets, including predictive models of wood properties from tree genomics, leukemia subtype classification from mixed genomic data, and robust prediction of intensive care unit mortality outcomes from metabolomic profiles. We also provide detailed example analysis on public metabolomic and gene expression datasets. CGBayesNets is implemented in MATLAB and available as MATLAB source code, under an Open Source license and anonymous download at http://www.cgbayesnets.com.

A new multivariate imputation method based on Bayesian networks

Dealing with incomplete data is a pervasive problem in statistical surveys. Bayesian networks have been recently used in missing data imputation. In this research, we propose a new methodology for the multivariate imputation of missing data using discrete Bayesian networks and conditional Gaussian Bayesian networks. Results from imputing missing values in coronary artery disease data set and milk composition data set as well as a simulation study from cancer-neapolitan network are presented to demonstrate and compare the performance of three Bayesian network-based imputation methods with those of multivariate imputation by chained equations (MICE) and the classical hot-deck imputation method. To assess the effect of the structure learning algorithm on the performance of the Bayesian network-based methods, two methods called Peter-Clark algorithm and greedy search-and-score have been applied. Bayesian network-based methods are: first, the method introduced by Di Zio et al. [Bayesian networks for imputation, J. R. Stat. Soc. Ser. A 167 (2004), 309–322] in which, each missing item of a variable is imputed using the information given in the parents of that variable; second, the method of Di Zio et al. [Multivariate techniques for imputation based on Bayesian networks, Neural Netw. World 15 (2005), 303–310] which uses the information in the Markov blanket set of the variable to be imputed and finally, our new proposed method which applies the whole available knowledge of all variables of interest, consisting the Markov blanket and so the parent set, to impute a missing item. Results indicate the high quality of our new proposed method especially in the presence of high missingness percentages and more connected networks. Also the new method have shown to be more efficient than the MICE method for small sample sizes with high missing rates.

Belief update in CLG Bayesian networks with lazy propagation

In recent years, Bayesian networks with a mixture of continuous and discrete variables have received an increasing level of attention. In this paper, we focus on the restricted class of mixture Bayesian networks known as conditional linear Gaussian Bayesian networks (CLG Bayesian networks) and present an architecture for exact belief update for this class of mixture networks. The proposed architecture is an extension of lazy propagation using operations of Lauritzen and Jensen [S.L. Lauritzen, F. Jensen, Stable local computation with mixed Gaussian distributions, Statistics and Computing 11(2) (2001) 191–203] and Cowell [R.G. Cowell, Local propagation in conditional Gaussian Bayesian networks, Journal of Machine Learning Research 6 (2005) 1517–1550]. By decomposing clique and separator potentials into sets of factors, the proposed architecture takes advantage of independence and irrelevance properties induced by the structure of the graph and the evidence. The resulting benefits are illustrated by examples and assessed by experiments. The performance of the proposed architecture has been evaluated using a set of randomly generated networks. The results indicate a significant potential of the proposed architecture.

Local Propagation in Conditional Gaussian Bayesian Networks

This paper describes a scheme for local computation in conditional Gaussian Bayesian networks that combines the approach of Lauritzen and Jensen (2001) with some elements of Shachter and Kenley (1989). Message passing takes place on an elimination tree structure rather than the more compact (and usual) junction tree of cliques. This yields a local computation scheme in which all calculations involving the continuous variables are performed by manipulating univariate regressions, and hence matrix operations are avoided.