Learning Bayesian Networks Research Articles

Searching for multiple equivalent predictors from oral squamous cell carcinoma dataset using statistically equivalent signature algorithm

Selecting highly predictive features from the high dimensional dataset is a formidable task. The existing feature selection algorithms available today are not dealing with multiple equally predictive subsets of features. We strongly believe that there is other subsets of features as well, which can give equivalent predictive accuracy as that of state-of-the-art algorithms. Statistically equivalent signature (SES) is one such feature selection algorithm, which is centred on constraint-based learning of Bayesian networks. The proposed model selects equivalent subsets of features from oral squamous cell carcinoma (OSCC) dataset with the help of SES. To inspect the validity of SES algorithms output, we are using K-nearest neighbour (KNN), support vector machine (SVM) and neural networks (NN) on each subset of predictive features. Finally, the results of proposed technique is compared with support vector machine - recursive feature elimination (SVM-RFE). SES produces more stable accuracy as compared to SVM-RFE.

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.

Co-expression Networks Identify DHX15 RNA Helicase as a B Cell Regulatory Factor.

Genome-wide co-expression analysis is often used for annotating novel gene functions from high-dimensional data. Here, we developed an R package with a Shiny visualization app that creates immuno-networks from RNAseq data using a combination of Weighted Gene Co-expression Network Analysis (WGCNA), xCell immune cell signatures, and Bayesian Network Learning. Using a large publicly available RNAseq dataset we generated a Gene Module-Immune Cell (GMIC) network that predicted causal relationships between DEAH-box RNA helicase (DHX)15 and genes associated with humoral immunity, suggesting that DHX15 may regulate B cell fate. Deletion of DHX15 in mouse B cells led to impaired lymphocyte development, reduced peripheral B cell numbers, and dysregulated expression of genes linked to antibody-mediated immune responses similar to the genes predicted by the GMIC network. Moreover, antigen immunization of mice demonstrated that optimal primary IgG1 responses required DHX15. Intrinsic expression of DHX15 was necessary for proliferation and survival of activated of B cells. Altogether, these results support the use of co-expression networks to elucidate fundamental biological processes.

Pigeon Inspired Optimization of Bayesian Network Structure Learning and a Comparative Evaluation

Bayesian networks are useful analytical models for designing the structure of knowledge in machine learning. Probabilistic dependency relationships among the variables can be represented by Bayesian networks. One strategy of a structure learning Bayesian Networks is the score and search technique. In this paper, we present a new method for structure learning of the Bayesian network which is based on Pigeon Inspired Optimization (PIO) Algorithm. The proposed algorithm is a simple one with fast convergence rate. In nature, the navigational ability of pigeons is unbelievable and highly impressive. In accordance with the PIO search algorithm, a set of directed acyclic graphs is defined. Every graph owns a score which shows its fitness. The algorithm is iterated until it gets the best solution or a satisfactory network structure using map and compass, and landmark operator. In this work, the proposed method compared with Simulated Annealing, Bee optimization and Simulated Annealing as a hybrid algorithm, Bee optimization and Greedy search as a hybrid algorithm, and Greedy Search using BDeu score function. We also investigated the confusion matrix performances of the methods. The paper presents the results of extensive evaluations of these algorithms based on common benchmark data sets. The results indicate that the proposed algorithm has better performance than the other algorithms and produces higher scores and accuracy values.

Integrated pipeline corrosion growth modeling and reliability analysis using dynamic Bayesian network and parameter learning technique

The present study integrates the corrosion growth modeling, reliability analysis and quantification of measurement errors of in-line inspection (ILI) tools in a single dynamic Bayesian network (DBN) model for the reliability-based corrosion management of oil and gas pipelines. The Expectation-Maximization algorithm in the context of the parameter learning technique is employed to learn the parameters of the DBN model. The application of the model on simulated and real-world corrosion data demonstrates the effectiveness of the parameter learning and accuracy of the corrosion growth predicted by the DBN model. In comparison with existing growth models, the integrating and graphical features of the developed model make the process of corrosion management more intuitive and transparent to users. The employment of the parameter learning technique provides an objective and convenient approach to elicit the probabilistic information from ILI and field measurement data. The above advantages make the model more amenable to the corrosion management practice in the pipeline industry.

Rapidly Learning Bayesian Networks for Complex System Diagnosis: A Reinforcement Learning Directed Greedy Search Approach

Bayesian networks are a popular diagnosis method, whose structures are usually defined by human experts and parameters are learned from data. For the increasing complexity of modern systems, building their structures based on physical behaviors is becoming a difficult task. However, the improvement of data collection techniques motivates learning their structures from data, where greedy search is a typical iterative method. In each iteration, it generates multiple structure candidates by modifying one edge, evaluates these structures by scores based on data and selects the best structure for the next iteration. This method is costly because there are too many structures to be evaluated. To solve this problem, we frame the traditional greedy search by Markov decision process and propose an efficient Bayesian network learning approach by integrating reinforcement learning into it. In our approach, a convolutional neural network is employed as the value function to approximate scores. Before evaluating structures using data, the neural network is used to predict scores. Structure candidates with a low predicted score are discarded. By avoiding unnecessary computation, the cooperation of reinforcement learning and greedy search effectively improves the learning efficiency. Two systems, a 10-tank system with 21 monitored variables and the classic Tennessee Eastman process with 52 variables, are employed to demonstrate our approach. The experiment results indicate that the computation cost of our method was reduced by 30%~50%, and the diagnosis accuracy was almost the same.

Modelling Single Cell B-Cell Receptor Signaling Reveals Enhanced Activity in Primary CLL Cells Compared to Non-Malignant Cells While Fundamental Network Circuit Topology Remains Stable Even with Novel Therapeutic Inhibitors

B-cell receptor (BCR) signalling is central for the pathomechanism of chronic lymphocytic leukemia (CLL). Novel inhibitors of BCR signalling have recently substantially improved treatment of CLL, and a better characterization of the molecular circuitry of leukemic BCR signalling will allow a more refined targeting of this Achilles heel. In order to model malignant and non-malignant BCR signalling, we quantified after stimulation 5 components of BCR signaling (ZAP70/SYK, BTK, PLCy2, AKT, ERK1/2) in single cells from primary human leukemic and non-malignant tissue via phospho-specific flow cytometry over 6 time points. We stimulated cells from 11 patients and non-malignant CD19 negative enriched B-cells from 5 healthy donors by crosslinking the BCR with anti-IgM and/or anti-CD19 and synchronous inhibition of phosphatases with H2O2. As expected, we found more phosphorylation of all BCR signalling components after stimulation in malignant vs non-malignant cells and in IGHV non-mutated CLL cells compared to IGHV mutated CLL cells. Intriguingly, inhibition of phosphatases with H2O2 led to higher phosphorylation of BCR components in CLL cells with mutated IGHV genes compared to CLL cells with non-mutated IGHV genes, suggesting a stronger dampening of signalling activity in mutated IGHV CLL by phosphatases. In order to characterize the signalling circuitry, we modelled the connectivity of the cascade components by correlating signal intensities across single cells of the cell populations of single samples (Figure 1). Surprisingly, upon stimulation no substantial differences in network topology were observed between malignant and non-malignant cells. To additionally test for changes in network topology, we challenged the BCR signaling cascade with inhibitors for BTK (ibrutinib), PI3K (idelalisib). Ibrutinib and idelalisib acted complementary, but not synergistic, and were similarly effective in IGHV mutated and non-mutated CLL. Effects of idelalisib were the same on malignant and non-malignant cells, whereas ibrutinib was mostly active on CLL cells, not on non-malignant B-cells. Upon stimulation with combinations of IgM and CD19 crosslinking augmented with H2O2, phosphorylation of PLCy2 could not be significantly inhibited by idelalisib or ibrutinib on a timescale of 28mins. We therefore aimed to identify central activating nodes of the BCR signalling cascade using targeted inhibitors. In fact, we found that inhibition of LYN with dasatinib and inhibition of SYK with entospletinib could substantially reduce phosphorylation of PLCy2, BTK and ERK but not AKT after all combinations of BCR stimulation. This suggests additional signalling cascades modulating AKT and a strong impact of SYK/LYN activity on the regulation of PLCy2. In summary, our findings underline the importance of single cell analysis of the dynamic circuitry of B-cell receptor signalling to understand development of resistance mechanisms and potential vulnerabilities. Figure 1: Workflow scheme of the Bayesian network learning and averaging approach. After discretizing the continuous single cell data, an optimal network is derived from each of R bootstrap samples. The Bayesian network learning strategy uses the BDe scoring function and a greedy hill-climbing algorithm to find the network model that represents the resampled data best. An average arc strength for each connection between nodes is derived from the number of occurrences of the respective connection in the set of R best scoring networks. Further averaging among networks derived from different data sets was applied for identifying conditional, temporal, and group-specific differences. Figure 1 Disclosures Döhner: Novartis: Consultancy, Honoraria, Research Funding; Astex: Consultancy, Honoraria; Bristol Myers Swuibb: Research Funding; Amgen: Consultancy, Honoraria, Research Funding; Arog: Research Funding; Seattle Genetics: Consultancy, Honoraria; Astellas: Consultancy, Honoraria; Roche: Consultancy, Honoraria; Janssen: Consultancy, Honoraria; Agios: Consultancy, Honoraria; Pfizer: Research Funding; Celgene Corporation: Consultancy, Honoraria, Research Funding; Jazz: Consultancy, Honoraria, Research Funding; AbbVie: Consultancy, Honoraria. Stilgenbauer:GSK: Consultancy, Honoraria, Research Funding, Speakers Bureau; Janssen: Consultancy, Honoraria, Research Funding, Speakers Bureau; Pharmacyclics: Other: Travel support; Amgen: Consultancy, Honoraria, Research Funding, Speakers Bureau; Novartis: Consultancy, Honoraria, Research Funding, Speakers Bureau; Gilead: Consultancy, Honoraria, Research Funding, Speakers Bureau; AstraZeneca: Consultancy, Honoraria, Research Funding, Speakers Bureau; Celgene: Consultancy, Honoraria, Research Funding, Speakers Bureau; Hoffmann La-Roche: Consultancy, Honoraria, Research Funding, Speakers Bureau; AbbVie: Consultancy, Honoraria, Research Funding, Speakers Bureau.

Bayesian network method for fault diagnosis of civil aircraft environment control system

This paper addresses the issues of fault diagnosis of the environmental control system of a certain commercial aircraft model of which the environmental control system has a high failure rate in field and causes many unplanned maintenance events. Because of the complexity and reciprocal compensation mechanism of the environmental control system, it is difficult to carry out fault isolation timely once the failure occurred during aircraft turnaround time, which thus may cause flight delay or even cancelation. The original contribution of this work is to propose a Bayesian network–based fault diagnosis method for commercial aircraft environmental control system where a multi-information fusion mechanism is used to incorporate the system first principle, expert experience and condition monitoring data. It incorporates extraction technology of sensor feature parameters and the structural learning of Bayesian network to realize the effective diagnosis of multiple faults. A case study is conducted based on a data set from a commercial aircraft fleet. The results show that the fault isolation ratio of this method is greater than 89%. The proposed Bayesian fault diagnosis network method can be used as a troubleshooting tool for airline maintenance technicians in fault isolation of environmental control system, reducing the time spent on-line troubleshooting and aircraft downtime.

Bayesian network modeling explorations of strategies on reducing perceived transfer time for urban rail transit service improvement in different seasons

A new Bayesian Network (BN) learning approach is developed in this work to analyze the effect of different factors on the Perceived Transfer Time (PTT) of the Urban Rail Transit (URT) passengers. It is shown that the newly developed approach is able to build a BN with a satisfactory ability to assess effective strategies on reducing the PTT for the URT service improvement. Moreover, it is found that mainly determined by the weather, the relative environment inside an URT station plays the key role in deciding the impacts of varied factors on the PTT in different seasons. Fully illuminating the transfer passageway and preparing adequate and clear transfer guidance in an URT station are the most important in spring for the reduction of the PTT. Effectively decreasing the passenger flow conflicts in an URT station is the only way to evidently reduce the PTT in summer. Not only fully illuminated and well decorated transfer passageway but also increased train service frequency is indispensable to the decrease of the PTT in autumn. Besides minimizing the passenger flow conflicts, improving both frequency and time coordination of train services is essential for reducing the PTT in winter as well.

PEnBayes: A Multi-Layered Ensemble Approach for Learning Bayesian Network Structure from Big Data.

Discovering the Bayesian network (BN) structure from big datasets containing rich causal relationships is becoming increasingly valuable for modeling and reasoning under uncertainties in many areas with big data gathered from sensors due to high volume and fast veracity. Most of the current BN structure learning algorithms have shortcomings facing big data. First, learning a BN structure from the entire big dataset is an expensive task which often ends in failure due to memory constraints. Second, it is quite difficult to select a learner from numerous BN structure learning algorithms to consistently achieve good learning accuracy. Lastly, there is a lack of an intelligent method that merges separately learned BN structures into a well structured BN network. To address these shortcomings, we introduce a novel parallel learning approach called PEnBayes (Parallel Ensemble-based Bayesian network learning). PEnBayes starts with an adaptive data preprocessing phase that calculates the Appropriate Learning Size and intelligently divides a big dataset for fast distributed local structure learning. Then, PEnBayes learns a collection of local BN Structures in parallel using a two-layered weighted adjacent matrix-based structure ensemble method. Lastly, PEnBayes merges the local BN Structures into a global network structure using the structure ensemble method at the global layer. For the experiment, we generate big data sets by simulating sensor data from patient monitoring, transportation, and disease diagnosis domains. The Experimental results show that PEnBayes achieves a significantly improved execution performance with more consistent and stable results compared with three baseline learning algorithms.

Hybrid Optimization Algorithm for Bayesian Network Structure Learning

Since the beginning of the 21st century, research on artificial intelligence has made great progress. Bayesian networks have gradually become one of the hotspots and important achievements in artificial intelligence research. Establishing an effective Bayesian network structure is the foundation and core of the learning and application of Bayesian networks. In Bayesian network structure learning, the traditional method of utilizing expert knowledge to construct the network structure is gradually replaced by the data learning structure method. However, as a result of the large amount of possible network structures, the search space is too large. The method of Bayesian network learning through training data usually has the problems of low precision or high complexity, which make the structure of learning differ greatly from that of reality, which has a great influence on the reasoning and practical application of Bayesian networks. In order to solve this problem, a hybrid optimization artificial bee colony algorithm is discretized and applied to structure learning. A hybrid optimization technique for the Bayesian network structure learning method is proposed. Experimental simulation results show that the proposed hybrid optimization structure learning algorithm has better structure and better convergence.

Learning parameters of Bayesian networks from datasets with systematically missing data: A meta–analytic approach

Previous research suggested that using additional data sources could improve parameter learning in Bayesian networks. However, when additional datasets do not include all network variables, neither standard Bayesian network learning techniques nor standard missing data methods can be applied. In such situations, the use of a meta–analytic approach is proposed. The performance of one such meta–analytic approach was evaluated by simulating several study results on two real–life biomedical examples (one discrete and one Gaussian Bayesian network). Regardless of the network type, the meta–analytic approach showed higher mean log–likelihood values, less sensitive to the presence of heterogeneity, than a single dataset analysis. The difference between the two methods was most pronounced when sample sizes were small (N=100). For the meta–analytic approach, the increase in log–likelihood was in most cases positively related to the number of nodes estimated with additional data. However, as in the case of single dataset analysis, care is needed when estimating rare event probabilities from small datasets due to the problems with unidentifiability and increased bias.

Learning Bayesian networks with local structure, mixed variables, and exact algorithms

Modern exact algorithms for structure learning in Bayesian networks first compute an exact local score of every candidate parent set, and then find a network structure by combinatorial optimization so as to maximize the global score. This approach assumes that each local score can be computed fast, which can be problematic when the scarcity of the data calls for structured local models or when there are both continuous and discrete variables, for these cases have lacked efficient-to-compute local scores. To address this challenge, we introduce a local score that is based on a class of classification and regression trees. We show that under modest restrictions on the possible branchings in the tree structure, it is feasible to find a structure that maximizes a Bayes score in a range of moderate-size problem instances. In particular, this enables global optimization of the Bayesian network structure, including the local structure. In addition, we introduce a related model class that extends ordinary conditional probability tables to continuous variables by employing an adaptive discretization approach. The two model classes are compared empirically by learning Bayesian networks from benchmark real-world and synthetic data sets. We discuss the relative strengths of the model classes in terms of their structure learning capability, predictive performance, and running time.

RNA-Seq Bayesian Network Exploration of Immune System in Bovine.

Background: The stress is one of main factors effects on production system. Several factors (both genetic and environmental elements) regulate immune response to stress.Objectives: In order to determine the major immune system regulatory genes underlying stress responses, a learning Bayesian network approach for those regulatory genes was applied to RNA-Seq data from a bovine leukocyte model system.Material and Methods: The transcriptome dataset GSE37447 was used from GEO and a Bayesian network on differentially expressed genes was learned to investigate the gene regulatory network.Results: Applying the method produced a strongly interconnected network with four genes (TERF2IP, PDCD10, DDX10 and CENPE) acting as nodes, suggesting these genes may be important in the transcriptome regulation program of stress response. Of these genes TERF2IP has been shown previously to regulate gene expression, act as a regulator of the nuclear factor-kappa B (NF-κB) signalling, and to activate expression of NF-κB target genes; PDCD10 encodes a conserved protein associated with cell apoptosis; DDX10 encodes a DEAD box protein and is believed to be associated with cellular growth and division; and CENPE involves unstable spindle microtubule capture at kinetochores. Together these genes are involved in DNA damage of apoptosis, RNA splicing, DNA repairing, and regulating cell division in the bovine genome. The topology of the learned Bayesian gene network indicated that the genes had a minimal interrelationship with each other. This type of structure, using the publically available computational tool, was also observed on human orthologous genes of the differentially expressed genes.Conclusions: Overall, the results might be used in transcriptomic-assisted selection and design of new drug targets to treat stress-related problems in bovines.

Learning Bayesian network structures using weakest mutual-information-first strategy

In Bayesian network structure learning, the quality of the directed graph learned by the constraint-based approaches can be greatly affected by the order of choosing variable pairs and the order of selecting condition sets for testing conditional independence. Inspired by the strong connection between the degree of mutual information shared by two variables and their conditional independence, we introduce the M-ordering concept, where a matrix is precomputed from the observational data with variables ordered increasingly by their respective degree of mutual information with the target variable under concern. Given the M-ordering matrix, we propose a strategy called Weakest Mutual-Information-First Strategy (WMIF), which is integrated into the PC-algorithm in two aspects: an MI-based edge removal strategy, and an MI-based condition set generation strategy. The MI-based edge removal strategy is to always select the variable pair with the weakest mutual information to test their conditional independence; the condition set generation strategy is to construct a conditioning set where variables bearing a weaker degree of mutual information with the target variable are always considered first. We prove that the weakest MI-based edge removal strategy is sound, and our PC-MI algorithm, a PC variant empowered by the WMIF strategy, is order-independent. Moreover, in PC algorithms, the number of conditional independence tests increases exponentially with the number of random variables; we show that the WMIF strategy can effectively reduce the complexity (bounded by o(|V|(2|adj(X)|−|V|22))). We have conducted experiments with both low-dimensional and high-dimensional data sets, and the results indicate that PC-MI outperforms the state-of-the-art approaches. More importantly, the order-agnostic property of PC-MI can be extremely useful when it is hard to prescribe a meaningful variable ordering as needed in some other PC algorithms.

Structure Learning of Bayesian Network Based on Adaptive Thresholding.

Direct dependencies and conditional dependencies in restricted Bayesian network classifiers (BNCs) are two basic kinds of dependencies. Traditional approaches, such as filter and wrapper, have proved to be beneficial to identify non-significant dependencies one by one, whereas the high computational overheads make them inefficient especially for those BNCs with high structural complexity. Study of the distributions of information-theoretic measures provides a feasible approach to identifying non-significant dependencies in batch that may help increase the structure reliability and avoid overfitting. In this paper, we investigate two extensions to the k-dependence Bayesian classifier, MI-based feature selection, and CMI-based dependence selection. These two techniques apply a novel adaptive thresholding method to filter out redundancy and can work jointly. Experimental results on 30 datasets from the UCI machine learning repository demonstrate that adaptive thresholds can help distinguish between dependencies and independencies and the proposed algorithm achieves competitive classification performance compared to several state-of-the-art BNCs in terms of 0–1 loss, root mean squared error, bias, and variance.

Model selection and local geometry

We consider problems in model selection caused by the geometry of models close to their points of intersection. In some cases—including common classes of causal or graphical models, as well as time series models—distinct models may nevertheless have identical tangent spaces. This has two immediate consequences: first, in order to obtain constant power to reject one model in favour of another we need local alternative hypotheses that decrease to the null at a slower rate than the usual parametric $n^{-1/2}$ (typically we will require $n^{-1/4}$ or slower); in other words, to distinguish between the models we need large effect sizes or very large sample sizes. Second, we show that under even weaker conditions on their tangent cones, models in these classes cannot be made simultaneously convex by a reparameterization. This shows that Bayesian network models, amongst others, cannot be learned directly with a convex method similar to the graphical lasso. However, we are able to use our results to suggest methods for model selection that learn the tangent space directly, rather than the model itself. In particular, we give a generic algorithm for learning Bayesian network models.

Factors Affecting Health Care Engagement of Patients With End-Stage Heart Failure: An Exploratory Survey Study.

Background. The decision to receive a permanent left ventricular assist device (LVAD) to treat end-stage heart failure (HF) involves understanding and weighing the risks and benefits of a highly invasive treatment. The goal of this study was to characterize end-stage HF patients across parameters that may affect their decision making and to inform the development of an LVAD decision support tool. Methods. A survey of 35 end-stage HF patients at an LVAD implant hospital was performed to characterize their information-seeking habits, interaction with physicians, technology use, numeracy, and concerns about their health. Survey responses were analyzed using descriptive statistics, grounded theory method, and Bayesian network learning. Results. Most patients indicated an interest in using some type of decision support tool (roadmap of health progression: 46%, n = 16; personal prognosis: 51%, n = 18; short videos of patients telling stories of their experiences with an LVAD: 57%, n = 20). Information patients desired in a hypothetical decision support tool fell into the following topics: prognoses for health outcomes, technical information seeking, expressing emotions, and treatment decisions. Desire for understanding their condition was closely related to whether they had difficult interpreting their electronic medical record in the past. Conclusions. Most patients reported interest in engaging in their health care decision making and seeing their prognosis and electronic health record information. Patients who were less interested in their own treatment decisions were characterized by having less success understanding their health information. Design of a decision support tool for potential LVAD patients should consider a spectrum of health literacy and include information beyond the technical specifications of LVAD support.

Learning Bayesian networks by constrained Bayesian estimation

Bayesian networks (BNs) have become increasingly popular in recent years due to their wide-ranging applications in modeling uncertain knowledge. An essential problem about discrete BNs is learning conditional probability table (CPT) parameters. If training data are sparse, purely data-driven methods often fail to learn accurate parameters. Then, expert judgments can be introduced to overcome this challenge. Parameter constraints deduced from expert judgments can cause parameter estimates to be consistent with domain knowledge. In addition, Dirichlet priors contain information that helps improve learning accuracy. This paper proposes a constrained Bayesian estimation approach to learn CPTs by incorporating constraints and Dirichlet priors. First, a posterior distribution of BN parameters is developed over a restricted parameter space based on training data and Dirichlet priors. Then, the expectation of the posterior distribution is taken as a parameter estimation. As it is difficult to directly compute the expectation for a continuous distribution with an irregular feasible domain, we apply the Monte Carlo method to approximate it. In the experiments on learning standard BNs, the proposed method outperforms competing methods. It suggests that the proposed method can facilitate solving real-world problems. Additionally, a case study of Wine data demonstrates that the proposed method achieves the highest classification accuracy.

Combining gene expression data and prior knowledge for inferring gene regulatory networks via Bayesian networks using structural restrictions.

Gene Regulatory Networks (GRNs) are known as the most adequate instrument to provide a clear insight and understanding of the cellular systems. One of the most successful techniques to reconstruct GRNs using gene expression data is Bayesian networks (BN) which have proven to be an ideal approach for heterogeneous data integration in the learning process. Nevertheless, the incorporation of prior knowledge has been achieved by using prior beliefs or by using networks as a starting point in the search process. In this work, the utilization of different kinds of structural restrictions within algorithms for learning BNs from gene expression data is considered. These restrictions will codify prior knowledge, in such a way that a BN should satisfy them. Therefore, one aim of this work is to make a detailed review on the use of prior knowledge and gene expression data to inferring GRNs from BNs, but the major purpose in this paper is to research whether the structural learning algorithms for BNs from expression data can achieve better outcomes exploiting this prior knowledge with the use of structural restrictions. In the experimental study, it is shown that this new way to incorporate prior knowledge leads us to achieve better reverse-engineered networks.