Construction Of Bayesian Networks Research Articles

UNDERSTANDING BAYES RULE: BAYESIAN NETWORKS IN ARTIFICIAL INTELLIGENCE

Bayes' Rule and Bayesian Networks are foundational elements of AI, enabling probabilistic reasoning and informed decision-making in uncertain domains. This article introduces the core concepts and practical applications of these tools. We explore the historical origins, step-by-step construction of Bayesian Networks, and real-world AI applications. By understanding Bayes' Rule and Bayesian Networks, readers can unlock their potential to tackle complex AI challenges and uncertainties. And this article underscores the undeniable importance of Bayes' Rule and Bayesian Networks in AI. We hope to inspire a deeper understanding of these foundational concepts and encourage the exploration of their vast potential in artificial intelligence. Keywords: Bayesian Networks, AI, probabilistic reasoning, informed decision-making

Capturing and quantifying the aggregate effects of multi-source factors affecting miners' health and well-being: Construction of Bayesian belief networks.

Factors originating at the organizational, work, and individual levels are closely interrelated and intricately intertwined, affecting health rates. There was limited research on the interdependence and aggregate effects between multi-source factors and occupational health and well-being (OHW). It is challenging to achieve management goals. Therefore, considering cross-level factors and across the "work environment-stress-exposure-OHW" chain, individual vulnerability was considered. A Fuzzy Bayesian Belief Network (FBBN) driven by both domain knowledge and data was constructed to carve out the logic between multi-source factors and OHW. Workers from four coal mines were surveyed twice in 6months. 714 valid samples were included in the analysis. The interdependencies among multi-source factors were identified by the Interpretive Structure Modeling method and the visual probability estimation was achieved based on FBBN. It revealed that the work and the organizational level were the root factors. Eight factors involved in work stress were mainly mediating, and actual exposure and individual vulnerability were direct factors. Pathway interventions and joint interventions were proposed. The prediction ability and scheme feasibility of FBBN were verified. The approach developed allows robust assessments of aggregate effects and obtains multi-source factor importance. This study provides vital insights and evaluation tools for understanding workplace stress and OHW management.

Practicalities of Bayesian network modeling for nuclear data evaluation with the nucdataBaynet package

Bayesian networks are a helpful abstraction in the modelization of the relationships between different variables for the purpose of uncertainty quantification. They are therefore especially well suited for the application to nuclear data evaluation to accurately model the relationships of experimental and nuclear models. Constraints, such as sum rules and the non-negativity of cross sections, can be rigorously taken into account in Bayesian inference within Bayesian networks. This contribution elaborates on the practical aspects of the construction of Bayesian networks with the nucdataBaynet package for the purpose of nuclear data evaluation.

Causal models versus reason models in Bayesian networks for legal evidence

In this paper we compare causal models with reason models in the construction of Bayesian networks for legal evidence. In causal models, arrows in the network are drawn from causes to effects. In a reason model, the arrows are instead drawn towards the evidence, from factum probandum to factum probans. We explore the differences between causal models and reason models and observe several distinct advantages with reason models. Reason models are better aligned with the philosophy of Bayesian inference, as they model reasons for up-dating beliefs. Reason models are better suited for measuring the combined support of the evidence, and a prior probability of guilt that reflects the number of possible perpetrators is accommodated more easily with reason models.

Branching time active inference: Empirical study and complexity class analysis

Active inference is a state-of-the-art framework for modelling the brain that explains a wide range of mechanisms such as habit formation, dopaminergic discharge and curiosity. However, recent implementations suffer from an exponential (space and time) complexity class when computing the prior over all the possible policies up to the time horizon. Fountas et al. (2020) used Monte Carlo tree search to address this problem, leading to very good results in two different tasks. Additionally, Champion et al. (2021a) proposed a tree search approach based on (temporal) structure learning. This was enabled by the development of a variational message passing approach to active inference (Champion, Bowman, Grześ, 2021), which enables compositional construction of Bayesian networks for active inference. However, this message passing tree search approach, which we call branching-time active inference (BTAI), has never been tested empirically. In this paper, we present an experimental study of the approach (Champion, Grześ, Bowman, 2021) in the context of a maze solving agent. In this context, we show that both improved prior preferences and deeper search help mitigate the vulnerability to local minima. Then, we compare BTAI to standard active inference (AcI) on a graph navigation task. We show that for small graphs, both BTAI and AcI successfully solve the task. For larger graphs, AcI exhibits an exponential (space) complexity class, making the approach intractable. However, BTAI explores the space of policies more efficiently, successfully scaling to larger graphs. Then, BTAI was compared to the POMCP algorithm (Silver and Veness, 2010) on the frozen lake environment. The experiments suggest that BTAI and the POMCP algorithm accumulate a similar amount of reward. Also, we describe when BTAI receives more rewards than the POMCP agent, and when the opposite is true. Finally, we compared BTAI to the approach of Fountas et al. (2020) on the dSprites dataset, and we discussed the pros and cons of each approach.

Classification of Village Development Index at Regency/Municipality Level Using Bayesian Network Approach with K-Means Discretization

Village development has been one of the most important targets of government policies in Indonesia in order to fully optimize its potential. Under Law 06 Year 2014 on Villages, local governments from regency/municipality level to village level are required to understand their respective village potentials in order to increase the village potentials in their regions. In this paper, we build and analyze the Bayesian network methods to classify the village development index at regency/municipality and gain a better understanding of the causal relationships between independent variables of the village potential status. Using a web scraping method of information retrieval, data are collected from the Ministry of Village, Development of Disadvantaged Regions, and Transmigration (Kemendesa) website, and Village Development Evaluation (Indeks Pembangunan Desa—IPD) of Statistics Indonesia (BPS) publication in 2018 data. Further, we combine the discretization using the K-Means clustering method to handle the continuous nature of retrieved data. An extensive comparison of different learning structures of the Bayesian Network is performed, which includes the learning structure of Naive Bayes, Maximum Spanning Tree with weighted Spearman correlation coefficient, Hill Climbing search, and Tabu Search during the construction of Bayesian networks. For fairness evaluation, all constructed models are built using 80% data as a training set and the remaining 20% as a testing set. The results show that Bayesian network approach can be applied in village development index status classification where the construction using maximum spanning tree with K-Means data discretization gain the best performance of 90.69% accuracy.

A human reliability analysis methodology based on an extended Phoenix method for severe accidents in nuclear power plants: Qualitative analysis framework

The mitigation of the Fukushima accident exposed the detrimental action of human errors once again. However, deficiencies in existing human reliability analysis (HRA) methods prevent the effective prediction and analysis of potential human errors during the mitigation of severe accidents following core damage. To address this problem, this study presents a qualitative analysis framework for emergency response personnel (ERP) reliability analysis under severe accident conditions. This framework is developed using the Phoenix HRA method in conjunction with analyzing the ERP response characteristics and human-related issues from previous accidents, literature surveys, drill observations and interviews, as well as an assessment of the applicability of existing HRA methods. The analysis framework includes the establishment of an ERP response tree and a human failure fault tree (FT), as well as the identification and compilation of ERP cognitive functions, human error modes (HEMs), performance-influencing factors (PIFs), and the construction of Bayesian belief networks, to provide methodological guidance for the prevention of human errors under severe accident conditions.

Equation Chapter 1 Section 1 Differentially Private High‐Dimensional Binary Data Publication via Adaptive Bayesian Network

When using differential privacy to publish high‐dimensional data, the huge dimensionality leads to greater noise. Especially for high‐dimensional binary data, it is easy to be covered by excessive noise. Most existing methods cannot address real high‐dimensional data problems appropriately because they suffer from high time complexity. Therefore, in response to the problems above, we propose the differential privacy adaptive Bayesian network algorithm PrivABN to publish high‐dimensional binary data. This algorithm uses a new greedy algorithm to accelerate the construction of Bayesian networks, which reduces the time complexity of the GreedyBayes algorithm from to O(nm4). In addition, it uses an adaptive algorithm to adjust the structure and uses a differential privacy Exponential mechanism to preserve the privacy, so as to generate a high‐quality protected Bayesian network. Moreover, we use the Bayesian network to calculate the conditional distribution with noise and generate a synthetic dataset for publication. This synthetic dataset satisfies ε‐differential privacy. Lastly, we carry out experiments against three real‐life high‐dimensional binary datasets to evaluate the functional performance.

Performance shaping factors dependence assessment through moderating and mediating effect analysis

Dependence assessment is an important task in human reliability analysis (HRA). The dependences in HRA include three categories, dependences between human failure events (HFEs) (CAT1), dependences between HEP and performance shaping factors (PSFs) (CAT2), and dependences between PSFs (CAT3). Among them, CAT3 dependences have not been well studied due to their complexity. According to their function mode, PSF dependences can be further distinguished as mediating effect and moderating effect. Taking the inter-dependences between PSFs for civil flight crew as examples, this paper proposes an empirical approach to assess dependences between PSFs. Firstly, 10 PSF categories including 59 lower level PSFs were identified for civil flight crew through literature review and focus groups screening. Then a 432-pilot-joined survey was carried out to collect pilots’ opinions on PSF influences on performance. After that, moderating and mediating effect analysis methods were used to identify the existence and type of PSF dependences. The results show that mediating effect is much more common than moderating effect between PSFs. The method proposed in this paper can provide a deeper insight to PSF dependences, and its results serve as important inputs to other HRA researches such as the construction of complex Bayesian networks for HRA.

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.

Inference From Randomized Transmissions by Many Backscatter Sensors

Attaining the vision of Smart Cities requires the deployment of an enormous number of sensors for monitoring various conditions of the environment. Backscatter-sensors have emerged to be a promising solution due to the uninterruptible energy supply and relative simple hardwares. On the other hand, backscatter-sensors with limited signal-processing capabilities are unable to support conventional algorithms for multiple-access and channel-training. Thus, the key challenge in designing backscatter-sensor networks is to enable readers to accurately detect sensing-values given simple ALOHA random access, primitive transmission schemes, and no knowledge of channel-states. We tackle this challenge by proposing the novel framework of backscatter sensing featuring random-encoding at sensors and statistical-inference at readers. Specifically, assuming the on/off keying for backscatter transmissions, the practical random-encoding scheme causes the on/off transmission of a sensor to follow a distribution parameterized by the sensing values. Facilitated by the scheme, statistical-inference algorithms are designed to enable a reader to infer sensing-values from randomized transmissions by multiple sensors. The specific design procedure involves the construction of Bayesian networks, namely deriving conditional distributions for relating unknown parameters and variables to signals observed by the reader. Then based on the Bayesian networks and the well-known expectation-maximization principle, inference algorithms are derived to recover sensing-values.

PrivBayes

Privacy-preserving data publishing is an important problem that has been the focus of extensive study. The state-of-the-art solution for this problem is differential privacy, which offers a strong degree of privacy protection without making restrictive assumptions about the adversary. Existing techniques using differential privacy, however, cannot effectively handle the publication of high-dimensional data. In particular, when the input dataset contains a large number of attributes, existing methods require injecting a prohibitive amount of noise compared to the signal in the data, which renders the published data next to useless. To address the deficiency of the existing methods, this paper presents P riv B ayes , a differentially private method for releasing high-dimensional data. Given a dataset D , P riv B ayes first constructs a Bayesian network N , which (i) provides a succinct model of the correlations among the attributes in D and (ii) allows us to approximate the distribution of data in D using a set P of low-dimensional marginals of D . After that, P riv B ayes injects noise into each marginal in P to ensure differential privacy and then uses the noisy marginals and the Bayesian network to construct an approximation of the data distribution in D . Finally, P riv B ayes samples tuples from the approximate distribution to construct a synthetic dataset, and then releases the synthetic data. Intuitively, P riv B ayes circumvents the curse of dimensionality, as it injects noise into the low-dimensional marginals in P instead of the high-dimensional dataset D . Private construction of Bayesian networks turns out to be significantly challenging, and we introduce a novel approach that uses a surrogate function for mutual information to build the model more accurately. We experimentally evaluate P riv B ayes on real data and demonstrate that it significantly outperforms existing solutions in terms of accuracy.

Prognostic and Diagnostic Capabilities of OOBN in Assessing Investment Risk of Complex Construction Projects

Modelling decision problems using Bayesian networks is extremely valuable especially in case of issues related to uncertainty; it is also very helpful in constructing and understanding visual representation of the elements and their relations. This approach facilitates subsequent application of Bayesian networks, however there can be situations where using simple Bayesian networks is impractical or even ineffective. The aim of this article is to present object-oriented Bayesian networks (OOBN) in the context of modeling investment risk. OOBN not only allow decomposition of a complex model into individual objects reflecting different groups of issues (for example risk areas) but also allow modeling time dependencies between those objects.The use of object-oriented Bayesian networks is presented using an example of urban regeneration project. On the basis of a complex construction project the author presents both advantages and disadvantages of OOBN in terms of diagnostic and prognostic efficiency.In course of the research it has been observed that during the construction of large Bayesian networks the possibility to automatically generate node probability tables is very useful, as it significantly accelerates construction of this type of models. The author also indicates additional recommendations in the field of defining object-oriented Bayesian networks instrumental in assessing investment risk of complex construction projects.

Verification of Economic and Agricultural Indicators With the Use of Statistical Methods on the Example of Individual Farms

Abstract The paper describes basic methodology assumptions related to construction of Bayesian networks. The paper aims at preparation of data for modeling to obtain fresh knowledge on economic and agricultural database and will constitute the first stage of research. Variables (economic and agricultural indicators) with discreet values were used for analysis with the use of two step grouping technique and previous non-typical data were explored. The research was carried out on the group of three hundred individual fanns from Malopolskie and Swiçtokrzyskie Voiovedship. The knowledge obtained from analyses will be used in practice in agricultural engineering in order to support agricultural activity.

Bayesian network construction using a fuzzy rule based approach for medical decision support

AbstractThis study proposes a novel method for the construction of efficient and convenient Bayesian networks (BNs) and influence diagrams regarding medical problems based on fuzzy rules. The general methodology that was developed is able to address decisions based on fuzzy medical rules that connect symptoms with the severity/rating scale of a disease. These fuzzy rules are rich enough to cover a large variety of medical decisions. The method overcomes the major disadvantage of Bayesian nets, that is, the need of a vast amount of subjective probabilities. Instead of filling conditional probability tables in BNs, physicians report their knowledge in the form of fuzzy rules. The knowledge of these rules after defuzzification is transformed according to certain equations into probabilities. This becomes possible, categorizing the rules into certain types. For each type of rule, a mathematical expression is determined, which sets correctly the conditional probabilities that relate a symptom with its child severity. A particular example of assessing pulmonary infections and making decisions on severity degree was explored, implementing a decision support system (DSS) to show the functionality of the proposed methodology. The developed front‐end DSS was evaluated and proved capable to drive fair decisions close to those obtained by physicians.

Bayesian Networks and the Value of the Evidence for the Forensic Two‐Trace Transfer Problem*

Forensic scientists face increasingly complex inference problems for evaluating likelihood ratios (LRs) for an appropriate pair of propositions. Up to now, scientists and statisticians have derived LR formulae using an algebraic approach. However, this approach reaches its limits when addressing cases with an increasing number of variables and dependence relationships between these variables. In this study, we suggest using a graphical approach, based on the construction of Bayesian networks (BNs). We first construct a BN that captures the problem, and then deduce the expression for calculating the LR from this model to compare it with existing LR formulae. We illustrate this idea by applying it to the evaluation of an activity level LR in the context of the two-trace transfer problem. Our approach allows us to relax assumptions made in previous LR developments, produce a new LR formula for the two-trace transfer problem and generalize this scenario to n traces.

Bayesian Methods for Multivariate Modeling of Pleiotropic SNP Associations and Genetic Risk Prediction

Genome-wide association studies (GWAS) have identified numerous associations between genetic loci and individual phenotypes; however, relatively few GWAS have attempted to detect pleiotropic associations, in which loci are simultaneously associated with multiple distinct phenotypes. We show that pleiotropic associations can be directly modeled via the construction of simple Bayesian networks, and that these models can be applied to produce single or ensembles of Bayesian classifiers that leverage pleiotropy to improve genetic risk prediction. The proposed method includes two phases: (1) Bayesian model comparison, to identify Single-Nucleotide Polymorphisms (SNPs) associated with one or more traits; and (2) cross-validation feature selection, in which a final set of SNPs is selected to optimize prediction. To demonstrate the capabilities and limitations of the method, a total of 1600 case-control GWAS datasets with two dichotomous phenotypes were simulated under 16 scenarios, varying the association strengths of causal SNPs, the size of the discovery sets, the balance between cases and controls, and the number of pleiotropic causal SNPs. Across the 16 scenarios, prediction accuracy varied from 90 to 50%. In the 14 scenarios that included pleiotropically associated SNPs, the pleiotropic model search and prediction methods consistently outperformed the naive model search and prediction. In the two scenarios in which there were no true pleiotropic SNPs, the differences between the pleiotropic and naive model searches were minimal. To further evaluate the method on real data, a discovery set of 1071 sickle cell disease (SCD) patients was used to search for pleiotropic associations between cerebral vascular accidents and fetal hemoglobin level. Classification was performed on a smaller validation set of 352 SCD patients, and showed that the inclusion of pleiotropic SNPs may slightly improve prediction, although the difference was not statistically significant. The proposed method is robust, computationally efficient, and provides a powerful new approach for detecting and modeling pleiotropic disease loci.

An ontology-based approach for constructing Bayesian networks

Bayesian networks are commonly used for determining the probability of events that are influenced by various variables. Bayesian probabilities encode degrees of belief about certain events, and a dynamic knowledge body is used to strengthen, update, or weaken these assumptions. The creation of Bayesian networks requires at least three challenging tasks: (i) the determination of relevant variables (nodes), (ii) the determination of relationships between the identified variables (links), and (iii) the calculation of the conditional probability tables (CPTs) for each node in the Bayesian network. Based on existing domain ontologies, we propose a method for the ontology-based construction of Bayesian networks. The method supports (i) the construction of the graphical Bayesian network structure (nodes and links), (ii) the construction of CPTs that preserve semantic constraints of the ontology, and (iii) the incorporation of already existing knowledge facts (findings). The developed method enables the efficient construction and modification of Bayesian networks based on existing ontologies.

Bayesian Feature Selection for Clustering Problems

Bayesian methods have been successfully used for feature selection in many supervised learning tasks. In this paper, the adaptation of such methods for unsupervised learning (clustering) is investigated. We adopt an algorithm that iterates between clustering (assuming that the number of clusters is unknown a priori) and feature selection. From this standpoint, two Bayesian approaches for feature selection are addressed: (i) Naïve Bayes Wrapper (NBW), and (ii) Markov Blanket Filter (MBF) obtained from the construction of Bayesian networks. Experiments in ten datasets illustrate the performance of each proposed method. Advantages of feature selection are demonstrated by comparing the results obtained from Bayesian feature selection with the results achieved without any kind of feature selection, i.e., using all the available features. In most of the performed experiments, NBW and MBF have allowed reducing the number of features, while providing good quality partitions in relation to those found by means of the full set of features. Also, NBW has outperformed its Bayesian feature selection counterpart (MBF) in most of the assessed datasets, mainly when the cardinality of the selected feature subset is taken into consideration.

Controlled generation of hard and easy Bayesian networks: Impact on maximal clique size in tree clustering

This article presents and analyzes algorithms that systematically generate random Bayesian networks of varying difficulty levels, with respect to inference using tree clustering. The results are relevant to research on efficient Bayesian network inference, such as computing a most probable explanation or belief updating, since they allow controlled experimentation to determine the impact of improvements to inference algorithms. The results are also relevant to research on machine learning of Bayesian networks, since they support controlled generation of a large number of data sets at a given difficulty level. Our generation algorithms, called BPART and MPART, support controlled but random construction of bipartite and multipartite Bayesian networks. The Bayesian network parameters that we vary are the total number of nodes, degree of connectivity, the ratio of the number of non-root nodes to the number of root nodes, regularity of the underlying graph, and characteristics of the conditional probability tables. The main dependent parameter is the size of the maximal clique as generated by tree clustering. This article presents extensive empirical analysis using the Hugin tree clustering approach as well as theoretical analysis related to the random generation of Bayesian networks using BPART and MPART.