Bayesian Network Theory Research Articles

Inference on the eigenvalues of the normalized precision matrix

Recent developments in the spectral theory of Bayesian Networks has led to a need for a developed theory of estimation and inference on the eigenvalues of the normalized precision matrix, Ω. In this paper, working under conditions where n→∞ and p remains fixed, we provide multivariate normal asymptotic distributions of the sample eigenvalues of Ω under general conditions and under normal populations, a formula for second-order bias correction of these sample eigenvalues, and a Stein-type shrinkage estimator of the eigenvalues. Numerical simulations are performed which demonstrate under what generative conditions each estimation technique is most effective. When the largest eigenvalue of Ω is small the simulations show that the second order bias-corrected eigenvalue was considerably less biased than the sample eigenvalue, whereas the smallest eigenvalue was estimated with less bias using either the sample eigenvalue or the proposed shrinkage method.

Enhancing the synergy governance capability of urban communities based on Bayesian network: A case of Jinan city

The rapid pace of urbanization has brought about a plethora of challenges for urban communities, prompting the advocacy of collaborative governance as a means to tackle management issues effectively. However, fostering strong collaboration among multiple governance entities remains a significant hurdle in urban communities governance. This study addresses this challenge by exploring the complex structure of urban communities' collaborative governance systems, with a focus on enhancing collaborative governance capability. Drawing on Bayesian network (BN) theory and utilizing the case of Jinan, this article investigates the intrinsic mechanisms of achieving collaboration in urban communities. This study establishes a Bayesian network model for collaborative governance of urban communities, providing a visual representation of the intricate interactions among multiple governance entities. We employ a data-knowledge-driven approach for BN structure learning. This approach tackles issues such as the lack of cyclic dependency capability and the impact of small datasets on model accuracy. Furthermore, we analyze the collaborative mechanism through Bayesian reasoning. The findings underscore the pivotal entities and five key factors that significantly influence collaborative governance capability. Lastly, policy implications are drawn to enhance the collaborative governance capability of urban communities.

Bayesian Network Inference for Low-Magnitude Nonnatural Seismic Event Discrimination

Abstract In response to the gaps in understanding the causal relationship between seismic waveform features and the types of seismic events, this research is focused on seismic events of low magnitude (ML≤3.0) in the North China region. Using the Bayesian network theory, we conduct an analysis to infer event types for natural earthquakes, artificial explosions, and mining collapses, and the outcomes achieved notable efficacy for the discrimination of seismic events. Through the analysis of seismic waveforms from 1818 events, we systematically extracted and quantified 55 features in temporal, spectral, and energy domains, which were then recoded as node variables for subsequent analysis. The new data set was subject to select nodes with strong associations to the node type. Subsequently, Bayesian network topologies were constructed using three different algorithms to reconstruct the custom network, calculating posterior probabilities and marginal probabilities. Simultaneously, an extensive evaluation with precision–recall curves of the network structure was carried out, encompassing accuracy, precision, recall, and F1-score. Ultimately, sensitivity analysis was performed on each node to reveal the extent of the influence of node variations on the inference of the node type. The findings showed that the sensitivity of discrimination of seismic events was notably high for several features, including high-frequency P/S spectral ratio values (11 to ∼20 Hz), central frequency, dominant frequency, average frequency, rise and decay average frequency, the real part of the complex cepstral coefficients, peak ground acceleration, and zero crossing. In the classification of natural earthquakes, artificial explosions, and mining collapses, it was observed that the probability of mining collapses was maximized when peak ground acceleration was less than 1526.08, and concurrently, the P/S spectral ratio (11 to ∼20 Hz) fell within the range of −0.25 to −0.02.

Research on entertainment robots based on artificial intelligence interaction for human posture recognition and sports activity monitoring

With the application of artificial intelligence technology in sports activity monitoring, new technologies such as interactive robots and the Internet of Things are being more widely used, which can provide entertainment and interactive guidance for sports training. This article analyzes the research on human pose recognition and sports activity monitoring of entertainment robots based on artificial intelligence interaction. This paper designs and develops an entertainment robot system that can recognize human posture and monitor physical activities. Users can interact with the robot and get real-time feedback about their posture and activities, thereby improving motor skills and physical fitness. After in-depth analysis of the theory of dynamic Bayesian network, we used EM algorithm to build a dynamic Bayesian network model, carried out detailed research on the random variables represented by the nodes of the dynamic model, and used the Internet of Things human posture recognition technology to extract the features of human behavior according to the characteristics of human behavior. The results show that the attitude recognition accuracy can be improved by adding the dynamic Bayesian network based on the random forest algorithm. The entertainment robot can accurately identify human posture and monitor sports activities, and has good real-time and stability. Through interaction with the robot, users can get personalized suggestions for individual postures and activities, improving the training effect and enjoyment of physical activities. Therefore, through the in-depth research and analysis of the dynamic Bayesian network and the human posture recognition of the Internet of Things, it is found that the sports activity monitoring system proposed in this paper can comprehensively monitor students’ sports activities, so as to achieve the goal of comprehensively improving students’ physical fitness.

Quality Risk Assessment of Prefabricated Steel Structural Components during Production Using Fuzzy Bayesian Networks

This study aims to address quality issues in the production of prefabricated steel structural components for buildings by investigating challenges in quality risk assessment. It identifies key factors contributing to quality problems and establishes an evaluation index system. Traditional methods encounter limitations in handling uncertainty and conducting quantitative analysis. Therefore, the fuzzy Bayesian network (FBN) theory is utilized to perform a probabilistic analysis of quality risks during the production phase. This research achieves a more accurate and dynamic risk assessment by integrating the strengths of fuzzy logic and Bayesian networks (BNs) and by utilizing expert knowledge, the similarity aggregation method (SAM), and the noisy-OR gate model. The study reveals that factors such as the “low professional level of designers”, “poor production refinement”, and “poor storage conditions for finished products” have a significant impact on quality risks. This study offers a scientific risk assessment tool designed to address the quality control challenges commonly experienced in the manufacturing of steel structural components. Identifying the critical risk factors that influence quality empowers actual production enterprises to develop risk management strategies and improvement measures in a more focused manner, thereby facilitating more effective resource allocation and risk prevention and control. Consequently, this approach has a significant impact on enhancing the overall production level and quality within the industry.

Extensions of results on phylogeny graphs of degree bounded digraphs

An acyclic digraph in which every vertex has indegree at most i and outdegree at most j is called an (i,j) digraph for some positive integers i and j. The phylogeny graph of a digraph D has V(D) as the vertex set and an edge uv if and only if one of the following is true: (u,v)∈A(D); (v,u)∈A(D); (u,w)∈A(D) and (v,w)∈A(D) for some w∈V(D). A graph G is a phylogeny graph (resp. an (i,j) phylogeny graph) if there is an acyclic digraph D (resp. an (i,j) digraph D) such that the phylogeny graph of D is isomorphic to G. Lee et al. (2017) and Eoh and Kim (2021) studied the (2,2) phylogeny graphs, (1,j) phylogeny graphs, (i,1) phylogeny graphs, and (2,j) phylogeny graphs. Their work was motivated by problems related to evidence propagation in a Bayesian network for which it is useful to know which acyclic digraphs have chordal moral graphs (phylogeny graphs are called moral graphs in Bayesian network theory). In this paper, we extend their work by giving necessary conditions of chordal (i,2) phylogeny graphs. We go further to give necessary conditions of (i,j) phylogeny graphs by listing forbidden induced subgraphs.

Application of the Bayesian network theory in clinical trial data: Severity shift in spasticity numeric rating scale in patients with multiple sclerosis

BackgroundData digitization expands data collection opportunities, representing both a chance to understand interrelationships between variables and a challenge to identify the most appropriate clinical factors. Applications of causal inference techniques to clinical trial data is becoming very attractive, especially with the intent to provide insights into the relationships between baseline characteristics and outcomes. Graphical representations of model structures and conditional probabilities can be powerful tools to illustrate relationships in a high-dimensional data setting. MethodsWe review and apply Bayesian network theory to a clinical case study, presenting an analytical approach to investigating and visualizing causal relationships. We propose the use of the adherence score to compare data networks’ patterns based on different variables’ discretization. Data from adult patients with spasticity related to multiple sclerosis (MSS) from two randomized placebo-controlled clinical trials of nabiximols were used as analysis sets. The training and validation sets included 106 (53 treated, 53 placebo) and 155 (76 treated, 79 placebo) participants, respectively. The primary objective was to create a network and estimate the causal dependencies between participants’ characteristics, changes in MSS severity as reflected by shifts in the patient-reported numeric rating scale (NRS), and changes in symptoms, functional abilities, and quality of life factors. ResultsA causal network was identified between the key factors of assigned treatment, end of study spasticity NRS, and mental health/vitality subscales of the 36-Item Short Form Health Survey questionnaire (4 nodes and 3 edges; adherence score = 93%). In patients with mild spasticity, the impact of nabiximols on mental health or vitality subscales resulted in a probability ratio of 1.63. The decomposed mediation effect of spasticity NRS was observed through a mediation analysis between treatment and mental health (99.4%) or vitality (93.7%) subscales. ConclusionsThe use of innovative methods such as causal networks is highly encouraged to identify dependent relationships among key factors in clinical trial data and drive insights for additional research.

Linear constraints on variables in influence diagrams for causal models

The paper considers some ways of representing probabilistic causal models using Bayesian network theory (hereafter referred to as BN). These models describe well problems with different types of uncertainty. The theory of BN extended with some additional types of nodes called influence diagrams or IDs. Influence diagrams make it possible to consider a number of solution options, to evaluate them quantitatively, and to select the best of the considered options. However, it is practically impossible to find an optimal solution in an ID. It is not even possible to create a system of linear constraints on some variables in an ID, although there is a large class of practical problems with such constraints. The paper describes the idea of extending ID to describe linear constraints on some variables of the BN. In the future, it will help to use the ideas of linear programming in ID to find an optimal solution in the sense of LP for problems with different types of uncertainties and causal relationships between some variables. This work has been done under grant AP19679142 "Search for optimal solutions in Bayesian networks in models with linear constraints and linear functionals. Development of algorithms and programs " (2023-2025) of MES RK. This project will develop the theory for finding optimal solutions in Bayesian networks. Optimality will be understood in the sense of linear programming - a system of linear constraints, extremum of a linear functional. The theory will be implemented in a software product.

Multi-status Bayesian network for analyzing collapse risk of excavation construction

In response to the need for effective collapse risk analysis in engineering projects, a decision support approach is presented. It is rooted in multi-status Bayesian network (MSBN) and fuzzy set theory, encompassing MSBN construction, risk analysis, and management. This research addresses the causative correlation between influential factors and excavation collapse, considering the inherent uncertainty and fuzziness of the project. To enhance the reliability of evaluation results, an expert confidence index, integrating judgment ability, subjective reliability, and risk preference, is introduced. The approach is applied to an excavation case study, demonstrating its viability and capacity. Furthermore, it offers actionable insights for decision-makers to proactively mitigate accident probabilities. Notably, sensitivity analysis identifies critical risk factors. This research contributes to the field of engineering project risk assessment and management. It serves as a foundation for future research and development, guiding the way for improved strategies and decision support systems.

Assessment of Financial Systemic Crisis on a Causal and Reliable Perspective

In financial network models, to assess systemic risk, a general understanding and prediction of precisely how a single financial institution is associated with systemic risk from the network perspective remains lacking. This paper proposes a framework for predicting and assessing system crises through inferring the cause–effect relationships between financial institutions and system state, which is structured in three steps: the assessment stage for system state based on the mean-variance framework, the prediction stage based on a Bayesian network and the reliability stage based on the Markov process. By applying them to monthly returns of financial institutions, it implies the need to pay attention to insurance and Broker sectors while regulating the banking system on the Bayesian network theory. Moreover, we find that the measure contains predictive power both during tranquil periods and during financial crisis periods. The results can be applied to derive interventions in financial crisis management with regard to systemic risk prediction and system state reliability.

Characteristics and propagation of meteorological and hydrological droughts in eastern Gansu, a typical semi‐arid region, China

AbstractThe meteorological drought (MD) is the precursor of the hydrological drought (HD), and understanding the propagation process from MD to HD is of great significance for the early warning of HD. Based on the theory of run and Bayesian networks, this study uses the standardized precipitation index (SPI), standardized precipitation evapotranspiration index (SPEI) and standardized streamflow index (SSI) to explore the characteristics and propagation of MD and HD in the regions of eastern Gansu, China. The results indicate that: (1) The region was mainly wet (dry) and the wetness (dryness) was stronger before (after) 2000 when reflected by SSI. The frequency is higher based on SPI and SPEI than that based on SSI, while the duration and magnitude are lower than those based on SSI. (2) The propagation time from MD to HD is generally within 1–10 months. After the occurrence of a certain level of MD, it is most likely to propagate to HD events that are relatively weaker than the MD. Besides, the higher the intensity level of MD, the shorter the propagation time to HD, and the shorter for cumulative occurrence probability of HD to approach 1.0. (3) The increase in temperature and decrease in precipitation, runoff and runoff coefficient may contribute to the dryness after 2000. Moreover, the weakened propagation from MD to HD may be due to the rapid increase of water resource consumption caused by intensive anthropogenic activities in the study area. From the above results, this study found some propagation characteristics from MD to HD in a semi‐arid and semi‐humid watershed, which can provide a supplement for revealing the drought mechanism and can assist in the management and planning of water resources in China.

Spectral Bayesian network theory

A Bayesian Network (BN) is a probabilistic model that represents a set of variables using a directed acyclic graph (DAG). Current algorithms for learning BN structures from data focus on estimating the edges of a specific DAG, and often lead to many ‘likely’ network structures. In this paper, we lay the groundwork for an approach that focuses on learning global properties of the DAG rather than exact edges. This is done by defining the structural hypergraph of a BN, which is shown to be related to the inverse-covariance matrix of the network. Spectral bounds are derived for the normalized inverse-covariance matrix, which are shown to be closely related to the maximum indegree of the associated BN.

Big Data-based Human Resource Performance Evaluation Model Using Bayesian Network of Deep Learning

ABSTRACT Human resource management was of great significance for enterprises to formulate development strategies and improve competitiveness. With the rapid development of new technologies such as knowledge economy and big data, the traditional human resource performance appraisal model had certain limitations and was not objective, which had been difficult to adapt to the increasingly highly integrated development needs of modern enterprises. Therefore, this paper used big data analysis and new technical means to put forward the study of human resource performance evaluation model based on Bayesian network, aiming to provide some theoretical reference for modern enterprise human resource management. First of all, it summarized the related concepts of performance appraisal and its important position in enterprise management, analyzed the characteristics of human resources performance appraisal indicators and their mutual relations, and expounded the common methods and characteristics needed to build a performance appraisal system. Secondly, it summarized the relevant theory of Bayesian network and its advantages in solving complex random problems, and proposed a performance appraisal model based on Bayesian network for the needs of enterprise human resources management. Finally, the balanced scorecard method was used to build a performance appraisal system, and the performance appraisal model proposed in this paper was tested by experiments, and compared with the traditional method. The results showed that the performance appraisal model proposed in this paper had significant advantages and could be better applied to the performance appraisal management of enterprise human resources. The research of this paper can not only provide theoretical guidance for further research on enterprise human resource allocation and management, but also provide reference for performance appraisal in other fields.

Coupling Bayesian Network and copula theory for water shortage assessment: A case study in source area of the South-to-North Water Division Project (SNWDP)

Updating the appropriate risk measures is vital for management practice in reservoir operation and offers new insights for decision-making. Water diversion may cause water shortage crises both in the source area and in the downstream flow. By focusing on the effect of water demand in the source area and reservoir operation, this study proposed a risk assessment framework with the Bayesian network and copula-based estimation of the parameters. The risk assessment framework comprised four parts: dependencies estimation, specifically established copula, a Bayesian network based on the copula-based estimation of the parameters, and scenario analysis. This framework was applied to the Danjiangkou Reservoir, part of the source area for the Middle Route Project of the South-to-North Water Division Project in China. The study results showed that the framework provided valuable decision-making information. The Clayton and Gumbel functions evidenced superior capabilities for simulating the dependence of hydrological variables using the copula family. Since it revealed the potential correlation of variables, the Bayesian network based on the copula-based estimation of the parameters was more robust and accurate compared with the classic Bayesian network. According to the results yielded in different scenarios, occurrences presenting the highest degree of disadvantage for the Danjiangkou Reservoir will be increased from 8.66% to 23.08% for upstream situations and 59.03% for downstream low-water situations. These results indicate the disadvantages and potential strategies for the successful operation of the reservoir, which will be helpful to both researchers and managers.

Inference of Factors for Labor Productivity Growth Used Randomized Experiment and Statistical Causality

The study of causal dependencies in economics is fraught with great difficulties, that it is required to consider not only the object structure, but also take into account a huge number of factors acting on the object, about which nothing is either known or difficult to measure. In this paper, we attempt to overcome this problem and apply the theory of statistical causality for labor productivity management. We suggest new technology that provides the inference of causal relations between the special programs implemented in the company’s and employee’s labor productivity. The novelty of the proposed technology is that it is based on a hybrid object model, combines two models: 1—the structural object model about its functioning and development to provide a causal inference and prediction the effect of explicit factors; 2—the model based on observed data to clarify causality and to test it empirically. The technology provides integration of the theory of causal Bayesian networks, methods of randomized controlled experiments and statistical methods, allows under nonlinearity, dynamism, stochasticity and non-stationarity of the initial data, to evaluate the effect of programs on the labor effeciency. The difference between the proposed technology and others is that it ensures determination the synergistic effect of the action of the cause (program) on the effect—labor productivity in condition of hidden factors. The practical significance of the research is the results of its testing the proposed theoretical provisions, methods and technologies on actual data about food service company. The results obtained could contribute to the labor productivity growth over uncertainty of the external and internal factors and provide the companies sustainable development and its profitability growth.

Применение третичной структуры алгебраической байесовской сети в задаче апостериорного вывода

In the theory of algebraic Bayesian networks, there are algorithms that allow to conduct a global posterior inference using secondary structures. At the same time, building secondary structures implies the use of tertiary structure. Consequently, the question about the separate application of the tertiary structure in the problem of a posterior inference arises. This issue has been considered earlier, but only a general description of the algorithm has been given, and only models with scalar estimates of the probability of truth have been taken into account. In this paper, we present an algorithm that extends the aforementioned algorithm to the possibility of using it in the case of interval estimates. In addition, an important property of an algebraic Bayesian network is acyclicality, and the correctness of the above-mentioned algorithms is ensured only for acyclic networks. Therefore, it is also necessary to be able to check the acyclicity of an algebraic Bayesian network using a tertiary structure. The description of this algorithm is also presented in this paper, it is based on the previously proved theorem that relates the number of knowledge pattern models in the network to the number of non-empty separators and the number of strong restriction connectivity components in acyclic algebraic Bayesian network, as well as the theorem proved in this paper that two knowledge pattern models belong to the same strong restriction connectivity component. For all the developed algorithms, the correctness of their performance is proved, and their time complexity estimation is calculated.

Despecialization: a systematic approach to (re-)engineer systems ensuring a better resilience to obsolescence and shortages

Obsolescence and shortages have a strong impact on all value chains today. They can be found in all areas. They have an impact on both consumers and manufacturers. They can affect all components, products, systems, etc. Facing these two phenomena, ABMI, a multi-specialty engineering company, proposes despecialization as a solution. It allows components to be remanufactured and upgraded without the original supplier's specifications in case of obsolescence or shortage. This despecialization generally makes the system more resilient and robust. However, when despecialization is carried out to address obsolescence and shortages, different sets of consequences may arise. The improvements made to one component may, for example, degrade the performance of certain functions, or they may change the behavior of other components, or even change the properties of the system, i.e. reliability, maintainability, and availability. All these changes are the result of the propagation of the consequences of obsolescence and shortages. It is therefore essential to study the dependencies, especially between components, in any despecialization action to ensure the proper functioning of the system and its sustainability over time. In this paper, certain dependencies are studied in a case study of a mechanical system. We use Bayesian network theory to explore the modeled dependencies. The objective is to show the propagation of the effects of architectural changes on the resilience of the redesigned or despecialized product. The paper concluded with conclusions and perspectives on future research undertaken.

Risk Assessment of Insider Threats Based on IHFACS-BN

Insider threats, as one of the pressing challenges that threaten an organization’s information assets, usually result in considerable losses to the business. It is necessary to explore the key human factors that enterprise information security management should focus on preventing to reduce the probability of insider threats effectively. This paper first puts forward the improved Human Factors Analysis and Classification System (IHFACS) based on actual enterprise management. Then, the enterprise internal threat risk assessment model is constructed using the Bayesian network, expert evaluation, and fuzzy set theory. Forty-three classic insider threat cases from China, the United States, and Israel during 2009–2021 are selected as samples. Then, reasoning and sensitivity analysis recognizes the top 10 most critical human factors of the accident and the most likely causal chain of unsafe acts. The result shows that the most unsafe behavior was not assessing employees’ familiarity with the company’s internal security policies. In addition, improving the organizational impact of information security can effectively reduce internal threats and promote the sustainable development of enterprises.

Deduction of sudden rainstorm scenarios: integrating decision makers' emotions, dynamic Bayesian network and DS evidence theory

Event scenarios serve as the basis for emergency decision making after sudden disasters, and the accuracy of scenario deduction directly determines the effectiveness of emergency management implementation. On July 20, 2021, an exceptionally heavy rainstorm disaster occurred in Zhengzhou, Henan Province, China, causing serious urban waterlogging, river floods, flash floods and landslides and resulting in major casualties and property losses:14.79 million people affected, 398 people killed or missing (380 people in Zhengzhou) and a direct economic loss of 120.06 billion RMB. In order to investigate the complex evolution process of this disaster, a dynamic Bayesian network, evidence theory and emotion update mechanism are integrated to develop an efficient and effective scenario deduction model, with an emphasis on combining subjective and objective factors. In this model, more attention is given to subjective factors such as decision makers' emotions. The elements of scenario deduction are classified into the situation status, meteorological factor, emergency activities, decision makers' emotions and emergency goals, the coupling relationship between the elements are comprehensively analyzed, and the influence of these elements on the evolution mechanism of the rainstorm disaster is investigated, so as to facilitate targeted emergency management measures for the rescue operations. The empirical results show that the proposed dynamic Bayesian network can effectively simulate the dynamic change process of scenario deduction, the improved Dempster–Shafer evidence theory can reduce the subjectivity of the model in dealing with the uncertainty of the evolution process, and the emotion update mechanism can adequately quantify and decrease the influence caused by the emotional changes of decision makers. The model may better replicate actual events, and it may apply to the scenario deduction of other disasters, making an impact on the study of sudden catastrophes.

Assessment of underwater navigation safety based on dynamic Bayesian network facing uncertain knowledge and various information

As ocean environment is complicated and varied, underwater vehicles (UVs) are facing great challenges in safe and precise navigation. Therefore, it is important to evaluate the underwater ocean environment safety for the UV navigation. To deal with the uncertain knowledge and various information in the safety assessment, we present an evaluation model based on the dynamic Bayesian network (DBN) theory. Firstly, characteristic indicators are extract from marine environment systems and discretized with Cloud model. Then, the DBN is constructed through structure learning and parameter learning based on Dempster-Shafer (DS) evidence theory. Finally, the dynamic evaluation and risk zoning of the navigation safety is realized based on Bayesian probabilistic reasoning. The DBN-based assessment model fully considers the uncertainty of influence relationships between marine environment and UV navigation, and effectively fuses expert knowledge and quantitative data for assessment modeling. The experimental results show the proposed model has high reliability and good value of application.