Special Issue "Bayesian Networks: Inference Algorithms, Applications, and Software Tools"

A special issue of Algorithms (ISSN 1999-4893).

Deadline for manuscript submissions: closed (30 July 2020).

Special Issue Editor

Dr. Daniele Codetta Raiteri
E-Mail Website
Guest Editor
Computer Science Institute, DiSIT, University of Piemonte Orientale, Alessandria, Italy
Interests: probabilistic graphical models; reliability; risk analysis; security
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

In the field of Artificial Intelligence, Bayesian Networks (BN) are a well-known framework for reasoning under uncertain knowledge. BN have been applied in a wide range of real-world domains, such as medical diagnosis, forensic analysis, dependability assessment, risk management, etc. With respect to other types of models, BN provide relevant advantages: at the modelling level, the compact representation of the joint distribution of the system variables leads to the factorization of the set of possible states, avoiding the generation of the complete state space of the system; at the analysis level, inference algorithms can compute the probability distribution of any variable, possibly conditioned on the observation of the value (state) of other variables, so that predictive and diagnostic measures can be easily evaluated. During the years, BN have been extended in order to increase their modelling and analysis power; for instance, Dynamic Bayesian Networks and Continuous-Time Bayesian Networks take time into account, Hybrid Bayesian Networks deal with both discrete and continuous variables, Decision Networks contain decision nodes and value nodes.

The aim of this Special Issue is to collect recent developments about inference algorithms, their applications to real-case studies, and their implementation in software tools. The topics include, but are not limited to, the following:

  • BN extensions
  • Inference algorithms for BN extensions
  • Automatic generation of BN from higher-level models
  • Software tools or libraries
  • Applications to real-case studies

Dr. Daniele Codetta Raiteri
Guest Editor

Manuscript Submission Information

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Keywords

  • BN extensions
  • Inference algorithms for BN extensions
  • Automatic generation of BN from higher-level models
  • Software tools or libraries
  • Applications to real-case studies.

Published Papers (6 papers)

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Research

Open AccessArticle
A Bayesian Nonparametric Learning Approach to Ensemble Models Using the Proper Bayesian Bootstrap
Algorithms 2021, 14(1), 11; https://0-doi-org.brum.beds.ac.uk/10.3390/a14010011 - 03 Jan 2021
Viewed by 760
Abstract
Bootstrap resampling techniques, introduced by Efron and Rubin, can be presented in a general Bayesian framework, approximating the statistical distribution of a statistical functional ϕ(F), where F is a random distribution function. Efron’s and Rubin’s bootstrap procedures can be extended, introducing an informative prior through the Proper Bayesian bootstrap. In this paper different bootstrap techniques are used and compared in predictive classification and regression models based on ensemble approaches, i.e., bagging models involving decision trees. Proper Bayesian bootstrap, proposed by Muliere and Secchi, is used to sample the posterior distribution over trees, introducing prior distributions on the covariates and the target variable. The results obtained are compared with respect to other competitive procedures employing different bootstrap techniques. The empirical analysis reports the results obtained on simulated and real data. Full article
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Open AccessArticle
Hard and Soft EM in Bayesian Network Learning from Incomplete Data
Algorithms 2020, 13(12), 329; https://0-doi-org.brum.beds.ac.uk/10.3390/a13120329 - 09 Dec 2020
Viewed by 729
Abstract
Incomplete data are a common feature in many domains, from clinical trials to industrial applications. Bayesian networks (BNs) are often used in these domains because of their graphical and causal interpretations. BN parameter learning from incomplete data is usually implemented with the Expectation-Maximisation [...] Read more.
Incomplete data are a common feature in many domains, from clinical trials to industrial applications. Bayesian networks (BNs) are often used in these domains because of their graphical and causal interpretations. BN parameter learning from incomplete data is usually implemented with the Expectation-Maximisation algorithm (EM), which computes the relevant sufficient statistics (“soft EM”) using belief propagation. Similarly, the Structural Expectation-Maximisation algorithm (Structural EM) learns the network structure of the BN from those sufficient statistics using algorithms designed for complete data. However, practical implementations of parameter and structure learning often impute missing data (“hard EM”) to compute sufficient statistics instead of using belief propagation, for both ease of implementation and computational speed. In this paper, we investigate the question: what is the impact of using imputation instead of belief propagation on the quality of the resulting BNs? From a simulation study using synthetic data and reference BNs, we find that it is possible to recommend one approach over the other in several scenarios based on the characteristics of the data. We then use this information to build a simple decision tree to guide practitioners in choosing the EM algorithm best suited to their problem. Full article
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Open AccessArticle
Application of Bayesian Hierarchical Negative Binomial Finite Mixture Model for Cost-Benefit Analysis of Barriers Optimization, Accounting for Severe Heterogeneity
Algorithms 2020, 13(11), 288; https://0-doi-org.brum.beds.ac.uk/10.3390/a13110288 - 10 Nov 2020
Viewed by 550
Abstract
The Wyoming Department of Transportation (WYDOT) initiated a project to optimize the heights of barriers that are not satisfying the barrier design criteria, while prioritizing them based on an ability to achieve higher monetary benefits. The equivalent property damage only (EPDO) was used [...] Read more.
The Wyoming Department of Transportation (WYDOT) initiated a project to optimize the heights of barriers that are not satisfying the barrier design criteria, while prioritizing them based on an ability to achieve higher monetary benefits. The equivalent property damage only (EPDO) was used in this study to account for both aspects of crash frequency and severity. Data of this type are known to have overdispersion, that is having a variance greater than the mean. Thus, a negative binomial model was implemented to address the over-dispersion issue of the dataset. Another challenge of the dataset used in this study was the heterogeneity of the dataset. The data heterogeneity resulted from various factors such as data being aggregated across two highway systems, and the presence of two barrier types in the whole state. Thus, it is not practical to assign a subjective hierarchy such as a highway system or barrier types to address the issue of severe heterogeneity in the dataset. Under these conditions, a finite mixture model (FMM) was implemented to find a best distribution parameter to characterize the observations. With this technique, after the optimum number of mixtures was identified, those clusters were assigned to various observations. However, previous studies mostly employed just the finite mixture model (FMM), with various distributions, to account for unobserved heterogeneity. The problem with the FMM approach is that it results in a loss of information: for instance, it would come up with N number of equations, where each result would use only part of the whole dataset. On the other hand, some studies used a subjective hierarchy to account for the heterogeneity in the dataset, such as the effect of seasonality or highway system; however, those subjective hierarchies might not account for the optimum heterogeneity in the dataset. Thus, we implement a new methodology, the Bayesian Hierarchical Finite Mixture (BHFMM) to employ the FMM without losing information, while also accounting for the heterogeneity in the dataset, by considering objective and unbiased hierarchies. As the Bayesian technique has the shortcoming of labeling the observations due to label switching; the FMM parameters were estimated by maximum likelihood technique. Results of the identified model were converted to an equation for implementation of machine learning techniques. The heights were optimized to an optimal value and the EPDO was predicted based on the changes. The results of the cost–benefit analysis indicated that after spending about 4 million dollars, the WYDOT would not only recover the expenses, but could also expect to save more than $4 million additional dollars through traffic barrier crash reduction. Full article
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Open AccessArticle
Two-Component Bayesian Hierarchical Models for Cost-Benefit Analysis of Traffic Barrier Crash Count
Algorithms 2020, 13(8), 179; https://0-doi-org.brum.beds.ac.uk/10.3390/a13080179 - 23 Jul 2020
Cited by 1 | Viewed by 1252
Abstract
Road departure crashes tend to be hazardous, especially in rural areas like Wyoming. Traffic barriers could be installed to mitigate the severity of those crashes. However, the severity of traffic barriers crashes still persists. Besides various drivers and environmental characteristics, the roadways and [...] Read more.
Road departure crashes tend to be hazardous, especially in rural areas like Wyoming. Traffic barriers could be installed to mitigate the severity of those crashes. However, the severity of traffic barriers crashes still persists. Besides various drivers and environmental characteristics, the roadways and barrier geometric characteristics play a critical role in the severity of barrier crashes. The Wyoming department of transportation (WYDOT) has initiated a project to identify and optimize the heights of those barriers that are below the design standard, while prioritizing them based on the monetary benefit. This is to optimize first barriers that need an immediate attention, considering the limited budget, and then all other barriers being under design. In order to account for both aspects of frequency and severity of crashes, equivalent property damage only (EPDO) was considered. The data of this type besides having an over-dispersion, exhibits excess amounts of zeroes. Thus, a two-component model was employed to provide a flexible way of addressing this problem. Beside this technique, one-component hierarchical modeling approach was considered for a comparison purpose. This paper presents an empirical cost-benefit analysis based on Bayesian hierarchical machine learning techniques. After identifying the best model in terms of the performance, deviance information criterion (DIC), the results were converted into an equation, and the equation was used for a purpose of machine learning technique. An automated method generated cost based on barriers’ current conditions, and then based on optimized barrier heights. The empirical analysis showed that cost-sensitive modeling and machine learning technique deployment could be used as an effective way for cost-benefit analysis. That could be achieved through measuring the associated costs of barriers’ enhancements, added benefits over years and consequently, barrier prioritization due to lack of available budget. A comprehensive discussion across the two-component models, zero-inflated and hurdle, is included in the manuscript. Full article
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Open AccessArticle
Embedded Bayesian Network Contribution for a Safe Mission Planning of Autonomous Vehicles
Algorithms 2020, 13(7), 155; https://0-doi-org.brum.beds.ac.uk/10.3390/a13070155 - 28 Jun 2020
Cited by 3 | Viewed by 1398
Abstract
Bayesian Networks (BN) are probabilistic models that are commonly used for the diagnosis in numerous domains (medicine, finance, transport, robotics, …). In the case of autonomous vehicles, they can contribute to elaborate intelligent monitors that can take the environmental context into account. We [...] Read more.
Bayesian Networks (BN) are probabilistic models that are commonly used for the diagnosis in numerous domains (medicine, finance, transport, robotics, …). In the case of autonomous vehicles, they can contribute to elaborate intelligent monitors that can take the environmental context into account. We show in this paper some main abilities of BN that can help in the elaboration of fault detection isolation and recovery (FDIR) modules. One of the main difficulty with the BN model is generally to elaborate these ones according to the case of study. Then, we propose some automatic generation techniques from failure mode and effects analysis (FMEA)-like tables using the pattern design approach. Once defined, these modules have to operate online for autonomous vehicles. In a second part, we propose a design methodology to embed the real-time and non-intrusive implementations of the BN modules using FPGA-SoC support. We show that the FPGA implementation can offer an interesting speed-up with very limited energy cost. Lastly, we show how these BN modules can be incorporated into the decision-making model for the mission planning of unmanned aerial vehicles (UAVs). We illustrate the integration by means of two models: the Decision Network model that is a straightforward extension of the BN model, and the BFM model that is an extension of the Markov Decision Process (MDP) decision-making model incorporating a BN. We illustrate the different proposals with realistic examples and show that the hybrid implementation on FPGA-SoC can offer some benefits. Full article
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Open AccessArticle
A Dynamic Bayesian Network Structure for Joint Diagnostics and Prognostics of Complex Engineering Systems
Algorithms 2020, 13(3), 64; https://0-doi-org.brum.beds.ac.uk/10.3390/a13030064 - 12 Mar 2020
Cited by 2 | Viewed by 2028
Abstract
Dynamic Bayesian networks (DBNs) represent complex time-dependent causal relationships through the use of conditional probabilities and directed acyclic graph models. DBNs enable the forward and backward inference of system states, diagnosing current system health, and forecasting future system prognosis within the same modeling [...] Read more.
Dynamic Bayesian networks (DBNs) represent complex time-dependent causal relationships through the use of conditional probabilities and directed acyclic graph models. DBNs enable the forward and backward inference of system states, diagnosing current system health, and forecasting future system prognosis within the same modeling framework. As a result, there has been growing interest in using DBNs for reliability engineering problems and applications in risk assessment. However, there are open questions about how they can be used to support diagnostics and prognostic health monitoring of a complex engineering system (CES), e.g., power plants, processing facilities and maritime vessels. These systems’ tightly integrated human, hardware, and software components and dynamic operational environments have previously been difficult to model. As part of the growing literature advancing the understanding of how DBNs can be used to improve the risk assessments and health monitoring of CESs, this paper shows the prognostic and diagnostic inference capabilities that are possible to encapsulate within a single DBN model. Using simulated accident sequence data from a model sodium fast nuclear reactor as a case study, a DBN is designed, quantified, and verified based on evidence associated with a transient overpower. The results indicate that a joint prognostic and diagnostic model that is responsive to new system evidence can be generated from operating data to represent CES health. Such a model can therefore serve as another training tool for CES operators to better prepare for accident scenarios. Full article
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