Bayesian Network Representation Research Articles

Staged trees and asymmetry-labeled DAGs

AbstractBayesian networks are a widely-used class of probabilistic graphical models capable of representing symmetric conditional independence between variables of interest using the topology of the underlying graph. For categorical variables, they can be seen as a special case of the much more general class of models called staged trees, which can represent any non-symmetric conditional independence. Here we formalize the relationship between these two models and introduce a minimal Bayesian network representation of a staged tree, which can be used to read conditional independences intuitively. A new labeled graph termed asymmetry-labeled directed acyclic graph is defined, with edges labeled to denote the type of dependence between any two random variables. We also present a novel algorithm to learn staged trees which only enforces a specific subset of non-symmetric independences. Various datasets illustrate the methodology, highlighting the need to construct models that more flexibly encode and represent non-symmetric structures.

A Mixed Assessment for the Science Learning via a Bayesian Network Representation

This study explored an alternative assessment model to examine Chemistry learners’ progress. “The Assessment of Problem-Solving in Chemistry Learning” as a model represented students’ mastery of chemistry study. The data were from journaling narratives and analyzed through cognitive task analysis. Based on the analyses, a student model was established, which represents the qualitative information in a structure, and provides a potential framework of the assessment model for the quantitative representation—a Bayesian network assessment model. The student’s performance was assessed via the Bayesian network assessment model, and classified into three categories: low level, middle level, and high level. The mastery level should be at least scored at and above 90.51/100 for Declarative, Procedural, and Strategic Knowledge respectively.

Negative Shannon Information Hides Networks

AbstractShannon information is defined for characterizing the uncertainty information of classical probabilistic distributions. As an uncertainty measure it is generally believed to be positive. This holds for any information quantity from two random variables because of the polymatroidal axioms. However, it is unknown why there is negative information for more than two random variables on finite dimensional spaces. It is first shown that the negative tripartite Shannon mutual information implies specific Bayesian network representations of its joint distribution. Then it is shown that the negative Shannon information is obtained from general tripartite Bayesian networks with quantum realizations. This provides a device‐independent witness of negative Shannon information. Finally the result is extended for general networks. The present result shows new insights in the network compatibility from non‐Shannon information inequalities.

Bayesian Network Representation of Joint Normal Distributions - Confounding Variables Model

Bayesian Network Representation of Joint Normal Distributions - Confounding Variables Model

Bayesian Network Representation of Joint Normal Distributions - Cascading Regressions Model

Bayesian Network Representation of Joint Normal Distributions - Cascading Regressions Model

Quantum circuit representation of Bayesian networks

Probabilistic graphical models such as Bayesian networks are widely used to model stochastic systems to perform various types of analysis such as probabilistic prediction, risk analysis, and system health monitoring, which can become computationally expensive in large-scale systems. While demonstrations of true quantum supremacy remain rare, quantum computing applications managing to exploit the advantages of amplitude amplification have shown significant computational benefits when compared against their classical counterparts. We develop a systematic method for designing a quantum circuit to represent a generic discrete Bayesian network with nodes that may have two or more states, where nodes with more than two states are mapped to multiple qubits. The marginal probabilities associated with root nodes (nodes without any parent nodes) are represented using rotation gates, and the conditional probability tables associated with non-root nodes are represented using controlled rotation gates. The controlled rotation gates with more than one control qubit are represented using ancilla qubits. The proposed approach is demonstrated for three examples: a 4-node oil company stock prediction, a 10-node network for liquidity risk assessment, and a 9-node naive Bayes classifier for bankruptcy prediction. The circuits were designed and simulated using Qiskit, a quantum computing platform that enables simulations and also has the capability to run on real quantum hardware. The results were validated against those obtained from classical Bayesian network implementations.

RETRACTED: Research on the HRM performance assessment model based on FPGA embedded system and bayesian network

Human Resource Management (HRM) is a structured and fully organized people-managed process. IT includes the person setting up the organization (employer), cash holding and benefits management, performance management, and alternative management and maintenance. One of the strategies for a successful company is to attract talented individuals to any particular position and retain key employees in a better and more energetic workforce. In any field, small or large, human resource management plays its traditional role, but its staff can expand its scope to evaluate performance. Due to the evolution of the new service comes the field of human resource management. The development of a new organization called a performance management system (PMS). Performance appraisal is the social irresponsible management center of companies and organizations, and each appraisal index of the proper allocation of human resources should be given appropriate weights that are important to organize and align the organizational structure and the performance management system at the limits of the individual goals of the sports organization's business goals. This article addresses the validity of PMS. Research programs that serve as a strategic tool for a performance management system achieve a strong foundation for employees to achieve their ambitions and goals for the company to achieve their core financial goals. Propose to implement a Bayesian Network (BN) Representation based Field Programmable Gate Arrays (FPGA) that allow for continuous monitoring of embedded systems under a time and resource basis. Advanced package tools integrated with hardware implementation provide a specific offline configuration. The proposed hybrid redesign device is evaluated to indicate potential acceleration. Some modifications to the hardware's functionality have been explored to better balance accuracy, performance, and resource allocation.

RAWLSNET: Altering Bayesian Networks to Encode Rawlsian Fair Equality of Opportunity

We present RAWLSNET, a system for altering Bayesian Network (BN) models to satisfy the Rawlsian principle of fair equality of opportunity (FEO). RAWLSNET's BN models generate aspirational data distributions: data generated to reflect an ideally fair, FEO-satisfying society. FEO states that everyone with the same talent and willingness to use it should have the same chance of achieving advantageous social positions (e.g., employment), regardless of their background circumstances (e.g., socioeconomic status). Satisfying FEO requires alterations to social structures such as school assignments. Our paper describes RAWLSNET, a method which takes as input a BN representation of an FEO application and alters the BN's parameters so as to satisfy FEO when possible, and minimize deviation from FEO otherwise. We also offer guidance for applying RAWLSNET, including on recognizing proper applications of FEO. We demonstrate the use of our system with publicly available data sets. RAWLSNET's altered BNs offer the novel capability of generating aspirational data for FEO-relevant tasks. Aspirational data are free from the biases of real-world data, and thus are useful for recognizing and detecting sources of unfairness in machine learning algorithms besides biased data.

Bayesian network modeling of accident investigation reports for aviation safety assessment

Safety assurance is of paramount importance in the air transportation system. In this paper, we analyze the historical passenger airline accidents that happened from 1982 to 2006 as reported in the National Transportation Safety Board (NTSB) aviation accident database. A four-step procedure is formulated to construct a Bayesian network to capture the causal relationships embedded in the sequences of these accidents. First of all, with respect to each accident, a graphical representation is developed to facilitate the visualization of the escalation of initiating events into aviation accidents in the system. Next, we develop a Bayesian network representation of all the accidents by aggregating the accident-wise graphical representations together, where the causal and dependent relationships among a wide variety of contributory factors and outcomes in terms of aircraft damage and personnel injury are captured. In the Bayesian network, the prior probabilities are estimated based on the accident occurrence times and the aircraft departure data from the Bureau of Transportation Statistics (BTS). To estimate the conditional probabilities in the Bayesian network, we develop a monotonically increasing function, whose parameters are calibrated using the probability information on single events in the available data. Finally, we develop a computer program to automate the generation of the Bayesian network in compliance with the XML format used in the commercial GeNIe modeler. The constructed Bayesian network is then fed into GeNIe modeler for accident analysis. The mapping of the NTSB data to a Bayesian network facilitates both forward propagation and backward inference in probabilistic analysis, thereby supporting accident investigations and risk analysis. Several accident cases are used to demonstrate the developed approach.

Conceptual Bayesian networks for contaminated site ecological risk assessment and remediation support

The causal pathways of stressors that lead to impacts on individuals, populations, and communities of organisms are useful to know for designing alternatives that manage or remediate ecological risks. The ecological risk assessment (ERA) framework (USEPA, 1998b) can help to identify and prioritize management of risks. One key product of the problem formulation step in an ERA, that captures and represents causal knowledge, is the conceptual site model (CSM). The CSM is a graphical depiction of the risk environment that traces the fate and transport pathways of contaminants from sources of contamination (e.g., a leaking storage tank) to receptors (i.e., the ecological endpoints of concern in the risk assessment). The CSM guides the development of methods for assessing ecological risk scenarios and for remediation design alternatives. The qualitative and quantitative aspects of Bayesian networks may support CSM development and risk characterization. Bayesian networks provide a graphical platform geared toward probabilistic modeling making them important candidates for calculating risks in environmental assessments. The diagrammatic representation of causal Bayesian networks (i.e., the directed acyclic graphs) also adds explanatory depth for developing the evidence-base for risk characterization and remediation interventions. We call these qualitative graphs conceptual Bayesian networks (CBNs). The components of CBNs can be used to represent the variables and relationships between sources of contamination, media transfer, bioaccumulation, and risk. The connections help to compose, piece together, and explore hypothesized relationships that bring about high-risk scenarios. Causal pathway analysis of the CBNs provides visualizations of exposure pathways from initial and intermediate sources to receptors. Remediation options that would interrupt or stop the transport of contaminants to ecological receptors can then be identified. Even if the CBN is not quantified, the structures can support mechanistic and statistical designs for exposure and effects analysis and risk characterization and evaluate information needs for resolving uncertainties. This paper will examine these and other unexplored benefits of CBNs to assessment and management of contaminated sites.

A probabilistic risk-based decision framework for structural health monitoring

Obtaining the ability to make informed decisions regarding the operation and maintenance of structures, provides a major incentive for the implementation of structural health monitoring (SHM) systems. Probabilistic risk assessment (PRA) is an established methodology that allows engineers to make risk-informed decisions regarding the design and operation of safety-critical and high-value assets in industries such as nuclear and aerospace. The current paper aims to formulate a risk-based decision framework for structural health monitoring that combines elements of PRA with the existing SHM paradigm. As an apt tool for reasoning and decision-making under uncertainty, probabilistic graphical models serve as the foundation of the framework. The framework involves modelling failure modes of structures as Bayesian network representations of fault trees and then assigning costs or utilities to the failure events. The fault trees allow for information to pass from probabilistic classifiers to influence diagram representations of decision processes whilst also providing nodes within the graphical model that may be queried to obtain marginal probability distributions over local damage states within a structure. Optimal courses of action for structures are selected by determining the strategies that maximise expected utility. The risk-based framework is demonstrated on a realistic truss-like structure and supported by experimental data. Finally, a discussion of the risk-based approach is made and further challenges pertaining to decision-making processes in the context of SHM are identified.

A Bayesian network approach to trophic metacommunities shows that habitat loss accelerates top species extinctions.

We develop a novel approach to analyse trophic metacommunities, which allows us to explore how progressive habitat loss affects food webs. Our method combines classic metapopulation models on fragmented landscapes with a Bayesian network representation of trophic interactions for calculating local extinction rates. This means that we can repurpose known results from classic metapopulation theory for trophic metacommunities, such as ranking the habitat patches of the landscape with respect to their importance to the persistence of the metacommunity as a whole. We use this to study the effects of habitat loss, both on model communities and the plant‐mammal Serengeti food web dataset as a case study. Combining straightforward parameterisability with computational efficiency, our method permits the analysis of species‐rich food webs over large landscapes, with hundreds or even thousands of species and habitat patches, while still retaining much of the flexibility of explicit dynamical models.

Event-Driven Continuous Time Bayesian Networks

We introduce a novel event-driven continuous time Bayesian network (ECTBN) representation to model situations where a system's state variables could be influenced by occurrences of events of various types. In this way, the model parameters and graphical structure capture not only potential “causal” dynamics of system evolution but also the influence of event occurrences that may be interventions. We propose a greedy search procedure for structure learning based on the BIC score for a special class of ECTBNs, showing that it is asymptotically consistent and also effective for limited data. We demonstrate the power of the representation by applying it to model paths out of poverty for clients of CityLink Center, an integrated social service provider in Cincinnati, USA. Here the ECTBN formulation captures the effect of classes/counseling sessions on an individual's life outcome areas such as education, transportation, employment and financial education.

Assessing the prior event rate ratio method via probabilistic bias analysis on a Bayesian network.

Background: Unmeasured confounders are commonplace in observational studies conducted using real‐world data. Prior event rate ratio (PERR) adjustment is a technique shown to perform well in addressing such confounding. However, it has been demonstrated that, in some circumstances, the PERR method actually increases rather than decreases bias. In this work, we seek to better understand the robustness of PERR adjustment. Methods: We begin with a Bayesian network representation of a generalized observational study, which is subject to unmeasured confounding. Previous work evaluating PERR performance used Monte Carlo simulation to calculate joint probabilities of interest within the study population. Here, we instead use a Bayesian networks framework. Results: Using this streamlined analytic approach, we are able to conduct probabilistic bias analysis (PBA) using large numbers of combinations of parameters and thus obtain a comprehensive picture of PERR performance. We apply our methodology to a recent study that used the PERR in evaluating elderly‐specific high‐dose (HD) influenza vaccine in the US Veterans Affairs population. That study obtained an HD relative effectiveness of 25% (95% CI: 2%‐43%) against influenza‐ and pneumonia‐associated hospitalization, relative to standard‐dose influenza vaccine. In this instance, we find that the PERR‐adjusted result is more like to underestimate rather than to overestimate the relative effectiveness of the intervention. Conclusions: Although the PERR is a powerful tool for mitigating the effects of unmeasured confounders, it is not infallible. Here, we develop some general guidance for when a PERR approach is appropriate and when PBA is a safer option.

A Hierarchical Hidden Markov Model Framework for Home Appliance Modeling

Correctly anticipating load characteristics of low voltage level is getting increased interest by distribution network operators. Energy disaggregation could be one of the potential approaches to exploit the massive amount of smart meter data to fulfill the task. Proper individual home appliance modeling is critical to the performance of NILM. In this paper, a hierarchical hidden Markov model (HHMM) framework to model home appliances is proposed. This model aims to provide better representation for those appliances that have multiple built-in modes with distinct power consumption profiles, such as washing machines and dishwashers. The dynamic Bayesian network representation of such an appliance model is built. A forward–backward algorithm, which is based on the framework of expectation maximization, is formalized for the HHMM fitting process. Tests on publically available data show that the HHMM and proposed algorithm can effectively handle the modeling of appliances with multiple functional modes, as well as better representing a general type of appliances. A disaggregation test also demonstrates that the fitted HHMM can be easily applied to a general inference solver to outperform conventional hidden Markov model in the estimation of energy disaggregation.

A Bayesian network based solution scheme for the constrained Stochastic On-line Equi-Partitioning Problem

A number of intriguing decision scenarios revolve around partitioning a collection of objects to optimize some application specific objective function. This problem is generally referred to as the Object Partitioning Problem (OPP) and is known to be NP-hard. We here consider a particularly challenging version of OPP, namely, the Stochastic On-line Equi-Partitioning Problem (SO-EPP). In SO-EPP, the target partitioning is unknown and has to be inferred purely from observing an on-line sequence of object pairs. The paired objects belong to the same partition with probability p and to different partitions with probability 1 − p, with p also being unknown. As an additional complication, the partitions are required to be of equal cardinality. Previously, only heuristic sub-optimal solution strategies have been proposed for SO- EPP. In this paper, we propose the first Bayesian solution strategy. In brief, the scheme that we propose, BN-EPP, is founded on a Bayesian network representation of SO-EPP problems. Based on probabilistic reasoning, we are not only able to infer the underlying object partitioning with superior accuracy. We are also able to simultaneously infer p, allowing us to accelerate learning as object pairs arrive. Furthermore, our scheme is the first to support a wide range of constraints on the partitioning (Constrained SO-EPP). Being Bayesian, BN-EPP provides superior performance compared to existing solution schemes. We additionally introduce Walk-BN-EPP, a novel WalkSAT inspired algorithm for solving large scale BN-EPP problems. Finally, we provide a BN-EPP based solution to the problem of order picking, a representative real-life application of BN-EPP.

Improving post-disaster road network accessibility by strengthening links against failures

We study a network improvement problem to increase the resilience of a transportation network against disasters. This involves optimizing pre-disaster investment decisions to strengthen the links of the network structurally. The goal is to improve the expected post-disaster accessibility. We first propose a new dependency model for random link failures to predict the post-disaster status of the network. We show that the probability of any network realization can be computed using a Bayesian network representation of the dependency model. As the computational effort grows with the network size, we use our proposed dependency model in a network sampling algorithm. We then estimate an accessibility measure, namely, the expected weighted average distance between supply and demand points by checking pre-generated short and dissimilar paths in the sample. We minimize this measure and decide on the links that should be strengthened in a two-stage stochastic programming framework. As the failure probability of a strengthened link decreases, the discrete scenario probabilities depend on the first-stage decisions. To tackle this challenge, we develop an efficient tabu search algorithm. We apply our methods to a case study of Istanbul under the risk of an earthquake, both to illustrate the use of the methods and to derive insights for decision makers.

Predictive Model Markup Language (PMML) Representation of Bayesian Networks: An Application in Manufacturing.

Bayesian networks (BNs) represent a promising approach for the aggregation of multiple uncertainty sources in manufacturing networks and other engineering systems for the purposes of uncertainty quantification, risk analysis, and quality control. A standardized representation for BN models will aid in their communication and exchange across the web. This paper presents an extension to the Predictive Model Markup Language (PMML) standard, for the representation of a BN, which may consist of discrete variables, continuous variables, or their combination. The PMML standard is based on Extensible Markup Language (XML) and used for the representation of analytical models. The BN PMML representation is available in PMML v4.3 released by the Data Mining Group. We demonstrate the conversion of analytical models into the BN PMML representation, and the PMML representation of such models into analytical models, through a Python parser. The BNs obtained after parsing PMML representation can then be used to perform Bayesian inference. Finally, we illustrate the developed BN PMML schema for a welding process.

Bit-wise Pseudo-Bayes genetic algorithms to model data distributions

This work introduces a method to generate implicit models from data. The algorithm is based on Bayesian networks, discrete codification and genetic algorithms. The concept of bit-wise Pseudo-Bayes networks is introduced in this work. It refers to Bayesian networks generated from discretized data. The network describes the model in function of the correlations between bits. The model is consider implicit in the sense the meaning of the original variables is lost during discretization, but it can provide random samples with a distribution that is similar to the one of the original data. These samples can be the input of other algorithms that rely on samples of data in a transparent fashion. Moreover, this approach alleviates the problem of storing and handling of larges volumes of data, a common occurrence in modern data science, and circumvent the problems of identification process. The algorithm to generate bit-wise Pseudo-Bayes models is described in detail, and introduces innovations to representation of Bayesian networks based on extended chain structures. Also, it introduces new discretization methods and compares them to others reported in the literature, which have been mainly used to evolutionary continuous optimization. The performance of the proposed algorithm is studied using two data sets: prices data from the stock of the Dow Jones industrial average, and prices data from the stocks of the Mexican Índice de precios y cotizaciones. The proposed method is compared against other discrete modeling techniques reported in the literature, attaining a higher performance. The results indicate direct discretization methods were effective when they are coupled with Bayesian networks, but further research is needed to guarantee scalability. The study indicated the Dow Jones data set was more difficult than the Mexican index data set, but this was attributed to 2008 American crisis.

Partition MCMC for Inference on Acyclic Digraphs

ABSTRACTAcyclic digraphs are the underlying representation of Bayesian networks, a widely used class of probabilistic graphical models. Learning the underlying graph from data is a way of gaining insights about the structural properties of a domain. Structure learning forms one of the inference challenges of statistical graphical models. Markov chain Monte Carlo (MCMC) methods, notably structure MCMC, to sample graphs from the posterior distribution given the data are probably the only viable option for Bayesian model averaging. Score modularity and restrictions on the number of parents of each node allow the graphs to be grouped into larger collections, which can be scored as a whole to improve the chain’s convergence. Current examples of algorithms taking advantage of grouping are the biased order MCMC, which acts on the alternative space of permuted triangular matrices, and nonergodic edge reversal moves. Here, we propose a novel algorithm, which employs the underlying combinatorial structure of DAGs to define a new grouping. As a result convergence is improved compared to structure MCMC, while still retaining the property of producing an unbiased sample. Finally, the method can be combined with edge reversal moves to improve the sampler further. Supplementary materials for this article are available online.