A Review of Inference Algorithms for Hybrid Bayesian Networks

Salmerón, Antonio; Rumí, Rafael; Langseth, Helge; Nielsen, Thomas D.; Madsen, Anders L.

doi:10.1613/jair.1.11228

Cited by 39 publications

(21 citation statements)

References 70 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This constraint is quite natural in the LR problem, as all the benchmark datasets contain only continuous variables. In the future, we plan to adapt our method to also allow discrete predictive attributes, which, in general, means learning constrained graphical structures by limiting the number of dependencies allowed [ 30 ] or even dealing with hybrid Bayesian networks [ 40 ]. Learning PGMs with hidden variables is not an easy task, but there are several approaches in the literature, most based on the use of the Structural EM ( SEM ) algorithm [ 41 ].…”

Section: Gaussian Mixture-based Semi-naive Bayes For Label Rankingmentioning

confidence: 99%

Mixture-Based Probabilistic Graphical Models for the Label Ranking Problem

Rodrigo

Alfaro

Aledo

et al. 2021

Entropy

View full text Add to dashboard Cite

The goal of the Label Ranking (LR) problem is to learn preference models that predict the preferred ranking of class labels for a given unlabeled instance. Different well-known machine learning algorithms have been adapted to deal with the LR problem. In particular, fine-tuned instance-based algorithms (e.g., k-nearest neighbors) and model-based algorithms (e.g., decision trees) have performed remarkably well in tackling the LR problem. Probabilistic Graphical Models (PGMs, e.g., Bayesian networks) have not been considered to deal with this problem because of the difficulty of modeling permutations in that framework. In this paper, we propose a Hidden Naive Bayes classifier (HNB) to cope with the LR problem. By introducing a hidden variable, we can design a hybrid Bayesian network in which several types of distributions can be combined: multinomial for discrete variables, Gaussian for numerical variables, and Mallows for permutations. We consider two kinds of probabilistic models: one based on a Naive Bayes graphical structure (where only univariate probability distributions are estimated for each state of the hidden variable) and another where we allow interactions among the predictive attributes (using a multivariate Gaussian distribution for the parameter estimation). The experimental evaluation shows that our proposals are competitive with the start-of-the-art algorithms in both accuracy and in CPU time requirements.

show abstract

Section: Gaussian Mixture-based Semi-naive Bayes For Label Rankingmentioning

confidence: 99%

Mixture-Based Probabilistic Graphical Models for the Label Ranking Problem

Rodrigo

Alfaro

Aledo

et al. 2021

Entropy

View full text Add to dashboard Cite

show abstract

“…28,30 Due to this limitation, approximate inference is pursued by large BNs for fast and efficient estimation. 31 Stochastic sampling algorithms and search-based algorithms are often adopted for approximate solutions.…”

Section: Posterior Probability Inferencementioning

confidence: 99%

Safety evaluation of truss structures using nested discrete Bayesian networks

Fang

Tan

Zhang

2020

Structural Health Monitoring

View full text Add to dashboard Cite

Truss structures have been widely adopted for civil structures such as long-span buildings and bridges. An actual truss system is usually statically indeterminate having numerous members and high redundancy. It is practically difficult to evaluate the truss safety through traditional reliability-based approaches in view of complex failure modes and uncertainties. Moreover, monitoring data are generally insufficient in reality due to limited sensors under cost consideration. Therefore, a nested discrete Bayesian network has been developed for safety evaluation of truss structures. A concept of member risk coefficient is first proposed based on the mechanical relationship between load effects and member resistance. According to the coefficients of all members, member risk sequences are found as the basis for establishing the topology of a member-level Bayesian network. Each network node represents a truss member and a nodal variable having three states: elasticity, plasticity, and failure. Two relevant member nodes are connected by a directed edge whose causality strength is expressed by a conditional probability table. Meanwhile, a system-level network topology is established to reflect the effects of member states on the truss system. The system is assigned with a node having two states: safety and failure. The directed edge of each member node directly points to the system node. Then, the two networks are combined to form a nested network topology. By this means, direct topology learning is avoided in order to find rational and concise topologies satisfying the mechanical characteristics of civil structures. After that, the conditional probability tables for the nested network are obtained through parameter learning on complete numerical observation data. The data acquirement procedure takes into account uncertainties by defining the randomness of cross-sectional areas and external loads. With the conditional probability tables, the nested network is ready for use. When new evidence from limited monitored members is input into the nested network, the state probabilities of the other members, as well as the system, are simultaneously updated using exact inference algorithms. The inference ability using insufficient information well accords with the demand of engineering practice. Finally, the proposed method has been successfully verified against both numerical and experimental truss structures. It was found that the network estimations could be further confirmed with more evidence.

show abstract

“…These have included using mixtures of polynomials (Shenoy, ; Shenoy & West, ) and mixtures of truncated basis functions (Langseth, Nielsen, Perez‐Bernabe, & Salmeron, ; Langseth, Nielsen, Rumi, & Salmeron, ; Perez‐Bernabe, Salmeron, & Langseth, ) to approximate the distributions of the data. However, to a large extent, many of these methods have focused on parameter learning of the network (Salmeron, Rumi, Langseth, Nielsen, & Madsen, ). Other methods for structure learning of hybrid Bayesian networks are still under development (Karra & Mili, ; Talvitie, Eggeling, & Koivisto, ).…”

Section: Other Tools For Hybrid Bayesian Network Modelingmentioning

confidence: 99%

Multiscalar genetic pathway modeling with hybrid Bayesian networks

Ziebarth

Cui

2019

WIREs Computational Stats

View full text Add to dashboard Cite

Bayesian network modeling of real world datasets is often complicated by the fact that they are hybrid datasets that contain both discrete and continuous variables.For example, recent advances in high throughput biotechnologies have made it possible to generate large-scale data across multiple biological scales-from discrete variables such as DNA variations to continuous variables such as omics traits and disease phenotypes. Such large heterogeneous and multiscalar datasets present a great challenge for biological knowledge discovery. Here we discuss the Bayesian Network Webserver (http://compbio.uthsc.edu/BNW), a web-based platform for creating hybrid Bayesian network models, and its use in discovering causal relationships from heterogeneous and multiscalar system genetics datasets. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data Statistical Models > Bayesian Models Statistical Models > Graphical Models Applications of Computational Statistics > Computational and Molecular Biology K E Y W O R D S Bayesian network, genetic pathway, probabilistic graphical model

show abstract

A Review of Inference Algorithms for Hybrid Bayesian Networks

Cited by 39 publications

References 70 publications

Mixture-Based Probabilistic Graphical Models for the Label Ranking Problem

Mixture-Based Probabilistic Graphical Models for the Label Ranking Problem

Safety evaluation of truss structures using nested discrete Bayesian networks

Multiscalar genetic pathway modeling with hybrid Bayesian networks

Contact Info

Product

Resources

About