Inference in hybrid Bayesian networks using mixtures of polynomials

Shenoy, Prakash P.; West, James C.

doi:10.1016/j.ijar.2010.09.003

Cited by 93 publications

(93 citation statements)

References 15 publications

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“…An important feature of the technique presented in this paper is that it can be directly applied using frameworks related to MTEs, like the Mixtures of Polynomials (MOPs) [32] and more generally, Mixtures of Truncated Basis Functions (MoTBFs) [19]. This can lead to improvements in inference efficiency, especially using MoTBFs, as they can provide accurate estimations with no need to split the domain of the densities [16].…”

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

Data clustering using hidden variables in hybrid Bayesian networks

et al. 2014

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In this paper, we analyze the problem of data clustering in domains where discrete and continuous variables coexist. We propose the use of hybrid Bayesian networks with naïve Bayes structure and hidden class variable. The model integrates discrete and continuous features, by representing the conditional distributions as mixtures of truncated exponentials (MTEs). The number of classes is determined through an iterative procedure based on a variation of the data augmentation algorithm. The new model is compared with an EM-based clustering algorithm where each class model is a product of conditionally independent probability distributions and the number of clusters is decided by using a cross-validation scheme. Experiments carried out over real-world and synthetic data sets show that the proposal is competitive with state-of-the-art methods. Even though the methodology introduced in this manuscript is based on the use of MTEs, it can be easily instantiated to other similar models, like the Mixtures of Polynomials or the mixtures of truncated basis functions in general.

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Section: Discussion and Concluding Remarksmentioning

confidence: 99%

Data clustering using hidden variables in hybrid Bayesian networks

et al. 2014

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“…For instance, a query consisting on finding the most probable explanation to an observed fact in terms of a set of target variables, which is called abductive inference [11]. We also plan to study the application of the proposed algorithm to MOPs [42]. The main difference would be in Alg.…”

Section: Discussionmentioning

confidence: 99%

“…A recent approach, similar in essence to MTEs, is based on representing the distribution in a hybrid Bayesian network as a Mixture of Polynomials (MOPs) [42]. Both MTEs and MOPs have been generalised in a global framework for representing hybrid Bayesian networks, called Mixtures of Truncated Basis Functions (MoTBFs) [23].…”

Section: Introductionmentioning

confidence: 99%

Answering queries in hybrid Bayesian networks using importance sampling

Fernández

Rumí

Salmerón

2012

Decision Support Systems

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“…In the context of hybrid influence diagrams, i.e., those that include continuous distributions, methods exist that address the shortcomings of conjugate distributions. Poland and Shachter (1993) Shenoy and West (2011) approximate the probability densities with mixtures of polynomials. All of these methods must be implemented ad hoc because they do not have any supporting software.…”

Section: Applicationsmentioning

confidence: 99%

Bayesian Inference Using Gibbs Sampling in Applications and Curricula of Decision Analysis

Díaz

Frances

2014

INFORMS Transactions on Education

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A pplications and curricula of decision analysis currently do not include methods to compute Bayes' rule and obtain posteriors for nonconjugate prior distributions. The current convention is to force the decision maker's belief to take the form of a conjugate distribution, leading to a suboptimal decision. Bayesian inference using Gibbs sampling (BUGS) software, which uses Markov chain Monte Carlo methods, numerically obtains posteriors for nonconjugate priors. By using the decision maker's true nonconjugate belief, the problems explored suggest that BUGS can produce a posterior distribution that leads to optimal decision making. Other methods exist that can use nonconjugate priors, but they must be implemented ad hoc because they do not have any supporting software. BUGS offers the distinct advantage of being implemented in existing software, and with simple coding can solve a wide range of decision analysis problems. BUGS is useful in making optimal decisions, and it is easy to learn and implement; therefore, including BUGS in decision analysis curricula is valuable.

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Inference in hybrid Bayesian networks using mixtures of polynomials

Cited by 93 publications

References 15 publications

Data clustering using hidden variables in hybrid Bayesian networks

Data clustering using hidden variables in hybrid Bayesian networks

Answering queries in hybrid Bayesian networks using importance sampling

Bayesian Inference Using Gibbs Sampling in Applications and Curricula of Decision Analysis

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