Article

Mixtures of Truncated Exponentials in Hybrid Bayesian Networks

Authors:

ECSQARU '01: Proceedings of the 6th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty

Pages 156 - 167

Published: 19 September 2001 Publication History

Abstract

In this paper we propose the use of mixtures of truncated exponential (MTE) distributions in hybrid Bayesian networks. We study the properties of the MTE distribution and show how exact probability propagation can be carried out by means of a local computation algorithm. One feature of this model is that no restriction is made about the order among the variables either discrete or continuous. Computations are performed over a representation of probabilistic potentials based on probability trees, expanded to allow discrete and continuous variables simultaneously. Finally, a Markov chain Monte Carlo algorithm is described with the aim of dealing with complex networks.

References

[1]

A. Cano, S. Moral, and A. Salmerón. Penniless propagation in join trees. International Journal of Intelligent Systems, 15:1027-1059, 2000.

Google Scholar

[2]

F.V. Jensen, S.L. Lauritzen, and K.G. Olesen. Bayesian updating in causal probabilistic networks by local computation. Comput Stat Quarterly, 4:269-282, 1990.

Google Scholar

[3]

D. Koller, U. Lerner, and D. Anguelov. A general algorithm for approximate inference and its application to hybrid Bayes nets. In K.B. Laskey and H. Prade, editors, Proceedings of the 15th Conference on Uncertainty in Artificial Intelligence, pages 324-333. Morgan & Kauffman, 1999.

Crossref

Google Scholar

[4]

D. Kozlov and D. Koller. Nonuniform dynamic discretization in hybrid networks. In D. Geiger and P.P. Shenoy, editors, Proceedings of the 13th Conference on Uncertainty in Artificial Intelligence, pages 302-313. Morgan & Kauffman, 1997.

Crossref

Google Scholar

[5]

S.L. Lauritzen. Propagation of probabilities, means and variances in mixed graphical association models. Journal of the American Statistical Association, 87:1098- 1108, 1992.

Google Scholar

[6]

S.L. Lauritzen and F. Jensen. Stable local computation with conditional Gaussian distributions. Statistics and Computing, 11:191-203, 2001.

Crossref

Google Scholar

[7]

S.L. Lauritzen and D.J. Spiegelhalter. Local computations with probabilities on graphical structures and their application to expert systems. Journal of the Royal Statistical Society, Series B, 50:157-224, 1988.

Google Scholar

[8]

A.L. Madsen and F.V. Jensen. Lazy propagation: a junction tree inference algorithm based on lazy evaluation. Artif Intell, 113:203-245, 1999.

Crossref

Google Scholar

[9]

K.G. Olesen. Causal probabilistic networks with both discrete and continuous variables. IEEE Trans on Pattern Analysis and Machine Intell, 15:275-279, 1993.

Crossref

Google Scholar

[10]

J. Pearl. Evidential reasoning using stochastic simulation of causal models. Artificial Intelligence, 32:247-257, 1987.

Crossref

Google Scholar

[11]

R.Y. Rubinstein. Simulation and the Monte Carlo Method. Wiley, 1981.

Crossref

Google Scholar

[12]

A. Salmerón, A. Cano, and S. Moral. Importance sampling in Bayesian networks using probability trees. Computational Statistics and Data Analysis, 34:387-413, 2000.

Crossref

Google Scholar

[13]

P.P. Shenoy and G. Shafer. Axioms for probability and belief function propagation. In R.D. Shachter, T.S. Levitt, J.F. Lemmer, and L.N. Kanal, editors, Uncertainty in Artificial Intelligence 4, pages 169-198. North Holland, Amsterdam, 1990.

Crossref

Google Scholar

Cited By

View all

Zhang JXue JMcKinley KFisher K(2019)Incremental precision-preserving symbolic inference for probabilistic programsProceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation10.1145/3314221.3314623(237-252)Online publication date: 8-Jun-2019
https://dl.acm.org/doi/10.1145/3314221.3314623
Salmerón ARumí RLangseth HNielsen TMadsen A(2018)A review of inference algorithms for hybrid Bayesian networksJournal of Artificial Intelligence Research10.1613/jair.1.1122862:1(799-828)Online publication date: 1-May-2018
https://dl.acm.org/doi/10.1613/jair.1.11228
Cobb BShenoy P(2017)Inference in Hybrid Bayesian Networks with Nonlinear Deterministic ConditionalsInternational Journal of Intelligent Systems10.1002/int.2189732:12(1217-1246)Online publication date: 11-Oct-2017
https://dl.acm.org/doi/10.1002/int.21897
Show More Cited By

Mixtures of Truncated Exponentials in Hybrid Bayesian Networks
1. Mathematics of computing
  1. Probability and statistics
    1. Probabilistic reasoning algorithms
    2. Probabilistic representations

Recommendations

Inference in hybrid Bayesian networks with mixtures of truncated exponentials

Mixtures of truncated exponentials (MTE) potentials are an alternative to discretization for solving hybrid Bayesian networks. Any probability density function (PDF) can be approximated with an MTE potential, which can always be marginalized in closed ...
Approximate probability propagation with mixtures of truncated exponentials

Mixtures of truncated exponentials (MTEs) are a powerful alternative to discretisation when working with hybrid Bayesian networks. One of the features of the MTE model is that standard propagation algorithms can be used. However, the complexity of the ...
Learning hybrid Bayesian networks using mixtures of truncated exponentials

In this paper we introduce an algorithm for learning hybrid Bayesian networks from data. The result of the algorithm is a network where the conditional distribution for each variable is a mixture of truncated exponentials (MTE), so that no restrictions ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

ECSQARU '01: Proceedings of the 6th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty

September 2001

814 pages

ISBN:3540424644

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 19 September 2001

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

28
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 04 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

View all

Zhang JXue JMcKinley KFisher K(2019)Incremental precision-preserving symbolic inference for probabilistic programsProceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation10.1145/3314221.3314623(237-252)Online publication date: 8-Jun-2019
https://dl.acm.org/doi/10.1145/3314221.3314623
Salmerón ARumí RLangseth HNielsen TMadsen A(2018)A review of inference algorithms for hybrid Bayesian networksJournal of Artificial Intelligence Research10.1613/jair.1.1122862:1(799-828)Online publication date: 1-May-2018
https://dl.acm.org/doi/10.1613/jair.1.11228
Cobb BShenoy P(2017)Inference in Hybrid Bayesian Networks with Nonlinear Deterministic ConditionalsInternational Journal of Intelligent Systems10.1002/int.2189732:12(1217-1246)Online publication date: 11-Oct-2017
https://dl.acm.org/doi/10.1002/int.21897
Maldonado AAguilera PSalmerón A(2016)Modeling zero-inflated explanatory variables in hybrid Bayesian network classifiers for species occurrence predictionEnvironmental Modelling & Software10.1016/j.envsoft.2016.04.00382:C(31-43)Online publication date: 1-Aug-2016
https://dl.acm.org/doi/10.1016/j.envsoft.2016.04.003
Kratochvil VVomlel J(2015)Influence diagrams for the optimization of a vehicle speed profileProceedings of the Twelfth UAI Conference on Bayesian Modeling Applications Workshop - Volume 156510.5555/3020313.3020323(44-53)Online publication date: 16-Jul-2015
https://dl.acm.org/doi/10.5555/3020313.3020323
Größl MWainwright RCorchado JBechini AHong J(2015)Modeling dependable systems with continuous time Bayesian networksProceedings of the 30th Annual ACM Symposium on Applied Computing10.1145/2695664.2695729(436-441)Online publication date: 13-Apr-2015
https://dl.acm.org/doi/10.1145/2695664.2695729
Salmerón ARamos-López DBorchani HMartínez AMasegosa AFernández ALangseth HMadsen ANielsen T(2015)Parallel Importance Sampling in Conditional Linear Gaussian NetworksProceedings of the 16th Conference of the Spanish Association for Artificial Intelligence on Advances in Artificial Intelligence - Volume 942210.1007/978-3-319-24598-0_4(36-46)Online publication date: 9-Nov-2015
https://dl.acm.org/doi/10.1007/978-3-319-24598-0_4
Maldonado ARopero RAguilera PRumí RSalmerón A(2015)Estimation of Species Richness Using Bayesian NetworksProceedings of the 16th Conference of the Spanish Association for Artificial Intelligence on Advances in Artificial Intelligence - Volume 942210.1007/978-3-319-24598-0_14(153-163)Online publication date: 9-Nov-2015
https://dl.acm.org/doi/10.1007/978-3-319-24598-0_14
Ye ZBouguettaya AZhou X(2014)Economic Model-Driven Cloud Service CompositionACM Transactions on Internet Technology10.1145/265142014:2-3(1-19)Online publication date: 28-Oct-2014
https://dl.acm.org/doi/10.1145/2651420
Ropero RAguilera PRumí R(2014)Soft Clustering Based on Hybrid Bayesian Networks in Socioecological CartographyProceedings of the 9th International Conference on Hybrid Artificial Intelligence Systems - Volume 848010.1007/978-3-319-07617-1_53(607-617)Online publication date: 11-Jun-2014
https://dl.acm.org/doi/10.1007/978-3-319-07617-1_53
Show More Cited By

Abstract

References

Cited By

Recommendations

Inference in hybrid Bayesian networks with mixtures of truncated exponentials

Approximate probability propagation with mixtures of truncated exponentials

Learning hybrid Bayesian networks using mixtures of truncated exponentials

Comments

Information

Published In

Publisher

Publication History

Qualifiers

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations