Learning Mixtures of Truncated Basis Functions from Data

Helge Langseth, Thomas Dyhre Nielsen, Inmaculada Pérez-Bernabé, Antonio Salmerón

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18 Citationer (Scopus)
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Resumé

In this paper we investigate methods for learning hybrid Bayesian networks from data. First we utilize a kernel density estimate of the data in order to translate the data into a mixture of truncated basis functions (MoTBF) representation using a convex optimization technique. When utilizing a kernel density representation of the data, the estimation method relies on the specification of a kernel bandwidth. We show that in most cases the method is robust wrt. the choice of band- width, but for certain data sets the bandwidth has a strong impact on the result. Based on this observation, we propose an alternative learning method that relies on the cumulative distribution function of the data.
Empirical results demonstrate the usefulness of the approaches: Even though the methods produce estimators that are slightly poorer than the state of the art (in terms of log-likelihood), they are significantly faster, and therefore indicate that the MoTBF framework can be used for inference and learning in reasonably sized domains. Furthermore, we show how a particular sub- class of MoTBF potentials (learnable by the proposed methods) can be exploited to significantly reduce complexity during inference.
OriginalsprogEngelsk
TidsskriftInternational Journal of Approximate Reasoning
Vol/bind55
Udgave nummer4
Sider (fra-til)940-966
ISSN0888-613X
DOI
StatusUdgivet - 2014

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Basis Functions
Bandwidth
Convex optimization
Bayesian networks
Distribution functions
Kernel Density Estimate
Kernel Density
Specifications
Hybrid Learning
Cumulative distribution function
Convex Optimization
Bayesian Networks
Optimization Techniques
Learning
Likelihood
Specification
kernel
Estimator
Alternatives
Demonstrate

Citer dette

Langseth, Helge ; Nielsen, Thomas Dyhre ; Pérez-Bernabé, Inmaculada ; Salmerón, Antonio. / Learning Mixtures of Truncated Basis Functions from Data. I: International Journal of Approximate Reasoning. 2014 ; Bind 55, Nr. 4. s. 940-966.
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Learning Mixtures of Truncated Basis Functions from Data. / Langseth, Helge; Nielsen, Thomas Dyhre; Pérez-Bernabé, Inmaculada; Salmerón, Antonio.

I: International Journal of Approximate Reasoning, Bind 55, Nr. 4, 2014, s. 940-966.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

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AB - In this paper we investigate methods for learning hybrid Bayesian networks from data. First we utilize a kernel density estimate of the data in order to translate the data into a mixture of truncated basis functions (MoTBF) representation using a convex optimization technique. When utilizing a kernel density representation of the data, the estimation method relies on the specification of a kernel bandwidth. We show that in most cases the method is robust wrt. the choice of band- width, but for certain data sets the bandwidth has a strong impact on the result. Based on this observation, we propose an alternative learning method that relies on the cumulative distribution function of the data.Empirical results demonstrate the usefulness of the approaches: Even though the methods produce estimators that are slightly poorer than the state of the art (in terms of log-likelihood), they are significantly faster, and therefore indicate that the MoTBF framework can be used for inference and learning in reasonably sized domains. Furthermore, we show how a particular sub- class of MoTBF potentials (learnable by the proposed methods) can be exploited to significantly reduce complexity during inference.

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