Learning Mixtures of Polynomials of Conditional Densities from Data

Pedro L. López-Cruz, Thomas Dyhre Nielsen, Concha Bielza, Pedro Larrañga

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Abstract

Mixtures of polynomials (MoPs) are a non-parametric density estimation technique for hybrid Bayesian networks with continuous and discrete variables. We propose two methods for learning MoP ap- proximations of conditional densities from data. Both approaches are based on learning MoP approximations of the joint density and the marginal density of the conditioning variables, but they differ as to how the MoP approximation of the quotient of the two densities is found. We illustrate the methods using data sampled from a simple Gaussian Bayesian network. We study and compare the performance of these meth- ods with the approach for learning mixtures of truncated basis functions from data.
Original languageEnglish
Title of host publicationAdvances in Artificial Intelligence : 15th Conference of the Spanish Association for Artificial Intelligence, CAEPIA 2013, Madrid, Spain, September 17-20, 2013. Proceedings
EditorsConcha Bielza et al.
Number of pages10
PublisherSpringer Publishing Company
Publication date2013
Pages363-372
ISBN (Print)978-3-642-40642-3
ISBN (Electronic)978-3-642-40643-0
DOIs
Publication statusPublished - 2013
Event15th Conference of the Spanish Association for Artificial Intelligence - Madrid, Spain
Duration: 17 Sep 201320 Sep 2013
Conference number: 15

Conference

Conference15th Conference of the Spanish Association for Artificial Intelligence
Number15
CountrySpain
CityMadrid
Period17/09/201320/09/2013
SeriesLecture Notes in Artificial Intelligence : Subseries of Lecture Notes in Computer Science
NumberXVIII
Volume8109
ISSN0302-9743

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Conditional Density
Bayesian Networks
Polynomial
Approximation
Nonparametric Density Estimation
Discrete Variables
Continuous Variables
Conditioning
Basis Functions
Quotient
Learning

Cite this

L. López-Cruz, P., Nielsen, T. D., Bielza, C., & Larrañga, P. (2013). Learning Mixtures of Polynomials of Conditional Densities from Data. In C. Bielza et al. (Ed.), Advances in Artificial Intelligence: 15th Conference of the Spanish Association for Artificial Intelligence, CAEPIA 2013, Madrid, Spain, September 17-20, 2013. Proceedings (pp. 363-372). Springer Publishing Company. Lecture Notes in Artificial Intelligence : Subseries of Lecture Notes in Computer Science, No. XVIII, Vol.. 8109 https://doi.org/10.1007/978-3-642-40643-0_37
L. López-Cruz, Pedro ; Nielsen, Thomas Dyhre ; Bielza, Concha ; Larrañga, Pedro. / Learning Mixtures of Polynomials of Conditional Densities from Data. Advances in Artificial Intelligence: 15th Conference of the Spanish Association for Artificial Intelligence, CAEPIA 2013, Madrid, Spain, September 17-20, 2013. Proceedings. editor / Concha Bielza et al. Springer Publishing Company, 2013. pp. 363-372 (Lecture Notes in Artificial Intelligence : Subseries of Lecture Notes in Computer Science; No. XVIII, Vol. 8109).
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L. López-Cruz, P, Nielsen, TD, Bielza, C & Larrañga, P 2013, Learning Mixtures of Polynomials of Conditional Densities from Data. in C Bielza et al. (ed.), Advances in Artificial Intelligence: 15th Conference of the Spanish Association for Artificial Intelligence, CAEPIA 2013, Madrid, Spain, September 17-20, 2013. Proceedings. Springer Publishing Company, Lecture Notes in Artificial Intelligence : Subseries of Lecture Notes in Computer Science, no. XVIII, vol. 8109, pp. 363-372, Madrid, Spain, 17/09/2013. https://doi.org/10.1007/978-3-642-40643-0_37

Learning Mixtures of Polynomials of Conditional Densities from Data. / L. López-Cruz, Pedro; Nielsen, Thomas Dyhre; Bielza, Concha; Larrañga, Pedro.

Advances in Artificial Intelligence: 15th Conference of the Spanish Association for Artificial Intelligence, CAEPIA 2013, Madrid, Spain, September 17-20, 2013. Proceedings. ed. / Concha Bielza et al. Springer Publishing Company, 2013. p. 363-372 (Lecture Notes in Artificial Intelligence : Subseries of Lecture Notes in Computer Science; No. XVIII, Vol. 8109).

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

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L. López-Cruz P, Nielsen TD, Bielza C, Larrañga P. Learning Mixtures of Polynomials of Conditional Densities from Data. In Bielza et al. C, editor, Advances in Artificial Intelligence: 15th Conference of the Spanish Association for Artificial Intelligence, CAEPIA 2013, Madrid, Spain, September 17-20, 2013. Proceedings. Springer Publishing Company. 2013. p. 363-372. (Lecture Notes in Artificial Intelligence : Subseries of Lecture Notes in Computer Science; No. XVIII, Vol. 8109). https://doi.org/10.1007/978-3-642-40643-0_37