Conditional Density Approximations with Mixtures of Polynomials

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

Research output: Contribution to journalJournal articleResearchpeer-review

2 Citations (Scopus)
89 Downloads (Pure)

Abstract

Mixtures of polynomials (MoPs) are a non-parametric density estimation technique especially designed for hybrid Bayesian networks with continuous and discrete variables. Algorithms to learn one- and multi-dimensional (marginal) MoPs from data have recently been proposed. In this paper we introduce two methods for learning MoP approximations 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 and study the methods using data sampled from known parametric distributions, and we demonstrate their applicability by learning models based on real neuroscience data. Finally, we compare the performance of the proposed methods with an approach for learning mixtures of truncated basis functions (MoTBFs). The empirical results show that the proposed methods generally yield models that are comparable to or significantly better than those found using the MoTBF-based method.
Original languageEnglish
JournalInternational Journal of Intelligent Systems
Volume30
Issue number3
Pages (from-to)236-264
ISSN0884-8173
DOIs
Publication statusPublished - 2015

Fingerprint

Conditional Density
Polynomials
Polynomial
Approximation
Basis Functions
Nonparametric Density Estimation
Bayesian networks
Discrete Variables
Neuroscience
Continuous Variables
Bayesian Networks
Conditioning
Quotient
Model-based
Learning
Demonstrate

Cite this

Varando, Gherardo ; López-Cruz, Pedro L. ; Nielsen, Thomas Dyhre ; Bielza, Concha ; Larrañga, Pedro. / Conditional Density Approximations with Mixtures of Polynomials. In: International Journal of Intelligent Systems. 2015 ; Vol. 30, No. 3. pp. 236-264.
@article{5c6442a505ba474588638066824b13af,
title = "Conditional Density Approximations with Mixtures of Polynomials",
abstract = "Mixtures of polynomials (MoPs) are a non-parametric density estimation technique especially designed for hybrid Bayesian networks with continuous and discrete variables. Algorithms to learn one- and multi-dimensional (marginal) MoPs from data have recently been proposed. In this paper we introduce two methods for learning MoP approximations 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 and study the methods using data sampled from known parametric distributions, and we demonstrate their applicability by learning models based on real neuroscience data. Finally, we compare the performance of the proposed methods with an approach for learning mixtures of truncated basis functions (MoTBFs). The empirical results show that the proposed methods generally yield models that are comparable to or significantly better than those found using the MoTBF-based method.",
author = "Gherardo Varando and L{\'o}pez-Cruz, {Pedro L.} and Nielsen, {Thomas Dyhre} and Concha Bielza and Pedro Larra{\~n}ga",
year = "2015",
doi = "10.1002/int.21699",
language = "English",
volume = "30",
pages = "236--264",
journal = "International Journal of Intelligent Systems",
issn = "0884-8173",
publisher = "Wiley",
number = "3",

}

Conditional Density Approximations with Mixtures of Polynomials. / Varando, Gherardo; López-Cruz, Pedro L.; Nielsen, Thomas Dyhre; Bielza, Concha; Larrañga, Pedro.

In: International Journal of Intelligent Systems, Vol. 30, No. 3, 2015, p. 236-264.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Conditional Density Approximations with Mixtures of Polynomials

AU - Varando, Gherardo

AU - López-Cruz, Pedro L.

AU - Nielsen, Thomas Dyhre

AU - Bielza, Concha

AU - Larrañga, Pedro

PY - 2015

Y1 - 2015

N2 - Mixtures of polynomials (MoPs) are a non-parametric density estimation technique especially designed for hybrid Bayesian networks with continuous and discrete variables. Algorithms to learn one- and multi-dimensional (marginal) MoPs from data have recently been proposed. In this paper we introduce two methods for learning MoP approximations 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 and study the methods using data sampled from known parametric distributions, and we demonstrate their applicability by learning models based on real neuroscience data. Finally, we compare the performance of the proposed methods with an approach for learning mixtures of truncated basis functions (MoTBFs). The empirical results show that the proposed methods generally yield models that are comparable to or significantly better than those found using the MoTBF-based method.

AB - Mixtures of polynomials (MoPs) are a non-parametric density estimation technique especially designed for hybrid Bayesian networks with continuous and discrete variables. Algorithms to learn one- and multi-dimensional (marginal) MoPs from data have recently been proposed. In this paper we introduce two methods for learning MoP approximations 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 and study the methods using data sampled from known parametric distributions, and we demonstrate their applicability by learning models based on real neuroscience data. Finally, we compare the performance of the proposed methods with an approach for learning mixtures of truncated basis functions (MoTBFs). The empirical results show that the proposed methods generally yield models that are comparable to or significantly better than those found using the MoTBF-based method.

U2 - 10.1002/int.21699

DO - 10.1002/int.21699

M3 - Journal article

VL - 30

SP - 236

EP - 264

JO - International Journal of Intelligent Systems

JF - International Journal of Intelligent Systems

SN - 0884-8173

IS - 3

ER -