Dirichlet Process Mixtures within Semiparametric Bayesian Networks: A Novel Conditional Density Estimation Approach
Abstract
Semiparametric Bayesian networks (SPBNs) are flexible probabilistic graphical models for representing joint distributions of continuous variables through lower-dimensional conditional probability distributions (CPDs). Existing SPBN models use kernel density estimators (KDEs) for non-parametric CPD modeling, but their one-component-per-observation mixture representation can lead to increased inference costs and density estimation errors, which can be limiting. In this work, we define a new CPD modeling approach for non-parametric components based on Bayesian non-parametric Dirichlet Process Mixtures (DPMs) within SPBNs. DPMs provide a data-adaptive clustering of observations, yielding a more compact representation while retaining the flexibility of non-parametric density estimation, unlike KDE. This results in lower inference costs while improving density estimation performance. We implement the proposed DPM-based SPBN (DPM-SPBN) by extending the open-source PyBNesian package and evaluate it on synthetic and real-world data. For a given network structure, DPM-based CPDs significantly outperform state-of-the-art Bayesian network models for continuous variables in density estimation, achieving lower absolute log-likelihood errors on synthetic data. We further investigate the impact of the proposed CPD modeling on structure learning methods relying on CPD-based scores. DPM-based SPBNs achieve lower structure learning and density estimation errors than KDE-based SPBNs. Experiments on real-world data corroborate these findings, identifying DPM-based CPD modeling as the most effective alternative among the evaluated non-parametric approaches for continuous variables.
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BibTeX
@misc{alejandre2026dirichlet,
title = {{Dirichlet Process Mixtures within Semiparametric Bayesian Networks: A Novel Conditional Density Estimation Approach}},
author = {Victor Alejandre and Pedro Larrañaga and Concha Bielza},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36110},
eprint = {2610.36110},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36110},
}
RIS
TY - UNPB
TI - Dirichlet Process Mixtures within Semiparametric Bayesian Networks: A Novel Conditional Density Estimation Approach
AU - Victor Alejandre
AU - Pedro Larrañaga
AU - Concha Bielza
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.36110
UR - https://arxiv.org/abs/2610.36110
AB - Semiparametric Bayesian networks (SPBNs) are flexible probabilistic graphical models for representing joint distributions of continuous variables through lower-dimensional conditional probability distributions (CPDs). Existing SPBN models use kernel density estimators (KDEs) for non-parametric CPD modeling, but their one-component-per-observation mixture representation can lead to increased inference costs and density estimation errors, which can be limiting. In this work, we define a new CPD modeling approach for non-parametric components based on Bayesian non-parametric Dirichlet Process Mixtures (DPMs) within SPBNs. DPMs provide a data-adaptive clustering of observations, yielding a more compact representation while retaining the flexibility of non-parametric density estimation, unlike KDE. This results in lower inference costs while improving density estimation performance. We implement the proposed DPM-based SPBN (DPM-SPBN) by extending the open-source PyBNesian package and evaluate it on synthetic and real-world data. For a given network structure, DPM-based CPDs significantly outperform state-of-the-art Bayesian network models for continuous variables in density estimation, achieving lower absolute log-likelihood errors on synthetic data. We further investigate the impact of the proposed CPD modeling on structure learning methods relying on CPD-based scores. DPM-based SPBNs achieve lower structure learning and density estimation errors than KDE-based SPBNs. Experiments on real-world data corroborate these findings, identifying DPM-based CPD modeling as the most effective alternative among the evaluated non-parametric approaches for continuous variables.
ER -