# Semiparametric Bayesian Networks

arXiv: https://arxiv.org/abs/2109.03008 · HTML: https://mlsanity.com/paper/2109.03008/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 47 references that are in the map.
- First posted on arXiv 7 Sep 2021.

## Builds on (most cited first, 7 of 7)

- [Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discovery](https://mlsanity.com/paper/1702.03877/) (2017)
- [Conditional independence testing based on a nearest-neighbor estimator of conditional mutual information](https://mlsanity.com/paper/1709.01447/) (2017)
- [Learning Gaussian Networks](https://mlsanity.com/paper/1302.6808/) (2013)
- [Estimating Continuous Distributions in Bayesian Classifiers](https://mlsanity.com/paper/1302.4964/) (2013)
- [Addendum on the scoring of Gaussian directed acyclic graphical models](https://mlsanity.com/paper/1402.6863/) (2014)
- [Gaussian Process Networks](https://mlsanity.com/paper/1301.3857/) (2013)
- [Learning Mixtures of DAG Models](https://mlsanity.com/paper/1301.7415/) (2013)

## Built on by (most cited first, 6 of 6)

- [bnRep: A repository of Bayesian networks from the academic literature](https://mlsanity.com/paper/2409.19158/) (2024)
- [Actionable Counterfactual Explanations Using Bayesian Networks and Path Planning with Applications to Environmental Quality Improvement](https://mlsanity.com/paper/2508.02634/) (2025)
- [Context-specific kernel-based hidden Markov model for time series analysis](https://mlsanity.com/paper/2301.09870/) (2023)
- [Bandwidth Selectors on Semiparametric Bayesian Networks](https://mlsanity.com/paper/2506.16844/) (2025)
- [Binned semiparametric Bayesian networks for efficient kernel density estimation](https://mlsanity.com/paper/2506.21997/) (2025)
- [Transfer learning for nonparametric Bayesian networks](https://mlsanity.com/paper/2604.01021/) (2026)

## Abstract (arXiv)

We introduce semiparametric Bayesian networks that combine parametric and nonparametric conditional probability distributions. Their aim is to incorporate the advantages of both components: the bounded complexity of parametric models and the flexibility of nonparametric ones. We demonstrate that semiparametric Bayesian networks generalize two well-known types of Bayesian networks: Gaussian Bayesian networks and kernel density estimation Bayesian networks. For this purpose, we consider two different conditional probability distributions required in a semiparametric Bayesian network. In addition, we present modifications of two well-known algorithms (greedy hill-climbing and PC) to learn the structure of a semiparametric Bayesian network from data. To realize this, we employ a score function based on cross-validation. In addition, using a validation dataset, we apply an early-stopping criterion to avoid overfitting. To evaluate the applicability of the proposed algorithm, we conduct an exhaustive experiment on synthetic data sampled by mixing linear and nonlinear functions, multivariate normal data sampled from Gaussian Bayesian networks, real data from the UCI repository, and bearings degradation data. As a result of this experiment, we conclude that the proposed algorithm accurately learns the combination of parametric and nonparametric components, while achieving a performance comparable with those provided by state-of-the-art methods.