aiqbench analysis
This paper proposes a probabilistic modeling method that adds nonlinear mean functions to Gaussian Bayesian networks while keeping the Gaussian conditional distributions. It uses penalized B-splines within generalized additive models and learns network structure with a greedy hill-climbing search. Its main claim is a fit and structure-recovery advantage over linear and semiparametric baselines on synthetic-style comparisons, with lower computational cost than fully nonparametric alternatives. Readers should weigh the gains against the narrow setting of approximately Gaussian, nonlinear-mean data, and check how the results hold on real datasets.
Semi-Linear Gaussian Bayesian Networks: Enhancing Flexibility in Node Dependencies via penalized B-Splines
arXiv:2610.30838v1 Announce Type: cross Abstract: Bayesian networks for continuous variables often rely on restrictive assumptions: linear Gaussian models lack flexibility to capture nonlinear dependencies, while non-parametric approaches provide greater flexibility at a high computational cost. This creates a gap for modeling scenarios where variables are approximately Gaussian but exhibit nonlinear relationships. We introduce Semi-Linear Gaussian Bayesian Networks (SLGBN), a novel class of continuous Bayesian networks designed to bridge this gap, preserving Gaussian conditional distributions while introducing nonlinear conditional mean functions. The proposed framework provides a unified probabilistic framework combining linear Gaussian and nonlinear Gaussian conditional models within the same Bayesian network Nonlinear conditional mean functions are estimated using generalized additive models (GAMs) with penalized B-splines. We present parameter estimation procedures for both types of nodes, as well as a greedy hill-climbing algorithm for learning the network structure under the SLGBN framework. To assess its performance, we compare SLGBN with other continuous Bayesian network models, including semiparametric Bayesian networks (SPBN) and Linear Gaussian Bayesian networks (LGBN). Experimental results evaluate both goodness of fit and the ability to recover the underlying network structure. The results show that, in the presence of nonlinear Gaussian relationships, SLGBN achieves better fit and improved structure recovery compared to alternative models, particularly when combined with the Extended Bayesian Information Criterion (EBIC*) score. Furthermore, by retaining Gaussian conditional distributions, SLGBN offers computational advantages over fully semiparametric approaches.
Abstract:Bayesian networks for continuous variables often rely on restrictive assumptions: linear Gaussian models lack flexibility to capture nonlinear dependencies, while non-parametric approaches provide greater flexibility at a high computational cost. This creates a gap for modeling scenarios where variables are approximately Gaussian but exhibit nonlinear relationships. We introduce Semi-Linear Gaussian Bayesian Networks (SLGBN), a novel class of continuous Bayesian networks designed to bridge this gap, preserving Gaussian conditional distributions while introducing nonlinear conditional mean functions. The proposed framework provides a unified probabilistic framework combining linear Gaussian and nonlinear Gaussian conditional models within the same Bayesian network Nonlinear conditional mean functions are estimated using generalized additive models (GAMs) with penalized B-splines. We present parameter estimation procedures for both types of nodes, as well as a greedy hill-climbing algorithm for learning the network structure under the SLGBN framework. To assess its performance, we compare SLGBN with other continuous Bayesian network models, including semiparametric Bayesian networks (SPBN) and Linear Gaussian Bayesian networks (LGBN). Experimental results evaluate both goodness of fit and the ability to recover the underlying network structure. The results show that, in the presence of nonlinear Gaussian relationships, SLGBN achieves better fit and improved structure recovery compared to alternative models, particularly when combined with the Extended Bayesian Information Criterion (EBIC*) score. Furthermore, by retaining Gaussian conditional distributions, SLGBN offers computational advantages over fully semiparametric approaches.
Artificial Intelligence (cs.AI); Machine Learning (cs.LG)
arXiv:2610.30838 [cs.AI]
(or arXiv:2610.30838v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2610.30838 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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