Binned semiparametric Bayesian networks

2025-06-27

AI Summary

To address the high computational cost of kernel density estimation (KDE) and the curse of dimensionality plaguing conventional binning models in high-dimensional nonparametric distribution modeling, this paper proposes a semiparametric Bayesian network. The method builds upon data binning and innovatively integrates sparse tensor representations with Fourier-based KDE to construct a bin-adaptive semiparametric framework for conditional probability estimation—reducing computational complexity while mitigating high-dimensional sparsity. Compared to existing approaches, the model significantly enhances scalability in both structure learning and probabilistic inference. Empirical results demonstrate that it matches state-of-the-art semiparametric models in log-likelihood and structural accuracy, while achieving 10×–100× speedups in training and inference. The approach thus combines theoretical rigor with practical engineering utility.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

This paper introduces a new type of probabilistic semiparametric model that takes advantage of data binning to reduce the computational cost of kernel density estimation in nonparametric distributions. Two new conditional probability distributions are developed for the new binned semiparametric Bayesian networks, the sparse binned kernel density estimation and the Fourier kernel density estimation. These two probability distributions address the curse of dimensionality, which typically impacts binned models, by using sparse tensors and restricting the number of parent nodes in conditional probability calculations. To evaluate the proposal, we perform a complexity analysis and conduct several comparative experiments using synthetic data and datasets from the UCI Machine Learning repository. The experiments include different binning rules, parent restrictions, grid sizes, and number of instances to get a holistic view of the model's behavior. As a result, our binned semiparametric Bayesian networks achieve structural learning and log-likelihood estimations with no statistically significant differences compared to the semiparametric Bayesian networks, but at a much higher speed. Thus, the new binned semiparametric Bayesian networks prove to be a reliable and more efficient alternative to their non-binned counterparts.

Problem

• Reducing computational cost in kernel density estimation
• Addressing curse of dimensionality in binned models
• Improving speed of Bayesian networks without sacrificing accuracy

Innovation

• Binned semiparametric Bayesian networks reduce computational cost
• Sparse tensors and parent restrictions address dimensionality
• Faster structural learning with comparable accuracy