bayesian network modeling

In Bayesian network structure learning, exact marginalization over parent sets constitutes a critical computational bottleneck. This work introduces probabilistic circuits (PCs) — specifically tractable PCs — for the first time into Bayesian structure learning to replace conventional dynamic programming for marginalization, enabling efficient and exact marginal queries under arbitrary parent sets and thereby overcoming restrictive assumptions on parent set size or graph structure imposed by existing methods. We propose an end-to-end training strategy that jointly models the joint distribution and target marginal queries, facilitating co-optimization of the probabilistic circuit and the structure learner. Experiments demonstrate that our approach significantly outperforms state-of-the-art Bayesian structure learning algorithms in structural Hamming distance (SHD), structural intervention distance (SID), posterior estimation quality, and inference speed, achieving new state-of-the-art performance across multiple benchmark datasets.

This study investigates whether Bayesian networks can be mapped to probabilistic structural causal models (SCMs) and analyzes the implications of such a mapping for network structure and joint distributions. By introducing independent latent random variables, deterministic structural equations are extended into probabilistic form, establishing correspondences between the two frameworks at semantic, structural, and distributional levels. Leveraging tools from linear algebra and linear programming, the work formulates criteria for the existence and uniqueness of such model transformations, revealing how these conditions depend on model dimensionality. The analysis further elucidates the theoretical consequences of the transformation for causal semantics and the resulting probability distributions.

The Bayesian network (BN) learning domain suffers from an abundance of heterogeneous tools and a lack of standardized evaluation criteria, posing significant challenges for beginners in tool selection. Method: This paper introduces the first beginner-oriented BN tool evaluation framework, integrating software engineering assessment principles, functional comparative analysis, user requirement mapping, and structured tabular modeling to systematically evaluate over 30 mainstream BN tools. It innovatively combines subjective expert recommendations with an objective, standardized feature matrix. Contribution/Results: The framework yields a comprehensive, multi-dimensional comparison table—covering functionality, usability, extensibility, and other key attributes—as well as a tiered recommendation list. This work fills a critical gap in practice-oriented BN tool surveys, substantially lowering the entry barrier for newcomers, improving tool selection efficiency, and accelerating practical deployment.

Markov Chain Monte Carlo (MCMC) sampling for large-scale Bayesian network structure learning suffers from low efficiency, primarily due to the computational overhead of single-edge operations (addition, deletion, reversal) and exponential complexity in parent-set marginalization. Method: This paper proposes an efficient graph-structure sampling framework. Its core innovations are: (1) an O(1)-time single-edge operation implementation that avoids repeated topological sorting; and (2) a conditional independence–guided parent-set space pruning strategy that significantly reduces enumeration while preserving posterior approximation accuracy. Results: Experiments on multiple benchmark datasets demonstrate that the proposed method achieves 3–10× speedup over state-of-the-art algorithms (e.g., GES-MCMC, MC³), scales effectively to networks with up to one thousand nodes, and substantially improves both computational efficiency and scalability of Bayesian network structure posterior inference.

To address the challenge of calibrating conditional probability table (CPT) parameters in Bayesian networks under data-scarce conditions, this paper proposes a structured CPT refinement and approximation framework. We systematically evaluate existing structural simplification methods and design CPT parameter reduction strategies tailored to varying levels of domain expertise and observational data availability, integrating expert knowledge with limited empirical evidence to achieve substantial parameter compression. Innovatively, we develop an actionable CPT approximation selection guideline. Empirical validation in cardiovascular risk assessment demonstrates that our approach reduces parameter count by over 60% compared to conventional fully parametrized models, while significantly enhancing model constructibility and clinical applicability. This work establishes a new pathway for small-sample Bayesian modeling that balances theoretical rigor with engineering feasibility.

This work proposes a structure compression method for Bayesian networks that preserves the consistency of probabilistic inference while significantly reducing computational complexity. The key innovation lies in introducing a novel combinatorial construct termed the “directed convex hull,” and establishing, for the first time, its equivalence to minimally localized Bayesian networks. Building on this theoretical foundation, the authors design polynomial-time algorithms for constructing and simplifying such structures using directed acyclic graphs. Empirical evaluations on real-world networks demonstrate that the proposed approach substantially improves inference efficiency compared to conventional techniques such as variable elimination and belief propagation. The implementation has been made publicly available as open-source software.

This work addresses the computational intractability of probabilistic inference in high-dimensional Bayesian networks, which stems from the exponential complexity of their joint distributions. The authors propose a novel framework based on directed convex subgraph decomposition, introducing a minimal d-decomposition tree as an alternative to conventional junction trees. This structure decomposes the joint distribution into low-dimensional submodels that can be learned and stored independently. The approach inherently supports localized and parallelized inference, achieving substantial gains in computational efficiency while preserving inference accuracy—particularly advantageous for low-dimensional queries. The core contributions lie in an improved structural decomposition mechanism and highly efficient algorithms for parallel parameter estimation and inference.

Probabilistic updating—i.e., conditioning on evidence—in Bayesian networks and causal inference is typically non-compositional due to normalization, hindering modular modeling and graphical derivation. This work introduces a formal framework for probabilistic reasoning based on string diagrams, whose core innovation is the “shadow normalization box” and its deletion rule, enabling fully compositional implementation of conditioning via graphical rewriting. By decoupling normalization from structural decomposition, the approach preserves the natural embedding of Bayesian network topology and uniformly supports observational, interventional, and counterfactual queries. Experiments demonstrate that the framework substantially improves modularity and verifiability of inference workflows, providing the first compositional, rigorously founded, and graphically intuitive basis for causal modeling.

This work establishes a formal proof-theoretic foundation for Bayesian inference and provides a graphical, compositional representation thereof. By forging a novel connection between Bayesian networks and proof nets from linear logic—inspired by the Curry–Howard correspondence—it develops a framework that unifies semantic rigor with computational efficiency. The approach introduces a flexible graph decomposition mechanism alongside a type inference system, enabling efficient and modular probabilistic reasoning. The primary contribution lies in formulating a proof-theoretic semantics for Bayesian inference, thereby offering a new theoretical toolkit for probabilistic programming and compositional reasoning.

This study addresses the problem of reliably learning the structures of Markov networks and Bayesian networks when conditional independence tests are subject to bounded errors. The work proposes a fault-tolerant structure learning algorithm based on graph-theoretic analysis and constraint satisfaction, tailored for an independence oracle that may err but with a limited number of mistakes. The main contributions include establishing that Markov networks remain robustly identifiable under exponentially many errors when the number of vertex-disjoint paths is bounded, while demonstrating that Bayesian networks cannot tolerate arbitrary errors even under structural constraints such as bounded treewidth. Furthermore, under conditions ensuring unique identifiability, the paper provides an efficient learning algorithm for Markov networks and establishes their theoretical identifiability in the presence of numerous errors for specific graph structures.