Genetic Algorithms for Tractable Bayesian Network Fusion via Pre-Fusion Edge Pruning

Bayesian Network (BN) fusion combines multiple input networks into a single structure, balancing dependency preservation with computational tractability. While unrestricted fusion retains all dependencies, it often results in overly complex networks with high treewidth, which affects inference scalability. Limited fusion mitigates this by pruning edges to control treewidth but risks overfitting to input-specific noise and omitting dependencies from the original BNs. This paper introduces a consensus framework that prioritizes shared structures among input networks while enforcing treewidth constraints, ensuring a good consensus. We propose genetic algorithms with advanced initialization, specialized operators, and a tailored fitness function. Additionally, we adapt existing methods to this problem and implement greedy baselines for benchmarking and further optimization. Experiments on synthetic and real-world BNs show the superiority of the proposed genetic algorithms over the adapted methods and greedy baselines.

LLM-Augmented Causal Discovery: Probabilistic Fusion of Edge Existence and Orientation

Bayesian network structure learning (BNSL) from observational data struggles with orientation identifiability, while large language models (LLMs) offer broad but often unreliable causal knowledge. We propose combining these complementary sources through a novel representation, termed Probabilistic Dependency Graphs (PDGs). In a PDG, each edge is associated with a distribution over directed, undirected, and absent states, enabling fusion via weighted averaging. We evaluate this approach on 26 benchmark networks, combining ensembles of three BNSL algorithms (FGES, Tabu, PC) with three LLMs (Gemini, Claude, GPT) across multiple prompts and random seeds. A simple 50/50 fusion improves F1 over the better of either source alone in 22 of 26 networks, with a statistically significant mean improvement of $0.056$ $(p<0.001)$. Analysis reveals that the two sources play complementary roles: BNSL contributes a high-recall edge skeleton (80\% vs 60\% for LLM), while LLM contributes accurate edge orientation (96\% vs 77\% for BNSL). Our results show that representing both sources as probabilistic uncertainty over edge existence and orientation is a practical and effective way to improve causal graph accuracy.

From probability to causality in probabilistic logic programming

Probabilistic logic programming is a formalism of statistical relational artificial intelligence that supports causal queries, including interventions from outside the system. When the structure of a probabilistic logic program is learned from data, however, only probabilistic information is used, and a single probability distribution may be compatible with several causal orders. This leads to ambiguity in interventional reasoning, raising the question of when the causal order is uniquely determined by the distribution. Exploiting the relationship between acyclic probabilistic logic programs and Bayesian networks, we derive conditions under which the probabilistic information encoded in a program determines a unique causal order. We also incorporate constraints arising from relational structure by taking into account prescribed sets of causal symmetries induced by the underlying relational vocabulary. The result is a method for verifying when a learned probabilistic logic program supports well-defined intervention semantics.

Human AI Construction of Bayesian Networks for Operational Decision Support -- A Virtual Survey Approach

Bayesian Belief Networks (BBNs) are powerful tools for decision-making under uncertainty. However, building their structures and estimating parameters are difficult. Currently, researchers must choose between relying on expert judgement or using large datasets to learn the structure and parameters of the network. We propose a new methodology using Large Language Models to bridge the gap between expert opinion and data-driven learning. This approach uses a panel of AI agents to estimate probabilities based on specific personas and context. We then apply a trimmed-mean rule to remove noise from these responses. We develop a six step BBN framework and illustrate it to model customer intention to consult a doctor in an alternative healthcare system. The model reveals that while self efficacy appears to be a major factor, its actual causal impact is small. In contrast, subjective norms have a much stronger effect in modelling customers' intention. The most effective strategy is to improve both confidence and community norms simultaneously.

Decomposition for Bayesian Networks: Local and Parallel Inference

Probabilistic inference in high-dimensional Bayesian networks is difficult because exact manipulation of the joint distribution scales exponentially with network size. We propose a decomposition framework based on directed convex subgraphs and introduce a minimal d-decomposition tree. Together, they provide a principled alternative to classical junction-tree constructions. The proposed framework represents the joint distribution by lower-dimensional sub-models that can be learned and stored separately. This decomposition reduces computational cost and naturally enables parallel computation. Based on a minimal d-decomposition tree, we further develop two parallel algorithms for parameter estimation and probabilistic inference. Experiments show that the proposed method substantially improves computational efficiency over junction-tree methods while maintaining inference accuracy, especially for low-dimensional queries.

Causal Atlases from Entropic Inference: Bayesian Networks beyond Optimal DAGs

Data-driven causal relationship identification is pertinent to advancing understanding of complex systems both within and beyond science. Bayesian networks offer a probabilistic method for modelling generic causal relationships via directed acyclic graphs (DAGs). However, typical techniques for constructing Bayesian networks rely on optimization, which can be ill-suited for learning causal relationships because the underlying data may admit multiple chains of causation. More data-faithful representations of causal relationships would provide frameworks for constructing multiple causal maps that are consistent with the variability that is inherent in underlying data. Here, we show that entropy-based inference generates atlases of plausible causal relationships that are consistent with underlying data. On simulated noisy data of 2- and 20-node linear structural equation models, we sample a maximum-entropy ensemble of graphs that allow us to quantify the inherent structural ambiguity in underlying causal relationships. Our method shows that "optimized" DAGs can contain causal artifacts are not consistent across equivalently accurate topologies.