ANCHOR: Abductive Network Construction with Hierarchical Orchestration for Reliable Probability Inference in Large Language Models

A central challenge in large-scale decision-making under incomplete information is estimating reliable probabilities. Recent approaches leverage Large Language Models (LLMs) to generate explanatory factors and elicit coarse-grained probability estimates. Typically, an LLM performs forward abduction to propose factors, each paired with two mutually exclusive attributes, and a Naïve Bayes model is trained over factor combinations to refine the final probabilities. However, sparse factor spaces often yield ``unknown'' outcomes, while expanding factors increases noise and spurious correlations, weakening conditional independence and degrading reliability. To address these limitations, we propose \textsc{Anchor}, an inference framework that orchestrates aggregated Bayesian inference over a hierarchically structured factor space. \textsc{Anchor} first constructs a dense and organized factor space via iterative generation and hierarchical clustering. It then performs context-aware mapping through hierarchical retrieval and refinement, substantially reducing ``unknown'' predictions. Finally, \textsc{Anchor} augments Naïve Bayes with a Causal Bayesian Network to capture latent dependencies among factors, relaxing the strict independence assumption. Experiments show that \textsc{Anchor} markedly reduces ``unknown'' predictions and produces more reliable probability estimates than direct LLM baselines, achieving state-of-the-art performance while significantly reducing time and token overhead.