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

Abstract: A central challenge in large-scale decision-making under incomplete information is estimating reliable probabilities. Recent approaches leverage 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 reducingunknown'' 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.