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

TL;DR

ANCHOR is a hierarchical Bayesian inference framework that improves probability estimation reliability in large language models by reducing unknown predictions and modeling factor dependencies.

Contribution

It introduces a novel hierarchical factor construction and causal modeling approach to enhance probability inference in LLMs, outperforming existing methods.

Findings

Reduces unknown predictions in probability estimates.

Achieves state-of-the-art performance with less computational overhead.

Improves reliability of probability estimates in large language models.

Abstract

A central challenge in large-scale decision-making under incomplete information is estimating reliable probabilities. Recent approaches use Large Language Models (LLMs) to generate explanatory factors and coarse-grained probability estimates, which are then refined by a Na\"ive Bayes model over factor combinations. However, sparse factor spaces often yield ``unknown'' predictions, while expanding factors increases noise and spurious correlations, weakening conditional independence and degrading reliability. To address these limitations, we propose \textsc{Anchor}, an aggregated Bayesian inference framework over a hierarchical factor space. It constructs dense factor hierarchies through iterative generation and clustering, maps contexts via hierarchical retrieval and refinement, and augments Na\"ive Bayes with a Causal Bayesian Network to model latent factor dependencies. 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.