用大模型自动生成符合数学要求的先验分布，解决贝叶斯建模中先验设定难的问题。
LLM-Prior: A Framework for Knowledge-Driven Prior Elicitation and Aggregation
- 将自然语言等非结构化信息通过大模型转为可计算的概率分布
- 构建基于LLM的混合密度网络，保证先验满足数学合理性
- 支持多智能体分布式先验聚合，适用于异构数据场景
先验分布的设定是贝叶斯推断的基础，但通常依赖人工、主观且难以扩展。本文提出一种新框架——LLMPrior，利用大语言模型（LLM）自动化和规模化该过程。我们设计了 exttt{LLMPrior}这一原则性算子，可将自然语言描述、数据或图表等非结构化上下文转化为有效且可计算的概率分布。该算子通过将LLM与显式可计算的生成模型（如高斯混合模型）架构耦合，形成基于LLM的混合密度网络，确保生成的先验具备基本数学性质。进一步地，我们将框架扩展至多智能体系统，采用对数意见池化方法聚合由分散知识诱导的先验分布。提出联邦先验聚合算法 exttt{Fed-LLMPrior}，可在应对智能体异质性的前提下，鲁棒地聚合分布式的、上下文相关的先验。本工作为降低复杂贝叶斯建模门槛提供了新工具基础。
原文摘要 · Abstract (English)
The specification of prior distributions is fundamental in Bayesian inference, yet it remains a significant bottleneck. The prior elicitation process is often a manual, subjective, and unscalable task. We propose a novel framework which leverages Large Language Models (LLMs) to automate and scale this process. We introduce \texttt{LLMPrior}, a principled operator that translates rich, unstructured contexts such as natural language descriptions, data or figures into valid, tractable probability distributions. We formalize this operator by architecturally coupling an LLM with an explicit, tractable generative model, such as a Gaussian Mixture Model (forming a LLM based Mixture Density Network), ensuring the resulting prior satisfies essential mathematical properties. We further extend this framework to multi-agent systems where Logarithmic Opinion Pooling is employed to aggregate prior distributions induced by decentralized knowledge. We present the federated prior aggregation algorithm, \texttt{Fed-LLMPrior}, for aggregating distributed, context-dependent priors in a manner robust to agent heterogeneity. This work provides the foundation for a new class of tools that can potentially lower the barrier to entry for sophisticated Bayesian modeling.
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