概率电路：人工智能中的推理机器（第一部分）
文章背景与核心概要
本文档是 Robert Peharz 教授资格论文的第一部分，旨在探讨概率电路（Probabilistic Circuits, PCs）作为一种稳健且易于处理的框架，如何解决人工智能中不确定性环境下的推理与学习问题。
概率论为人工智能提供了一种概念上简洁且自然的语言，与逻辑学、信息论及人类认知深度关联。然而，传统的概率推理通常面临 NP-hard 的计算瓶颈。概率电路通过引入特定的结构约束，成功克服了这一障碍，实现了包括边缘概率、条件概率、最大后验概率及期望值在内的多种推理查询的精确多项式时间计算。
该论文总结了作者过去十年的研究成果，涵盖了概率电路的基础理论、贝叶斯学习方法、可扩展的深度学习集成、混合模型以及与符号机器学习的联系。
概率电路：人工智能中的推理机器（第一部分）
摘要
本文档介绍了 Robert Peharz 教授资格论文的第一部分，探讨了概率电路（PCs）作为人工智能（AI）中处理不确定性推理与学习的一种强大且易于处理的框架。本文首先倡导将概率论作为 AI 的核心语言，强调其与逻辑学和信息论的联系；概率推理在概念上的简洁性（主要基于求和与乘积规则）；概率推理与人类认知之间的相似性；以及概率在最优决策中的作用。
This document presents the first part of a cumulative habilitation thesis by Robert Peharz, exploring Probabilistic Circuits (PCs) as a robust, tractable framework for reasoning and learning under uncertainty in Artificial Intelligence (AI).
While probability provides a natural, conceptually simple language for AI—sharing deep connections with logic, information theory, human cognition, and optimal decision-making—it traditionally suffers from severe computational limitations (probabilistic inference is typically NP-hard). Probabilistic Circuits overcome this hurdle by employing specific structural constraints. These constraints allow for the exact, polynomial-time computation of diverse inference queries, including marginals, conditionals, most probable explanations, and expectations.
Synthesizing a decade of research, this thesis covers foundational theory, Bayesian learning approaches, scalable deep learning integrations, hybrid models, and connections to symbolic machine learning.
然而，概率论也面临着巨大的计算挑战，因为在几乎所有的概率模型中，概率推理都是 NP-hard 的。概率电路通过结构约束解决了这些挑战，确保了在多项式时间内精确计算各种推理查询，例如边缘概率、条件概率、最大后验概率、期望值以及更高级的推理任务。
However, probability also faces significant computational challenges, as probabilistic inference is NP-hard in almost all probabilistic models. PCs address these challenges through structural constraints that ensure exact computation of a wide range of inference queries in polynomial time, such as marginals, conditionals, most probable explanations, expectations, and more advanced inference tasks.
本论文综合了过去十年在概率电路的基础理论、算法开发和实证验证方面的研究。本工作强调的关键贡献包括：概率电路的基础理论、学习概率电路的贝叶斯方法、可扩展的实现及其与深度学习的集成、将概率电路与难以处理的模型相结合的混合模型，以及与符号机器学习范式的联系。
This thesis synthesizes a decade of research across foundations, algorithmic developments, and empirical validation of PCs. Key contributions highlighted in this work are foundational theory of PCs, Bayesian approaches for learning PCs, scalable implementations and integration with deep learning, hybrid models that combine PCs with intractable models, and connections with symbolic machine learning paradigms.
（注：这是教授资格论文的第一部分。第二部分包含已发表文章的累积合集，此处省略。）
(Note: This is the first part of the Habilitation Thesis. The second part comprises the cumulative collection of published articles and has been omitted here.)
文档元数据
- arXiv ID: arXiv:2608.16565 [cs.AI]
- DOI: 10.48550/arXiv.2608.16565
- 作者: Robert Peharz
- 提交日期: 2026年8月17日
- 学科: 人工智能 (
cs.AI); 机器学习 (cs.LG); 概率论 (math.PR) - 备注: 教授资格论文
- arXiv ID: arXiv:2608.16565 [cs.AI]
- DOI: 10.48550/arXiv.2608.16565
- Author: Robert Peharz
- Submitted: August 17, 2026
- Subjects: Artificial Intelligence (
cs.AI); Machine Learning (cs.LG); Probability (math.PR)- Comments: Habilitation Thesis
