发表机构
Graz University of Technology（格拉茨工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该论文第一部分研究概率电路（PCs）这一可处理框架，阐述其解决概率推理 NP 难问题的结构约束，涵盖其基础理论、学习方法、与深度学习集成等贡献，为人工智能不确定性推理提供支撑。
AI 中文摘要
本累积 habilitation 论文研究概率电路（Probabilistic Circuits，简称 PCs），将其作为人工智能（Artificial Intelligence，简称 AI）中不确定性下推理与学习的强大且可处理的框架。论文首先倡导概率作为 AI 的核心语言，强调其与逻辑和信息论的关联；概率推理的概念简洁性——主要基于求和与乘积规则；概率推理与人类认知的相似性；以及概率在最优决策制定中的作用。然而，概率也面临重大计算挑战，因为几乎所有概率模型中的概率推理都是 NP 难问题。PCs 通过结构约束解决这些挑战，确保在多项式时间内精确计算广泛的推理查询，如边缘概率、条件概率、最可能解释、期望以及更高级的推理任务。本论文综合了过去十年在 PCs 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：PCs 的基础理论、学习 PCs 的贝叶斯方法、可扩展实现及与深度学习的集成、将 PCs 与难处理模型结合的混合模型，以及与符号机器学习范式的关联。这是作者 habilitation 论文的第一部分，第二部分因包含论文的累积内容且已在不同 venues 发表（见第 5 章）而被省略。
英文摘要
This cumulative habilitation thesis studies probabilistic circuits (PCs) as a powerful and tractable framework for reasoning and learning under uncertainty in artificial intelligence (AI). It first advocates for probability as a core language for AI, emphasizing its connections to logic and information theory; the conceptual simplicity of probabilistic reasoning---based primarily on the sum and product rules; the parallels between probabilistic inference and human cognition; and the role of probability in optimal decision making. 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. 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. This is the first part of my Habilitation Thesis. The second part is omitted, as it comprises the cumulative part of the thesis and has been published at various venues (see Chapter 5).
CommentsHabilitation Thesis
