高阶贝叶斯网络，精确版（扩展版）
Higher-Order Bayesian Networks, Exactly (Extended version)
AI总结：
本文提出一种可编译为贝叶斯网络的高阶λ演算语言，证明其可靠且完备，并给出基于因子的组合式成本感知语义。
摘要：
贝叶斯网络（BN）是图形化的一阶概率模型，能够紧凑表示大型概率分布，并支持精确与近似的高效推理。我们引入一种高阶编程语言——以λ演算的理想化形式呈现——并证明其相对于BN是可靠且完备的：每个BN都可编码为一个项，反之，每个基类型的（可能是高阶且递归的）程序都可编译为一个BN。该语言支持规范递归概率模型和层次结构。此外，我们提供了一种基于因子的组合式、成本感知语义；因子是贝叶斯推理中使用的标准数学工具。我们的结果依赖于源于线性逻辑、交集类型、重写理论和Girard交互几何的先进技术，并在此以新颖方式将其结合。
英文摘要：
Bayesian networks (BNs) are graphical \emph{first-order} probabilistic models that allow for a compact representation of large probability distributions, and for efficient inference, both exact and approximate. We introduce a \emph{higher-order} programming language -- in the idealized form of a $λ$-calculus -- which we prove \emph{sound and complete} w.r.t. BNs: each BN can be encoded as a term, and conversely each (possibly higher-order and recursive) program of ground type \emph{compiles} into a BN. The language allows for the specification of recursive probability models and hierarchical structures. Moreover, we provide a \emph{compositional} and \emph{cost-aware} semantics which is based on factors, the standard mathematical tool used in Bayesian inference. Our results rely on advanced techniques rooted into linear logic, intersection types, rewriting theory, and Girard's geometry of interaction, which are here combined in a novel way.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
