一句话：提出高阶 λ-演算，可编译为贝叶斯网络，并给出精确、组合且考虑代价的语义。
论文研究如何为高阶概率模型提供精确且可组合的语义基础。作者提出一个以 λ-演算为理想形式的高阶概率编程语言，支持递归概率模型与层次结构；证明每个贝叶斯网络可编码为项，且任意（可能高阶、递归的）基类型程序都可编译为贝叶斯网络，从而建立语言与贝叶斯网络之间的可靠性与完备性。语义基于贝叶斯推断中的 factor，并显式跟踪代价。技术手段结合线性逻辑、交集类型、重写理论和 Girard 的 interaction 几何。结果给出精确推理的语义框架，而非近似推断。
Bayesian networks are graphical 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 higher-order programming language—in the idealized form of a λ -calculus—which we prove sound and complete w.r.t. Bayesian networks: each Bayesian network can be encoded as a term, and conversely each (possibly higher-order and recursive) program of ground type compiles into a Bayesian network. The language allows for the specification of recursive probability models and hierarchical structures. Moreover, we provide a compositional and 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.
@article{paperbot2647,
title = {Higher Order Bayesian Networks, Exactly},
author = {Claudia Faggian and Daniele Pautasso and Gabriele Vanoni},
journal = {Proceedings of the ACM on Programming Languages},
volume = {8},
number = {POPL},
year = {2024},
doi = {10.1145/3632926}
}