近似交换性下的提升模型构建
Lifted Model Construction under Approximate Commutativity
- Institute for Humanities-Centered Artificial Intelligence, University of Hamburg（汉堡大学人文中心人工智能研究所）
- Data Science Group, University of Münster（明斯特大学数据科学组）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对实际中因子仅近似交换的问题，提出ε-交换性概念并将其用于提升模型构建，证明了诱导近似误差的严格界，实验显示其可在更低运行时间下达到相当的查询准确率。
AI中文摘要：
提升推理算法通过利用概率分布中对象的不可区分性，即使对于大型对象域也能实现可扩展的概率推理。构建提升表示的一个必要前提是在基于势的因子分解中识别交换因子，即其输出值在输入值子集的排列下保持不变的函数。然而在实践中，即使关联对象不可区分，从数据中学习到的参数也不可避免地会出现偏差，导致对应的因子仅为近似交换而非完全交换。我们通过引入ε-交换性的概念来解决这一问题，它是交换性的一种松弛形式，其中输出值仅在输入值子集的排列下近似不变。具体而言，我们展示了如何将ε-交换性应用于提升模型构建、下游概率推理，并证明了诱导近似误差的严格界，从而在保持高度准确查询结果的同时确保提升模型构建的实用性。这些理论保证通过实验得到验证，表明在更低的运行时间下可达到相当的查询准确率。
英文摘要：
Lifted inference algorithms enable scalable probabilistic inference even for large object domains by leveraging the indistinguishability of objects in a probability distribution. An essential prerequisite for constructing a lifted representation is to identify commutative factors, i.e., functions whose output values are invariant under permutations of a subset of their input values, in a potential-based factorisation. In practice, however, parameters learned from data inevitably deviate even if associated objects are indistinguishable, causing their corresponding factors to be only approximately commutative instead of being exactly commutative. We address this problem by introducing the concept of ε-commutativity, a relaxation of commutativity where output values are only approximately invariant under permutations of input values. Specifically, we show how ε-commutativity can be exploited for lifted model construction, downstream probabilistic inference, and prove strict bounds on the induced approximation error, thereby ensuring the practical applicability of lifted model construction while maintaining highly accurate query results. These theoretical guarantees are confirmed empirically, demonstrating comparable query accuracy at lower runtime.
