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由缺失机制支配的含缺失值数据库

Databases with Missing Values that are Governed by Missingness Mechanisms

Leopoldo Bertossi, Farouk Toumani

arXiv 2609.26692首次发表:更新:

发表机构

Carleton University; IMFD, Chile; LIMOS, CNRS, Clermont Auvergne University(卡尔顿大学; 智利IMFD; 克莱蒙奥弗涅大学CNRS LIMOS)

机构由 AI 辅助整理,请以论文原文为准。

AI 中文总结

本文提出用贝叶斯网络建模缺失机制,为含缺失值的关系数据库赋予语义,构建块独立概率数据库,并识别两个最优可能世界类别以支持查询,同时给出计算可行性与复杂性分析。

AI 中文摘要

我们解决了为具有缺失值(MVs)的关系数据库(RDB)赋予语义的问题。缺失值的原因由缺失机制支配,该机制被建模为一个贝叶斯网络(BN),其中数据库属性作为变量。该贝叶斯网络被称为缺失图(MG)。我们的方法在很大程度上不同于对带有NULL(值)的关系数据库的处理方式。缺失图与观测到的数据库的结合使我们能够构建一个块独立概率数据库。我们确定了其可能世界的两个最优类别,在这些类别上可以执行查询应答(QA)。这两个类别共同捕捉了缺失值隐式插补的概率不确定性和统计合理性。我们获得了计算某些最优类别的易处理性结果;同时,我们也获得了刻画我们方法计算可行性的复杂性结果。

英文摘要

We address the problems of giving a semantics to a relational database (RDB) that has missing values (MVs). The causes for the latter are governed by a Missingness Mechanism that is modelled as a Bayesian Network (BN) that involves the DB attributes as variables. The BN is called a Missingness Graph (MG). Our approach considerable departs from the treatment of RDBs with NULL (values). The combination of the MG and the observed DB allows us to build a block-independent probabilistic DB. We identify two optimal classes of its possible worlds on which QA can be performed. Those classes jointly capture probabilistic uncertainty and statistical plausibility of the implicit imputation of MVs. We obtain tractability results for the computation of some optimal classes; and we also obtain complexity results that characterize the computational feasibility of our approach.

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