On Constrained Open-World Probabilistic Databases

Abstract

Increasing amounts of available data have led to a heightened need for representing large-scale probabilistic knowledge bases. One approach is to use a probabilistic database, a model with strong assumptions that allow for efficiently answering many interesting queries. Recent work on openworld probabilistic databases strengthens the semantics of these probabilistic databases by discarding the assumption that any information not present in the data must be false. While intuitive, these semantics are not sufficiently precise to give reasonable answers to queries. We propose overcoming these issues by using constraints to restrict this open world. We provide an algorithm for one class of queries, and establish a basic hardness result for another. Finally, we propose an efficient and tight approximation for a large class of queries.

Collaborative Policy Learning for Open Knowledge Graph Reasoning

“…(Shi and Weninger, 2018) defines an Open World KG Completion problem, in which they complete the KG with unseen entities. (Friedman and Broeck, 2019) introduces the Open-World Probabilistic Databases, an analogy to KGs. Unlike our setting, they try to complete the KG with logical inferences without extra information.…”

Open-world probabilistic databases: Semantics, algorithms, complexity

“…One way of excluding spurious possible worlds, and limiting the probability mass of open atoms is by using an additional knowledge representation layer towards more informative probability bounds [75]. An alternative way is to define schema-level constraints on the probability space, ensuring more informative bounds [78]. Our study focuses on finite domains, which may not be satisfactory in every application domain, which motivated an extension to infinite universes [79].…”

“…Work in probabilistic logic programming has studied their complexity for different semantics, including credal semantics [77]. OpenPDBs also motivated further research to extend the open-world probabilistic database model to have schema-level constraints on completion probabilities [78]. OpenPDBs are defined over a finite domain, and the work of Grohe and Lindner [79] extends the open-world probabilistic database model to infinite universes.…”

Closed-Form Results for Prior Constraints in Sum-Product Networks

“…Incorporating constraints is a major concern in data mining and probabilistic machine learning (Raedt et al, 2010;Kisa et al, 2014;Friedman and Van den Broeck, 2019). A wide variety of problems require the prediction to be integrated with reasoning about various forms of constraints, ranging from constraining the support of a distribution, such as when modeling routes on maps (Shen et al, 2018;Xu et al, 2018), to enforcing certain independence relationships, such as when approving loan predictions (Mahoney and Mohen, 2007).…”