Non-Parametric Class Completeness Estimators for Collaborative Knowledge Graphs -- The Case of Wikidata

Collaborative Knowledge Graph platforms allow humans and automated scripts to collaborate in creating, updating and interlinking entities and facts. To ensure both the completeness of the data as well as a uniform coverage of the different topics, it is crucial to identify underrepresented classes in the Knowledge Graph. In this paper, we tackle this problem by developing statistical techniques for class cardinality estimation in collaborative Knowledge Graph platforms. Our method is able to estimate the completeness of a class - as defined by a schema or ontology - hence can be used to answer questions such as "Does the knowledge base have a complete list of all {Beer Brands|Volcanos|Video Game Consoles}?" As a use-case, we focus on Wikidata, which poses unique challenges in terms of the size of its ontology, the number of users actively populating its graph, and its extremely dynamic nature. Our techniques are derived from species estimation and data-management methodologies, and are applied to the case of graphs and collaborative editing. In our empirical evaluation, we observe that i) the number and frequency of unique class instances drastically influence the performance of an estimator, ii) bursts of inserts cause some estimators to overestimate the true size of the class if they are not properly handled, and iii) one can effectively measure the convergence of a class towards its true size by considering the stability of an estimator against the number of available instances.