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Open knowledge, including open data and publicly available knowledge bases, offers a rich opportunity for data scientists for analysis and query answering, but comes with big obstacles due to the diverse, noisy, and incomplete nature of its data eco-system. This paper proposes a vision for enabling approximate QUery answering over Open Knowledge (Quok), with a focus on supporting analytic tasks that involve identifying relevant data and computing aggregations. We define the problem, outline a system architecture, and discuss challenges and approaches to taming the uncertainty and incompleteness of open knowledge. 

We study the top-k set similarity search problem using semantic overlap. While vanilla overlap requires exact matches between set elements, semantic overlap allows elements that are syntactically different but semantically related to increase the overlap. The semantic overlap is the maximum matching score of a bipartite graph, where an edge weight between two set elements is defined by a user-defined similarity function, e.g., cosine similarity between embeddings. Common techniques like token indexes fail for semantic search since similar elements may be unrelated at the character level. Further, verifying candidates is expensive (cubic versus linear for syntactic overlap), calling for highly selective filters. We propose Koios, the first exact and efficient algorithm for semantic overlap search. Koios leverages sophisticated filters to minimize the number of required graph-matching calculations. Our experiments show that for medium to large sets less than 5% of the candidate sets need verification, and more than half of those sets are further pruned without requiring the expensive graph matching. We show the efficiency of our algorithm on four real datasets and demonstrate the improved result quality of semantic over vanilla set similarity search. 

Acyclic schemes have numerous applications in databases and in machine learning, such as improved design, more efficient storage, and increased performance for queries and ma- chine learning algorithms. Multivalued dependencies (MVDs) are the building blocks of acyclic schemes. The discovery from data of both MVDs and acyclic schemes is more challenging than other forms of data dependencies, such as Functional Dependencies, because these dependencies do not hold on subsets of data, and because they are very sensitive to noise in the data; for example a single wrong or missing tuple may invalidate the schema. In this paper we present Maimon, a system for discovering approximate acyclic schemes and MVDs from data. We give a principled definition of approximation, by using notions from information theory, then describe the two components of Maimon: mining for approximate MVDs, then reconstructing acyclic schemes from approximate MVDs. We conduct an experimental evaluation of Maimon on 20 real-world datasets, and show that it can scale up to 1M rows, and up to 30 columns.