Probabilistic databases (PDBs) provide users with a principled way to query data that is incomplete or imprecise. In this work, we study computing expected multiplicities of query results over probabilistic databases under bag semantics which has PTIME data complexity. However, does this imply that bag probabilistic databases are practical? We strive to answer this question from both a theoretical as well as a systems perspective. We employ concepts from fine-grained complexity to demonstrate that exact bag probabilistic query processing is fundamentally less efficient than deterministic bag query evaluation, but that fast approximations are possible by sampling monomials from a circuit representation of a result tuple's lineage. A remaining issue, however, is that constructing such circuits, while in PTIME, can nonetheless have significant overhead. To avoid this cost, we utilize approximate query processing techniques to directly sample monomials without materializing lineage upfront. Our implementation in FastPDB provides accurate anytime approximation of probabilistic query answers and scales to datasets orders of magnitude larger than competing methods.

Incomplete and probabilistic database techniques are principled methods for coping with uncertainty in data. Unfortunately, the class of queries that can be answered efficiently over such databases is severely limited, even when advanced approximation techniques are employed.We introduce attribute-annotated uncertain databases (AU-DBs), an uncertain data model that annotates tuples and attribute values with bounds to compactly approximate an incomplete database. AU-DBs are closed under relational algebra with aggregation using an efficient evaluation semantics. Using optimizations that trade accuracy for performance, our approach scales to complex queries and large datasets, and produces accurate results.

Certain answers are a principled method for coping with uncertainty that arises in many practical data management tasks. Unfortunately, this method is expensive and may ex- clude useful (if uncertain) answers. Thus, users frequently resort to less principled approaches to resolve uncertainty. In this paper, we propose Uncertainty Annotated Databases (UA-DBs), which combine an under- and over-approximation of certain answers to achieve the reliability of certain answers, with the performance of a classical database system. Furthermore, in contrast to prior work on certain answers, UA-DBs achieve a higher utility by including some (explicitly marked) answers that are not certain. UA-DBs are based on incomplete K-relations, which we introduce to generalize the classical set-based notion of incomplete databases and certain answers to a much larger class of data models. Using an implementation of our approach, we demonstrate experimentally that it efficiently produces tight approximations of certain answers that are of high utility.