Technical Perspective

The paper entitled "Probabilistic Data with Continuous Distributions" overviews recent work on the foundations of infinite probabilistic databases [3, 2]. Prior work on probabilistic databases (PDBs) focused almost exclusively on the finite case: A finite PDB represents a discrete probability distribution over a finite set of possible worlds [4]. In contrast, an infinite PDB models a continuous probability distribution over an infinite set of possible worlds. In both cases, each world is a finite relational database instance. Continuous distributions are essential and commonplace tools for reasoning under uncertainty in practice. Accommodating them in the framework of probabilistic databases brings us closer to applications that naturally rely on both continuous distributions and relational databases.

Probabilistic Data with Continuous Distributions

Statistical models of real world data typically involve continuous probability distributions such as normal, Laplace, or exponential distributions. Such distributions are supported by many probabilistic modelling formalisms, including probabilistic database systems. Yet, the traditional theoretical framework of probabilistic databases focuses entirely on finite probabilistic databases. Only recently, we set out to develop the mathematical theory of infinite probabilistic databases. The present paper is an exposition of two recent papers which are cornerstones of this theory. In (Grohe, Lindner; ICDT 2020) we propose a very general framework for probabilistic databases, possibly involving continuous probability distributions, and show that queries have a well-defined semantics in this framework. In (Grohe, Kaminski, Katoen, Lindner; PODS 2020) we extend the declarative probabilistic programming language Generative Datalog, proposed by (B´ar´any et al. 2017) for discrete probability distributions, to continuous probability distributions and show that such programs yield generative models of continuous probabilistic databases.