Probabilistic Data with Continuous Distributions

ACM SIGMOD Record, vol. 50, pp. 69–76

Abstract

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.

Authors 4

1. Martin Grohe Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Germany

   RWTH Aachen University (Germany)

2. Benjamin Lucien Kaminski

   University College London

   Affiliation as printed

   University College London, London, United Kingdom

3. Joost-Pieter Katoen Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Germany

   RWTH Aachen University (Germany)

4. Peter Lindner Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Germany

   RWTH Aachen University (Germany)