Monads for Measurable Queries in Probabilistic Databases

TL;DR

This paper explores the use of monads in probabilistic databases to ensure measurable queries, extending previous results and providing a framework for probabilistic data generation.

Contribution

It introduces a monad-based approach to measurable queries in probabilistic databases and extends existing measurability results to more complex query languages.

Findings

Measurability of probabilistic database queries follows from monad-based formulations.

Extension of measurability results to fuller query languages.

Distributive law between probability and bag monads aids in probabilistic database generation.

Abstract

We consider a bag (multiset) monad on the category of standard Borel spaces, and show that it gives a free measurable commutative monoid. Firstly, we show that a recent measurability result for probabilistic database queries (Grohe and Lindner, ICDT 2020) follows quickly from the fact that queries can be expressed in monad-based terms. We also extend this measurability result to a fuller query language. Secondly, we discuss a distributive law between probability and bag monads, and we illustrate that this is useful for generating probabilistic databases.