The Consistency of Probabilistic Databases with Independent Cells

TL;DR

This paper investigates the computational complexity of ensuring consistency in probabilistic databases with attribute-level uncertainty, focusing on functional dependencies and related problems.

Contribution

It provides a comprehensive classification of the complexity of key problems related to constraint satisfaction in probabilistic databases with functional dependencies.

Findings

Decides the satisfiability of constraints in probabilistic databases.

Identifies tractable and intractable cases for various classes of dependencies.

Analyzes the probability computation of constraint satisfaction.

Abstract

A probabilistic database with attribute-level uncertainty consists of relations where cells of some attributes may hold probability distributions rather than deterministic content. Such databases arise, implicitly or explicitly, in the context of noisy operations such as missing data imputation, where we automatically fill in missing values, column prediction, where we predict unknown attributes, and database cleaning (and repairing), where we replace the original values due to detected errors or violation of integrity constraints. We study the computational complexity of problems that regard the selection of cell values in the presence of integrity constraints. More precisely, we focus on functional dependencies and study three problems: (1) deciding whether the constraints can be satisfied by any choice of values, (2) finding a most probable such choice, and (3) calculating the probability of satisfying the constraints. The data complexity of these problems is determined by the combination of the set of functional dependencies and the collection of uncertain attributes. We give full classifications into tractable and intractable complexities for several classes of constraints, including a single dependency, matching constraints, and unary functional dependencies.