Approximate denial constraints

Abstract

The problem of mining integrity constraints from data has been extensively studied over the past two decades for commonly used types of constraints, including the classic Functional Dependencies (FDs) and the more general Denial Constraints (DCs). In this paper, we investigate the problem of mining from data approximate DCs, that is, DCs that are "almost" satisfied. Approximation allows us to discover more accurate constraints in inconsistent databases and detect rules that are generally correct but may have a few exceptions. It also allows to avoid overfitting and obtain constraints that are more general, more natural, and less contrived. We introduce the algorithm ADCMiner for mining approximate DCs. An important feature of this algorithm is that it does not assume any specific approximation function for DCs, but rather allows for arbitrary approximation functions that satisfy some natural axioms that we define in the paper. We also show how our algorithm can be combined with sampling to return highly accurate results considerably faster.