On the Usability of Probably Approximately Correct Implication Bases

TL;DR

This paper explores the use of probably approximately correct implication bases within formal concept analysis, assessing their practicality as substitutes for exact bases through quantitative and qualitative analysis.

Contribution

It introduces a formalization of probably approximately correct implication bases in formal concept analysis and evaluates their effectiveness on various data sets.

Findings

Probably approximately correct bases have comparable precision and recall to exact bases.

Implication bases from this approach can still capture meaningful knowledge.

Quantitative analysis shows potential for practical applications.

Abstract

We revisit the notion of probably approximately correct implication bases from the literature and present a first formulation in the language of formal concept analysis, with the goal to investigate whether such bases represent a suitable substitute for exact implication bases in practical use-cases. To this end, we quantitatively examine the behavior of probably approximately correct implication bases on artificial and real-world data sets and compare their precision and recall with respect to their corresponding exact implication bases. Using a small example, we also provide qualitative insight that implications from probably approximately correct bases can still represent meaningful knowledge from a given data set.