General upper bounds for well-behaving goodness measures on dependency rules

TL;DR

This paper demonstrates that various well-behaving goodness measures for dependency rules reach their maximum at the same points, enabling a unified search strategy across different measures.

Contribution

It introduces the concept of well-behaving goodness measures and proves their maxima coincide, simplifying the search process for dependency rules.

Findings

All well-behaving measures attain their maxima at the same points.

The concept extends to negative dependencies.

Common measures are shown to be well-behaving.

Abstract

In the search for statistical dependency rules, a crucial task is to restrict the search space by estimating upper bounds for the goodness of yet undiscovered rules. In this paper, we show that all well-behaving goodness measures achieve their maximal values in the same points. Therefore, the same generic search strategy can be applied with any of these measures. The notion of well-behaving measures is based on the classical axioms for any proper goodness measures, and extended to negative dependencies, as well. As an example, we show that several commonly used goodness measures are well-behaving.