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SHARQ: Explainability Framework for Association Rules on Relational Data

Hadar Ben-Efraim, Susan B. Davidson, Amit Somech

TL;DR

This paper tackles the explainability gap for association rules mined from relational data by introducing SHARQ, a Shapley-value-based measure of an element's contribution to a rule set. It presents SHARQ*, an exact, efficient algorithm for a single element with near-linear scalability in the number of rules, and a multi-element SHARQ* that amortizes computation across many elements. The framework enables element importance, rule importance, and attribute importance, with extensive experiments on 45 rule-set instances demonstrating significant speedups and meaningful element rankings over naive or baseline approaches. Overall, SHARQ provides a principled, scalable approach to understanding and pruning rule sets, with practical implications for rule-based data exploration and feature analysis.

Abstract

Association rules are an important technique for gaining insights over large relational datasets consisting of tuples of elements (i.e. attribute-value pairs). However, it is difficult to explain the relative importance of data elements with respect to the rules in which they appear. This paper develops a measure of an element's contribution to a set of association rules based on Shapley values, denoted SHARQ (ShApley Rules Quantification). As is the case with many Shapely-based computations, the cost of a naive calculation of the score is exponential in the number of elements. To that end, we present an efficient framework for computing the exact SharQ value of a single element whose running time is practically linear in the number of rules. Going one step further, we develop an efficient multi-element SHARQ algorithm which amortizes the cost of the single element SHARQ calculation over a set of elements. Based on the definition of SHARQ for elements we describe two additional use cases for association rules explainability: rule importance and attribute importance. Extensive experiments over a novel benchmark dataset containing 45 instances of mined rule sets show the effectiveness of our approach.

SHARQ: Explainability Framework for Association Rules on Relational Data

TL;DR

This paper tackles the explainability gap for association rules mined from relational data by introducing SHARQ, a Shapley-value-based measure of an element's contribution to a rule set. It presents SHARQ*, an exact, efficient algorithm for a single element with near-linear scalability in the number of rules, and a multi-element SHARQ* that amortizes computation across many elements. The framework enables element importance, rule importance, and attribute importance, with extensive experiments on 45 rule-set instances demonstrating significant speedups and meaningful element rankings over naive or baseline approaches. Overall, SHARQ provides a principled, scalable approach to understanding and pruning rule sets, with practical implications for rule-based data exploration and feature analysis.

Abstract

Association rules are an important technique for gaining insights over large relational datasets consisting of tuples of elements (i.e. attribute-value pairs). However, it is difficult to explain the relative importance of data elements with respect to the rules in which they appear. This paper develops a measure of an element's contribution to a set of association rules based on Shapley values, denoted SHARQ (ShApley Rules Quantification). As is the case with many Shapely-based computations, the cost of a naive calculation of the score is exponential in the number of elements. To that end, we present an efficient framework for computing the exact SharQ value of a single element whose running time is practically linear in the number of rules. Going one step further, we develop an efficient multi-element SHARQ algorithm which amortizes the cost of the single element SHARQ calculation over a set of elements. Based on the definition of SHARQ for elements we describe two additional use cases for association rules explainability: rule importance and attribute importance. Extensive experiments over a novel benchmark dataset containing 45 instances of mined rule sets show the effectiveness of our approach.

Paper Structure

This paper contains 23 sections, 1 theorem, 15 equations, 6 figures, 6 tables, 2 algorithms.

Table of Contents

  1. introduction
  2. Contributions
  3. Outline
  4. SHARQ Model & Problem definition
  5. Model and definitions
  6. The SHARQ Formula
  7. Efficient SHARQ Algorithms
  8. Improved Formula: $SHARQ{}^{*}$
  9. The $SHARQ{}^{*}$ Algorithm (Single Element)
  10. Cost Analysis
  11. Multi-Element $SHARQ{}^{*}$ Algorithm
  12. Rules Explainability Use Cases
  13. SHARQ Element Importance
  14. Rule Importance: Detecting Redundancy
  15. Rules-driven Attribute Importance
  16. ...and 8 more sections

Key Result

Proposition 3.1

$\forall e \in E$ , $SHARQ^*_{(E ,{}{}{} , R)}(e) = SHARQ_{(E ,{}{}{} , R)}(e)$

Figures (6)

  • Figure 1: Example SHARQ scores alongside rules statistics , using rules mined from the Adult adults_dataset dataset.
  • Figure 2: R-SHARQ rule score examples.
  • Figure 3: A-SHARQ attribute importance scores
  • Figure 4: Comparison of naive and optimized approaches
  • Figure 5: Comparison between multi-element and sequential approaches
  • ...and 1 more figures

Theorems & Definitions (5)

  • Example 1.1
  • Example 1.2
  • Example 1.3
  • Example 2.1
  • Proposition 3.1