Discovering Reliable Dependencies from Data: Hardness and Improved Algorithms

TL;DR

This paper examines the computational difficulty of discovering dependencies using the reliable fraction of information, proves NP-hardness, and introduces improved algorithms with better pruning and empirical performance.

Contribution

It establishes the NP-hardness of dependency discovery with the reliable fraction of information and proposes enhanced algorithms with superior pruning and efficiency.

Findings

NP-hardness of the dependency discovery problem

A novel admissible bounding function improves pruning

Greedy algorithm yields competitive results faster

Abstract

The reliable fraction of information is an attractive score for quantifying (functional) dependencies in high-dimensional data. In this paper, we systematically explore the algorithmic implications of using this measure for optimization. We show that the problem is NP-hard, which justifies the usage of worst-case exponential-time as well as heuristic search methods. We then substantially improve the practical performance for both optimization styles by deriving a novel admissible bounding function that has an unbounded potential for additional pruning over the previously proposed one. Finally, we empirically investigate the approximation ratio of the greedy algorithm and show that it produces highly competitive results in a fraction of time needed for complete branch-and-bound style search.