Heuristic Algorithms for the Approximation of Mutual Coherence

TL;DR

This paper introduces heuristic algorithms to efficiently approximate mutual coherence, a measure of opinion similarity, by modeling confirmation values with Gaussian mixtures, significantly reducing computation time while maintaining high accuracy.

Contribution

It presents the first methods to accelerate mutual coherence computation using Gaussian mixture modeling and heuristics, including polynomial-time algorithms and SAT problem approximations.

Findings

Average squared error below 0.0035

Algorithms are efficient and suitable for Wahl-O-Mat systems

Some algorithms are fully polynomial-time

Abstract

Mutual coherence is a measure of similarity between two opinions. Although the notion comes from philosophy, it is essential for a wide range of technologies, e.g., the Wahl-O-Mat system. In Germany, this system helps voters to find candidates that are the closest to their political preferences. The exact computation of mutual coherence is highly time-consuming due to the iteration over all subsets of an opinion. Moreover, for every subset, an instance of the SAT model counting problem has to be solved which is known to be a hard problem in computer science. This work is the first study to accelerate this computation. We model the distribution of the so-called confirmation values as a mixture of three Gaussians and present efficient heuristics to estimate its model parameters. The mutual coherence is then approximated with the expected value of the distribution. Some of the presented algorithms are fully polynomial-time, others only require solving a small number of instances of the SAT model counting problem. The average squared error of our best algorithm lies below 0.0035 which is insignificant if the efficiency is taken into account. Furthermore, the accuracy is precise enough to be used in Wahl-O-Mat-like systems.