Computational Efficient Approximations of the Concordance Probability in a Big Data Setting

TL;DR

This paper introduces two fast and accurate approximation methods for computing the concordance probability, applicable to large datasets and both discrete and continuous responses, significantly reducing computational time.

Contribution

The paper proposes novel estimation techniques that efficiently approximate the concordance probability in big data settings, improving speed without sacrificing accuracy.

Findings

Estimation methods perform well in simulations.

Methods are computationally efficient for large datasets.

Real data experiments confirm simulation results.

Abstract

Performance measurement is an essential task once a statistical model is created. The Area Under the receiving operating characteristics Curve (AUC) is the most popular measure for evaluating the quality of a binary classifier. In this case, AUC is equal to the concordance probability, a frequently used measure to evaluate the discriminatory power of the model. Contrary to AUC, the concordance probability can also be extended to the situation with a continuous response variable. Due to the staggering size of data sets nowadays, determining this discriminatory measure requires a tremendous amount of costly computations and is hence immensely time consuming, certainly in case of a continuous response variable. Therefore, we propose two estimation methods that calculate the concordance probability in a fast and accurate way and that can be applied to both the discrete and continuous setting. Extensive simulation studies show the excellent performance and fast computing times of both estimators. Finally, experiments on two real-life data sets confirm the conclusions of the artificial simulations.