Bayesian Performance Analysis for Algorithm Ranking Comparison

Presentation code for the paper: Bayesian Performance Analysis for Algorithm Ranking Comparison.

This repository contains the presentation code and tools used in the published paper. More recent versions can be found in:

• BayesPermus Package: https://github.com/ml-opt/BayesPermus
• Presentation code: https://github.com/ml-opt/BayesPermusPresentation

Abstract

In the field of optimization and machine learning, the statistical assessment of results has played a key role in conducting algorithmic performance comparisons. Classically, null hypothesis statistical tests have been used, however, recently, alternatives based on Bayesian statistics have shown great potential in complex scenarios, especially, when dealing with the uncertainty in the comparison.

In this work, we delve deep into the Bayesian statistical assessment of experimental results by proposing a framework for the analysis of several algorithms on several problems/instances. To this end, experimental results for each experiment are transformed to their corresponding rankings of algorithms assuming that these rankings have been generated by a probability distribution (defined on permutation spaces). From the set of rankings, we estimate the posterior distribution of the parameters of the probability models considered, and several inferences concerning the analysis of the results are analysed. Particularly, we study questions related to the probability of having one algorithm in the first position of the ranking or the probability that one algorithm is in the ranking before another. Not limited to that, the assumptions, strengths, and weaknesses of the models in each case are studied. Finally, we provide some guidelines for the authors to avoid the misuse of the presented analysis.