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The Bayes error rate (BER) is a fundamental concept in machine learning thatquantifies the best possible accuracy any classifier can achieve on a fixedprobability distribution. Despite years of research on building estimators oflower and upper bounds for the BER, these were usually compared only onsynthetic datasets with known probability distributions, leaving two keyquestions unanswered: (1) How well do they perform on real-world datasets?, and(2) How practical are they? Answering these is not trivial. Apart from theobvious challenge of an unknown BER for real-world datasets, there are two mainaspects any BER estimator needs to overcome in order to be applicable inreal-world settings: (1) the computational and sample complexity, and (2) thesensitivity and selection of hyper-parameters. In this work, we propose FeeBee,the first principled framework for analyzing and comparing BER estimators onany modern real-world dataset with unknown probability distribution. We achievethis by injecting a controlled amount of label noise and performing multipleevaluations on a series of different noise levels, supported by a theoreticalresult which allows drawing conclusions about the evolution of the BER. Byimplementing and analyzing 7 multi-class BER estimators on 6 commonly useddatasets of the computer vision and NLP domains, FeeBee allows a thorough studyof these estimators, clearly identifying strengths and weaknesses of each,whilst being easily deployable on any future BER estimator.

Evaluating Bayes Error Estimators on Real-World Datasets with FeeBee