Evaluating State-of-the-Art Classification Models Against Bayes Optimality
This provides a method for establishing absolute benchmarks in classification, which is important for researchers and practitioners to gauge progress and model performance.
The paper tackles the problem of evaluating classification models by computing the exact Bayes error using generative models learned with normalizing flows, finding that state-of-the-art models achieve accuracy near optimal in some cases and assessing the intrinsic hardness of benchmark datasets.
Evaluating the inherent difficulty of a given data-driven classification problem is important for establishing absolute benchmarks and evaluating progress in the field. To this end, a natural quantity to consider is the \emph{Bayes error}, which measures the optimal classification error theoretically achievable for a given data distribution. While generally an intractable quantity, we show that we can compute the exact Bayes error of generative models learned using normalizing flows. Our technique relies on a fundamental result, which states that the Bayes error is invariant under invertible transformation. Therefore, we can compute the exact Bayes error of the learned flow models by computing it for Gaussian base distributions, which can be done efficiently using Holmes-Diaconis-Ross integration. Moreover, we show that by varying the temperature of the learned flow models, we can generate synthetic datasets that closely resemble standard benchmark datasets, but with almost any desired Bayes error. We use our approach to conduct a thorough investigation of state-of-the-art classification models, and find that in some -- but not all -- cases, these models are capable of obtaining accuracy very near optimal. Finally, we use our method to evaluate the intrinsic "hardness" of standard benchmark datasets, and classes within those datasets.