Learning to Benchmark: Determining Best Achievable Misclassification Error from Training Data
This work provides a more precise benchmarking tool for evaluating classifier performance, though it is incremental as it builds on existing methods for error estimation.
The paper tackles the problem of estimating the Bayes misclassification error rate directly from training data without constructing an optimal classifier, achieving a parametric mean squared error rate of O(N^{-1}) and showing improved accuracy over prior methods in experiments.
We address the problem of learning to benchmark the best achievable classifier performance. In this problem the objective is to establish statistically consistent estimates of the Bayes misclassification error rate without having to learn a Bayes-optimal classifier. Our learning to benchmark framework improves on previous work on learning bounds on Bayes misclassification rate since it learns the {\it exact} Bayes error rate instead of a bound on error rate. We propose a benchmark learner based on an ensemble of $ε$-ball estimators and Chebyshev approximation. Under a smoothness assumption on the class densities we show that our estimator achieves an optimal (parametric) mean squared error (MSE) rate of $O(N^{-1})$, where $N$ is the number of samples. Experiments on both simulated and real datasets establish that our proposed benchmark learning algorithm produces estimates of the Bayes error that are more accurate than previous approaches for learning bounds on Bayes error probability.