Classification with minimum expected error over an uncertainty class of Gaussian distributions

In biomedicine, it is typical to find studies discriminating between types of pathology or stages of disease based on as few as 30 sample points and tens of thousands of genes. Unfortunately, out-of-the-box classification and error estimation rules come with no small-sample performance guarantees, which has greatly contributed to the crisis in biomarker reproducibility. Recent work addresses this by supplementing the data with expert biological knowledge via a prior distribution over an uncertainty class of feature-label distributions, and uses the resulting probabilistic framework to define minimum mean-square-error (MMSE) estimators for the misclassification rate of any fixed classifier, as well as the sample-conditioned MSE itself for arbitrary error estimators. Here, we use the same framework to also define minimum expected error (MEE) classifiers, completing a Bayesian optimized theory of classification. We also present examples on real genomic data resulting in classifiers that greatly outperform popular rules.