Classifier risk analysis under Bayesian uncertainty models

There are a number of important small-sample phenotype discrimination problems in biomedicine, typically based on classifying between types of pathology, stages of disease, response to treatment or survivability. In contrast to the usual heuristic classifier and error estimation rules, recent work proposes a Bayesian modeling framework over an uncertainty class of feature-label distributions, which when combined with data facilitates optimal MMSE error estimation, optimal classifier design and sample-conditioned MSE error estimation analysis. To date, this theory has only been formulated relative to the basic misclassification rate for simple binary classification problems. Here, we extend Bayesian classifier learning theory to a risk based analysis over multiple classes, which is often more sensible in medical applications.