Distribution-based Bayesian Minimum Expected Risk for Discriminant Analysis

This paper considers a distribution-based Bayesian estimation for classification by quadratic discriminant analysis, instead of the standard parameter-based Bayesian estimation. This approach also yields closed form solutions, but removes the parameter-based restriction of requiring more training samples than feature dimensions. We investigate how to define a prior so that it has an adaptively regularizing effect: yielding robust estimation when the number of training samples are small compared to the number of feature dimensions, but converging as the number of data points grows large. Comparative performance on a suite of simulations shows that the distribution-based Bayesian discriminant analysis is advantageous in terms of average error