Classification Asymptotics in the Random Matrix Regime

This article discusses the asymptotic performance of classical machine learning classification methods (from discriminant analysis to neural networks) for simultaneously large and numerous Gaussian mixture modelled data. We first provide theoretical bounds on the minimally discriminable class means and covariances under an oracle setting, which are then compared to recent theoretical findings on the performance of machine learning. Non-obvious phenomena are discussed, among which surprising phase transitions in the optimal performance rates for specific hyperparameter settings.