B1659
Title: Linear discriminant analysis with label noise
Authors: Timothy Cannings - University of Edinburgh (United Kingdom) [presenting]
Abstract: The effect of label noise in linear discriminant analysis is investigated. The main goal is to derive the minimax rate of convergence in this problem, where our results capture the explicit dependence of the minimax rate on all of the key parameters in the model. Our theory reveals a delicate interplay between the level of separation between the class conditional distributions (as measured by the Mahalanobis distance), the proportion of the training data points that are labelled incorrectly, as well as the dimension of the feature space and training sample size. Somewhat surprisingly, applying the vanilla approach to linear discriminant analysis is suboptimal in several regimes under label noise. We, therefore, introduce a new approach to classification in this setting, based on higher-order moment estimators and the midhinge estimator, which is rate optimal in all regimes.
