Binary classification with pFDR-pFNR losses

Connecting multiple testing with binary classification, we derive a false discovery rate-based classification approach for two-class mixture models, where the available data (represented as feature vectors) for each individual comparison take values in Rd for some d≥1 and may exhibit certain forms of autocorrelation. This generalizes previous findings for the independent case in dimension d=1. Two resulting classification procedures are described which allow for incorporating prior knowledge about class probabilities and for user-supplied weighting of the severity of misclassifying a member of the "0"-class as "1" and vice versa. The key mathematical tools to be employed are multivariate estimation methods for probability density functions or density ratios. We compare the two algorithms with respect to their theoretical properties and with respect to their performance in practice. Computer simulations indicate that they can both successfully be applied to autocorrelated time series data with moving average structure. Our approach was inspired and its practicability will be demonstrated by applications from the field of brain-computer interfacing and the processing of electroencephalography data.