  We introduce a novel bias-variance decomposition for a range of strictly
convex margin losses, including the logistic loss (minimized by the classic
LogitBoost algorithm), as well as the squared margin loss and canonical
boosting loss. Furthermore, we show that, for all strictly convex margin
losses, the expected risk decomposes into the risk of a "central" model and a
term quantifying variation in the functional margin with respect to variations
in the training data. These decompositions provide a diagnostic tool for
practitioners to understand model overfitting/underfitting, and have
implications for additive ensemble models -- for example, when our
bias-variance decomposition holds, there is a corresponding "ambiguity"
decomposition, which can be used to quantify model diversity.
