Bias-Variance Decompositions for Margin Losses
This work offers a theoretical framework for practitioners to analyze model behavior in machine learning, particularly for additive ensemble models, though it appears incremental as it extends existing decomposition concepts to margin losses.
The authors introduced a novel bias-variance decomposition for strictly convex margin losses, such as logistic loss, and showed that expected risk decomposes into a central model risk and a term for functional margin variation, providing a diagnostic tool for understanding overfitting/underfitting.
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.