Bias-Variance Decompositions for Margin Losses

TL;DR

This paper develops a new bias-variance decomposition for strictly convex margin losses, offering insights into model behavior and ensemble diversity, with practical diagnostic implications for overfitting and underfitting.

Contribution

It introduces a novel bias-variance decomposition applicable to a range of convex margin losses, enhancing understanding of model risk and diversity.

Findings

Decomposition applies to logistic, squared, and canonical boosting losses.

Provides a diagnostic tool for overfitting and underfitting analysis.

Establishes a link between bias-variance and ensemble diversity.

Abstract

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.