What killed the Convex Booster ?

TL;DR

This paper revisits a classic negative result in supervised learning, identifying the model class as the true cause of failure rather than the loss or algorithm, and advocates for a broader perspective on parameterization issues.

Contribution

It extends Long and Servedio's findings by analyzing proper loss functions and introduces a new boosting algorithm, highlighting the impact of model class and parameterization.

Findings

The negative result is primarily due to the linear model class.

Proper loss functions for class probability estimation are insufficient to overcome the failure.

Parameterization plays a critical role in the success or failure of boosting algorithms.

Abstract

A landmark negative result of Long and Servedio established a worst-case spectacular failure of a supervised learning trio (loss, algorithm, model) otherwise praised for its high precision machinery. Hundreds of papers followed up on the two suspected culprits: the loss (for being convex) and/or the algorithm (for fitting a classical boosting blueprint). Here, we call to the half-century+ founding theory of losses for class probability estimation (properness), an extension of Long and Servedio's results and a new general boosting algorithm to demonstrate that the real culprit in their specific context was in fact the (linear) model class. We advocate for a more general stanpoint on the problem as we argue that the source of the negative result lies in the dark side of a pervasive -- and otherwise prized -- aspect of ML: \textit{parameterisation}.