When Analytic Calculus Cracks AdaBoost Code

TL;DR

This paper critically analyzes AdaBoost's implementation, revealing it as a logical combination of weak classifiers rather than an optimization process, and provides an analytical formula for the exact classifier weights.

Contribution

It demonstrates that AdaBoost can be explicitly calculated using a truth table and introduces a system to find the true risk minimum, challenging the conventional understanding of AdaBoost.

Findings

AdaBoost weights can be explicitly derived from a truth table.

The scikit-learn implementation does not follow the original AdaBoost algorithm.

A new method computes the exact risk minimum for AdaBoost classifiers.

Abstract

The principle of boosting in supervised learning involves combining multiple weak classifiers to obtain a stronger classifier. AdaBoost has the reputation to be a perfect example of this approach. This study analyzes the (two classes) AdaBoost procedure implemented in scikit-learn. This paper shows that AdaBoost is an algorithm in name only, as the resulting combination of weak classifiers can be explicitly calculated using a truth table. Indeed, using a logical analysis of the training set with weak classifiers constructing a truth table, we recover, through an analytical formula, the weights of the combination of these weak classifiers obtained by the procedure. We observe that this formula does not give the point of minimum of the risk, we provide a system to compute the exact point of minimum and we check that the AdaBoost procedure in scikit-learn does not implement the algorithm described by Freund and Schapire.