A Log-linear Gradient Descent Algorithm for Unbalanced Binary Classification using the All Pairs Squared Hinge Loss

TL;DR

This paper introduces a new gradient descent algorithm for unbalanced binary classification that efficiently optimizes the squared hinge loss, enabling larger batch sizes and improved AUC performance on imbalanced datasets.

Contribution

The authors present a novel functional representation of the squared hinge loss that reduces gradient computation time to linear or log-linear, facilitating large batch training.

Findings

Achieves higher test AUC on imbalanced datasets

Enables use of larger batch sizes in training

Provides faster gradient computation for squared hinge loss

Abstract

Receiver Operating Characteristic (ROC) curves are plots of true positive rate versus false positive rate which are used to evaluate binary classification algorithms. Because the Area Under the Curve (AUC) is a constant function of the predicted values, learning algorithms instead optimize convex relaxations which involve a sum over all pairs of labeled positive and negative examples. Naive learning algorithms compute the gradient in quadratic time, which is too slow for learning using large batch sizes. We propose a new functional representation of the square loss and squared hinge loss, which results in algorithms that compute the gradient in either linear or log-linear time, and makes it possible to use gradient descent learning with large batch sizes. In our empirical study of supervised binary classification problems, we show that our new algorithm can achieve higher test AUC values on imbalanced data sets than previous algorithms, and make use of larger batch sizes than were previously feasible.