Surrogate regret bounds for generalized classification performance metrics

TL;DR

This paper establishes theoretical bounds linking surrogate loss minimization to the optimization of complex binary classification metrics, providing a framework for improving performance measures like F-measure and Jaccard similarity.

Contribution

It introduces a two-step procedure with regret bounds for generalized metrics, extending analysis to multilabel classification and averaging measures.

Findings

Regret of the classifier is bounded by surrogate loss regret.

Theoretical guarantees hold for multilabel and averaging metrics.

Empirical results validate the theoretical bounds.

Abstract

We consider optimization of generalized performance metrics for binary classification by means of surrogate losses. We focus on a class of metrics, which are linear-fractional functions of the false positive and false negative rates (examples of which include $F_{\beta}$-measure, Jaccard similarity coefficient, AM measure, and many others). Our analysis concerns the following two-step procedure. First, a real-valued function $f$ is learned by minimizing a surrogate loss for binary classification on the training sample. It is assumed that the surrogate loss is a strongly proper composite loss function (examples of which include logistic loss, squared-error loss, exponential loss, etc.). Then, given $f$, a threshold $\widehat{\theta}$ is tuned on a separate validation sample, by direct optimization of the target performance metric. We show that the regret of the resulting classifier (obtained from thresholding $f$ on $\widehat{\theta}$) measured with respect to the target metric is upperbounded by the regret of $f$ measured with respect to the surrogate loss. We also extend our results to cover multilabel classification and provide regret bounds for micro- and macro-averaging measures. Our findings are further analyzed in a computational study on both synthetic and real data sets.