Surrogate regret bounds for generalized classification performance metrics
This work addresses the challenge of directly optimizing complex performance metrics in binary and multilabel classification, which is important for practitioners in machine learning, though it is incremental as it builds on existing surrogate loss frameworks.
The paper tackles the problem of optimizing generalized classification metrics like Fβ-measure and Jaccard coefficient by using surrogate losses, showing that the regret with respect to the target metric is bounded by the surrogate loss regret. It extends results to multilabel classification and includes computational validation on synthetic and real datasets.
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 $F_β$-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 $\widehatθ$ 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 $\widehatθ$) 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.