An Empirical Study of MAUC in Multi-class Problems with Uncertain Cost Matrices

Cost-sensitive learning relies on the availability of a known and fixed cost matrix. However, in some scenarios, the cost matrix is uncertain during training, and re-train a classifier after the cost matrix is specified would not be an option. For binary classification, this issue can be successfully addressed by methods maximizing the Area Under the ROC Curve (AUC) metric. Since the AUC can measure performance of base classifiers independent of cost during training, and a larger AUC is more likely to lead to a smaller total cost in testing using the threshold moving method. As an extension of AUC to multi-class problems, MAUC has attracted lots of attentions and been widely used. Although MAUC also measures performance of base classifiers independent of cost, it is unclear whether a larger MAUC of classifiers is more likely to lead to a smaller total cost. In fact, it is also unclear what kinds of post-processing methods should be used in multiclass problems to convert base classifiers into discrete classifiers such that the total cost is as small as possible. In the paper, we empirically explore the relationship between MAUC and the total cost of classifiers by applying two categories of postprocessing methods. Our results suggest that a larger MAUC is also beneficial. Interestingly, simple calibration methods that convert the output matrix into posterior probabilities perform better than existing sophisticated post re-optimization methods. Keywords-AUC; MAUC; multi-class classification; costsensitive learning;