In real world applications of multiclass classification models, misclassification in an important class (e.g., stop sign) can be significantly more harmful than in other classes (e.g., no parking). Thus, it is crucial to improve the recall of an important class while maintaining overall accuracy. For this problem, we found that improving the separation of important classes relative to other classes in the feature space is effective. Existing methods that give a class-sensitive penalty for cross-entropy loss do not improve the separation. Moreover, the methods designed to improve separations between all classes are unsuitable for our purpose because they do not consider the important classes. To achieve the separation, we propose a loss function that explicitly gives loss for the feature space, called class-sensitive additive angular margin (CAMRI) loss. CAMRI loss is expected to reduce the variance of an important class due to the addition of a penalty to the angle between the important class features and the corresponding weight vectors in the feature space. In addition, concentrating the penalty on only the important class hardly sacrifices separating the other classes. Experiments on CIFAR-10, GTSRB, and AwA2 showed that CAMRI loss could improve the recall of a specific class without sacrificing accuracy. In particular, compared with GTSRB's second-worst class recall when trained with cross-entropy loss, CAMRI loss improved recall by 9%.

Software defect prediction (SDP) plays a vital role in allocating testing resources reasonably and ensuring software quality. When there are not enough labeled historical modules, considerable semi-supervised SDP methods have been proposed, and these methods utilize limited labeled modules and abundant unlabeled modules simultaneously. Nevertheless, most of them make use of traditional features rather than the powerful deep feature representations. Besides, the cost of the misclassification of the defective modules is higher than that of defect-free ones, and the number of the defective modules for training is small. Taking the above issues into account, we propose a cost-sensitive and sparse ladder network (CSLN) for SDP. We firstly introduce the semi-supervised ladder network to extract the deep feature representations. Besides, we introduce the cost-sensitive learning to set different misclassification costs for defective-prone and defect-free-prone instances to alleviate the class imbalance problem. A sparse constraint is added on the hidden nodes in ladder network when the number of hidden nodes is large, which enables the model to find robust structures of the data. Extensive experiments on the AEEEM dataset show that the CSLN outperforms several state-of-the-art semi-supervised SDP methods.

We extend the framework of cost-sensitive classification to mitigate risks of huge costs occurring with low probabilities, and propose an algorithm that achieves this goal. Instead of minimizing the expected cost commonly used in cost-sensitive learning, our algorithm minimizes conditional value-at-risk, also known as expected shortfall, which is considered a good risk metric in the area of financial engineering. The proposed algorithm is a general meta-learning algorithm that can exploit existing example-dependent cost-sensitive learning algorithms, and is capable of dealing with not only alternative actions in ordinary classification tasks, but also allocative actions in resource-allocation type tasks. Experiments on tasks with example-dependent costs show promising results.