Set-valued Classification with Out-of-distribution Detection for Many Classes

Set-valued classification, a new classification paradigm that aims to identify all the plau-sible classes that an observation belongs to, improves over the traditional classification paradigms in multiple aspects. Existing set-valued classification methods do not consider the possibility that the test set may contain out-of-distribution data, that is, the emergence of a new class that never appeared in the training data. Moreover, they are computation-ally expensive when the number of classes is large. We propose a Generalized Prediction Set (GPS) approach to set-valued classification while considering the possibility of a new class in the test data. The proposed classifier uses kernel learning and empirical risk mini-mization to encourage a small expected size of the prediction set while guaranteeing that the class-specific accuracy is at least some value specified by the user. For high-dimensional data, further improvement is obtained through kernel feature selection. Unlike previous methods, the proposed method achieves a good balance between accuracy, efficiency, and out-of-distribution detection rate. Moreover, our method can be applied in parallel to all the classes to alleviate the computational burden. Both theoretical analysis and numerical experiments are conducted to illustrate the effectiveness of the proposed method.