A Generalized Backward Compatibility Metric

Retraining a classifier with new data is inseparable from ML/AI applications, but most of the existing ML methods do not take into account the backward compatibility of predictions. That is, although the overall performance of a new classifier is improved, users will be confused by the wrong predictions of the new classifier, especially when the predictions of the old classifier are correct for the same samples. To this end, several metrics and learning methods for backward compatibility have been actively studied recently. Despite significant interest in backward compatibility, the metrics and methods are not well known from a theoretical perspective. In this paper, we first analyze the existing backward compatibility metrics and reveal that these metrics essentially assess the same quantity between old and new models. In addition, to obtain a unified view of backward compatibility metrics, we propose a generalized backward compatibility (GBC) metric that can represent the existing backward compatibility metrics. We formulate a learning objective based on the GBC metric and derive the estimation error bound, and the result is applied to one of the existing methods. Through further analysis, we reveal that the existing backward compatibility metrics are not suitable for imbalanced classification. We then design a backward compatibility metric for imbalanced classification on the basis of the GBC metric and empirically demonstrate the practicality of the proposed metric.