Abstract
We consider a framework for taking into consideration the relative importance (ordinality) of object labels in the process of learning a label predictor function. The commonly used loss functions are not well matched to this problem, as they exhibit deficiencies in capturing natural correlations of the labels and the corresponding data. We propose to incorporate such correlations into our learning algorithm using an optimal transport formulation. Our approach is to learn the ground metric, which is partly involved in forming the optimal transport distance, by leveraging ordinality as a general form of side information in its formulation. Based on this idea, we then develop a novel loss function for training deep neural networks. A highly efficient alternating learning method is then devised to alternatively optimise the ground metric and the deep model in an end-to-end learning manner. This scheme allows us to adaptively adjust the shape of the ground metric, and consequently the shape of the loss function for each application. We back up our approach by theoretical analysis and verify the performance of our proposed scheme by applying it to two learning tasks, i.e. chronological age estimation from the face and image aesthetic assessment. The numerical results on several benchmark datasets demonstrate the superiority of the proposed algorithm.