Unimodal regularisation based on beta distribution for deep ordinal regression

Currently, the use of deep learning for solving ordinal classification problems, where categories follow a natural order, has not received much attention. In this paper, we propose an unimodal regularisation based on the beta distribution applied to the cross-entropy loss. This regularisation encourages the dis-tribution of the labels to be a soft unimodal distribution, more appropriate for ordinal problems. Given that the beta distribution has two parameters that must be adjusted, a method to automatically deter-mine them is proposed. The regularised loss function is used to train a deep neural network model with an ordinal scheme in the output layer. The results obtained are statistically analysed and show that the combination of these methods increases the performance in ordinal problems. Moreover, the proposed beta distribution performs better than other distributions proposed in previous works, achieving also a reduced computational cost. (c) 2021 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )