In recent times, deep neural networks achieved outstanding predictive performance on various classification and pattern recognition tasks. However, many real-world prediction problems have ordinal response variables, and this ordering information is ignored by conventional classification losses such as the multi-category cross-entropy. Ordinal regression methods for deep neural networks address this. One such method is the CORAL method, which is based on an earlier binary label extension framework and achieves rank consistency among its output layer tasks by imposing a weight-sharing constraint. However, while earlier experiments showed that CORAL's rank consistency is beneficial for performance, it is limited by a weight-sharing constraint in a neural network's fully connected output layer, which may restrict the expressiveness and capacity of a network trained using CORAL. We propose a new method for rank-consistent ordinal regression without this limitation. Our rank-consistent ordinal regression framework (CORN) achieves rank consistency by a novel training scheme. This training scheme uses conditional training sets to obtain the unconditional rank probabilities through applying the chain rule for conditional probability distributions. Experiments on various datasets demonstrate the efficacy of the proposed method to utilize the ordinal target information, and the absence of the weight-sharing restriction improves the performance substantially compared to the CORAL reference approach. Additionally, the suggested CORN method is not tied to any specific architecture and can be utilized with any deep neural network classifier to train it for ordinal regression tasks.

翻译：近年来，深度神经网络在各种分类和模式识别任务中取得了卓越的预测性能。然而，许多实际预测问题涉及有序响应变量，而传统的分类损失函数（如多类别交叉熵）忽略了这一排序信息。针对深度神经网络的有序回归方法旨在解决这一问题。其中CORAL方法基于早期二元标签扩展框架，通过施加权重共享约束实现输出层任务的秩一致性。但早期实验表明，尽管CORAL的秩一致性有利于性能提升，其神经网络全连接输出层中的权重共享约束可能限制CORAL训练网络的表达能力和容量。我们提出了一种无此限制的新型秩一致有序回归方法。我们的秩一致有序回归框架（CORN）通过新颖的训练方案实现秩一致性：该方案利用条件训练集，通过链式法则应用于条件概率分布，从而获得无条件秩概率。多数据集实验表明，所提方法能有效利用有序目标信息，且消除权重共享约束显著提升了相比CORAL参考方法的性能。此外，CORN方法不依赖特定架构，可与任何深度神经网络分类器结合用于有序回归任务。