🤖 AI Summary
Existing ordinal regression methods typically employ standard cross-entropy loss, disregarding the inherent ordinal structure among class labels; moreover, prevailing unimodality modeling strategies lack theoretical foundations and rely on heuristic designs.
Method: This paper systematically characterizes the geometric structure of unimodal distributions within the probability simplex for the first time, proposes a theory-driven loss term based on set projection, and designs an end-to-end unimodal neural network architecture. The method strictly constrains predicted distributions to the unimodal set via differentiable projection, enabling efficient optimization.
Contribution/Results: On multiple benchmark datasets, the proposed architecture achieves top-2 performance. The new loss significantly outperforms state-of-the-art baselines while maintaining high unimodality—establishing the first theoretically grounded unimodal modeling paradigm for ordinal regression.
📝 Abstract
In many real-world prediction tasks, class labels contain information about the relative order between labels that are not captured by commonly used loss functions such as multicategory cross-entropy. Recently, the preference for unimodal distributions in the output space has been incorporated into models and loss functions to account for such ordering information. However, current approaches rely on heuristics that lack a theoretical foundation. Here, we propose two new approaches to incorporate the preference for unimodal distributions into the predictive model. We analyse the set of unimodal distributions in the probability simplex and establish fundamental properties. We then propose a new architecture that imposes unimodal distributions and a new loss term that relies on the notion of projection in a set to promote unimodality. Experiments show the new architecture achieves top-2 performance, while the proposed new loss term is very competitive while maintaining high unimodality.
