Learning Probabilistic Ordinal Embeddings for Uncertainty-Aware Regression

Uncertainty is the only certainty there is. Modeling data uncertainty is essential for regression, especially in unconstrained settings. Traditionally the direct regression formulation is considered and the uncertainty is modeled by modifying the output space to a certain family of probabilistic distributions. On the other hand, classification based regression and ranking based solutions are more popular in practice while the direct regression methods suffer from the limited performance. How to model the uncertainty within the present-day technologies for regression remains an open issue. In this paper, we propose to learn probabilistic ordinal embeddings which represent each data as a multivariate Gaussian distribution rather than a deterministic point in the latent space. An ordinal distribution constraint is proposed to exploit the ordinal nature of regression. Our probabilistic ordinal embeddings can be integrated into popular regression approaches and empower them with the ability of uncertainty estimation. Experimental results show that our approach achieves competitive performance. Code is available at https://github.com/Li-Wanhua/POEs .