Li Wanhua ; Huang Xiaoke ; Lu Jiwen ; Feng Jianjiang ; Zhou Jie

Abstract

Uncertainty is the only certainty there is. Modeling data uncertainty isessential for regression, especially in unconstrained settings. Traditionallythe direct regression formulation is considered and the uncertainty is modeledby modifying the output space to a certain family of probabilisticdistributions. On the other hand, classification based regression and rankingbased solutions are more popular in practice while the direct regressionmethods suffer from the limited performance. How to model the uncertaintywithin the present-day technologies for regression remains an open issue. Inthis paper, we propose to learn probabilistic ordinal embeddings whichrepresent each data as a multivariate Gaussian distribution rather than adeterministic point in the latent space. An ordinal distribution constraint isproposed to exploit the ordinal nature of regression. Our probabilistic ordinalembeddings can be integrated into popular regression approaches and empowerthem with the ability of uncertainty estimation. Experimental results show thatour approach achieves competitive performance. Code is available athttps://github.com/Li-Wanhua/POEs.