  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.
