  In regression tasks, aleatoric uncertainty is commonly addressed by
considering a parametric distribution of the output variable, which is based on
strong assumptions such as symmetry, unimodality or by supposing a restricted
shape. These assumptions are too limited in scenarios where complex shapes,
strong skews or multiple modes are present. In this paper, we propose a generic
deep learning framework that learns an Uncountable Mixture of Asymmetric
Laplacians (UMAL), which will allow us to estimate heterogeneous distributions
of the output variable and shows its connections to quantile regression.
Despite having a fixed number of parameters, the model can be interpreted as an
infinite mixture of components, which yields a flexible approximation for
heterogeneous distributions. Apart from synthetic cases, we apply this model to
room price forecasting and to predict financial operations in personal bank
accounts. We demonstrate that UMAL produces proper distributions, which allows
us to extract richer insights and to sharpen decision-making.
