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

Modelling heterogeneous distributions with an Uncountable Mixture of Asymmetric Laplacians