Modelling heterogeneous distributions with an Uncountable Mixture of Asymmetric Laplacians

TL;DR

This paper introduces UMAL, a deep learning framework that models complex, heterogeneous output distributions in regression tasks by learning an uncountable mixture of asymmetric Laplacians, improving uncertainty estimation.

Contribution

The paper proposes a novel deep learning approach, UMAL, capable of modeling complex output distributions as an uncountable mixture, extending beyond traditional parametric assumptions.

Findings

UMAL accurately models complex, multimodal distributions.

The approach improves uncertainty quantification in real-world tasks.

UMAL outperforms existing methods in distribution estimation.

Abstract

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.