# Modelling heterogeneous distributions with an Uncountable Mixture of Asymmetric Laplacians

arXiv: https://arxiv.org/abs/1910.12288 · HTML: https://mlsanity.com/paper/1910.12288/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Oct 2019.

## Built on by (most cited first, 9 of 9)

- [Gluformer: Transformer-Based Personalized Glucose Forecasting with Uncertainty Quantification](https://mlsanity.com/paper/2209.04526/) (2022)
- [Deep Non-Crossing Quantiles through the Partial Derivative](https://mlsanity.com/paper/2201.12848/) (2022)
- [Distributional Learning of Variational AutoEncoder: Application to Synthetic Data Generation](https://mlsanity.com/paper/2302.11294/) (2023)
- [Retrospective Uncertainties for Deep Models using Vine Copulas](https://mlsanity.com/paper/2302.12606/) (2023)
- [Learning Proposals for Practical Energy-Based Regression](https://mlsanity.com/paper/2110.11948/) (2021)
- [Adaptive Conditional Quantile Neural Processes](https://mlsanity.com/paper/2305.18777/) (2023)
- [Improving Uncertainty Quantification of Variance Networks by Tree-Structured Learning](https://mlsanity.com/paper/2212.12658/) (2022)
- [Uncertainty Surrogates for Deep Learning](https://mlsanity.com/paper/2104.08147/) (2021)
- [On Feature Diversity in Energy-based Models](https://mlsanity.com/paper/2306.01489/) (2023)

## Abstract (arXiv)

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.