# Deep Distribution Regression

arXiv: https://arxiv.org/abs/1903.06023 · HTML: https://mlsanity.com/paper/1903.06023/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Mar 2019.

## Built on by (most cited first, 16 of 16)

- [Machine learning methods for postprocessing ensemble forecasts of wind gusts: A systematic comparison](https://mlsanity.com/paper/2106.09512/) (2021)
- [A review of predictive uncertainty estimation with machine learning](https://mlsanity.com/paper/2209.08307/) (2022)
- [A review of machine learning concepts and methods for addressing challenges in probabilistic hydrological post-processing and forecasting](https://mlsanity.com/paper/2206.08998/) (2022)
- [Multivariate Probabilistic Regression with Natural Gradient Boosting](https://mlsanity.com/paper/2106.03823/) (2021)
- [Aggregating distribution forecasts from deep ensembles](https://mlsanity.com/paper/2204.02291/) (2022)
- [Deconvolutional Density Network: Modeling Free-Form Conditional Distributions](https://mlsanity.com/paper/2105.14367/) (2021)
- [An Efficient Model-Agnostic Approach for Uncertainty Estimation in Data-Restricted Pedometric Applications](https://mlsanity.com/paper/2409.11985/) (2024)
- [Bivariate DeepKriging for Large-scale Spatial Interpolation of Wind Fields](https://mlsanity.com/paper/2307.08038/) (2023)
- [Density Regression and Uncertainty Quantification with Bayesian Deep Noise Neural Networks](https://mlsanity.com/paper/2206.05643/) (2022)
- [Deep Modeling of Non-Gaussian Aleatoric Uncertainty](https://mlsanity.com/paper/2405.20513/) (2024)
- [Masked Language Modeling Becomes Conditional Density Estimation for Tabular Data Synthesis](https://mlsanity.com/paper/2405.20602/) (2024)
- [Distributional Refinement Network: Distributional Forecasting via Deep Learning](https://mlsanity.com/paper/2406.00998/) (2024)
- [Probabilistic Modeling of Disparity Uncertainty for Robust and Efficient Stereo Matching](https://mlsanity.com/paper/2412.18703/) (2024)
- [Efficient and Scalable Estimation of Distributional Treatment Effects with Multi-Task Neural Networks](https://mlsanity.com/paper/2507.07738/) (2025)
- [LearnedWMP: Workload Memory Prediction Using Distribution of Query Templates](https://mlsanity.com/paper/2401.12103/) (2024)
- [A CDF-First Framework for Free-Form Density Estimation](https://mlsanity.com/paper/2603.25204/) (2026)

## Abstract (arXiv)

Due to their flexibility and predictive performance, machine-learning based regression methods have become an important tool for predictive modeling and forecasting. However, most methods focus on estimating the conditional mean or specific quantiles of the target quantity and do not provide the full conditional distribution, which contains uncertainty information that might be crucial for decision making. In this article, we provide a general solution by transforming a conditional distribution estimation problem into a constrained multi-class classification problem, in which tools such as deep neural networks. We propose a novel joint binary cross-entropy loss function to accomplish this goal. We demonstrate its performance in various simulation studies comparing to state-of-the-art competing methods. Additionally, our method shows improved accuracy in a probabilistic solar energy forecasting problem.