# Conditional Density Estimation with Neural Networks: Best Practices and Benchmarks

arXiv: https://arxiv.org/abs/1903.00954 · HTML: https://mlsanity.com/paper/1903.00954/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Mar 2019.

## Built on by (most cited first, 30 of 38)

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- [Deep Learning of Multivariate Extremes via a Geometric Representation](https://mlsanity.com/paper/2406.19936/) (2024)
- [Doubly robust estimation of causal effects for random object outcomes with continuous treatments](https://mlsanity.com/paper/2506.22754/) (2025)
- [Conditional Density Estimation with Histogram Trees](https://mlsanity.com/paper/2410.11449/) (2024)
- [Deconvolutional Density Network: Modeling Free-Form Conditional Distributions](https://mlsanity.com/paper/2105.14367/) (2021)
- [Causal Deep Reinforcement Learning Using Observational Data](https://mlsanity.com/paper/2211.15355/) (2022)
- [Conformal Inference of Individual Treatment Effects Using Conditional Density Estimates](https://mlsanity.com/paper/2501.14933/) (2025)
- [Conditional Kernel Imitation Learning for Continuous State Environments](https://mlsanity.com/paper/2308.12573/) (2023)
- [Deep Limit Model-free Prediction in Regression](https://mlsanity.com/paper/2408.09532/) (2024)
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- [Deep Modeling of Non-Gaussian Aleatoric Uncertainty](https://mlsanity.com/paper/2405.20513/) (2024)
- [Nonparametric estimation of conditional probability distributions using a generative approach based on conditional push-forward neural networks](https://mlsanity.com/paper/2511.14455/) (2025)
- [GGMPs: Generalized Gaussian Mixture Processes](https://mlsanity.com/paper/2603.10442/) (2026)
- [Construction de variables a l'aide de classifieurs comme aide a la regression](https://mlsanity.com/paper/2112.03703/) (2021)
- [MCD: Marginal Contrastive Discrimination for conditional density estimation](https://mlsanity.com/paper/2206.01592/) (2022)
- [Wasserstein Distributional Learning](https://mlsanity.com/paper/2209.04991/) (2022)
- [Neural Network Predicts Ion Concentration Profiles under Nanoconfinement](https://mlsanity.com/paper/2304.04896/) (2023)
- [Constructing Variables Using Classifiers as an Aid to Regression: An Empirical Assessment](https://mlsanity.com/paper/2403.06829/) (2024)
- [Predictability Analysis of Regression Problems via Conditional Entropy Estimations](https://mlsanity.com/paper/2406.03824/) (2024)

## Abstract (arXiv)

Given a set of empirical observations, conditional density estimation aims to capture the statistical relationship between a conditional variable x and a dependent variable y by modeling their conditional probability p(y|x). The paper develops best practices for conditional density estimation for finance applications with neural networks, grounded on mathematical insights and empirical evaluations. In particular, we introduce a noise regularization and data normalization scheme, alleviating problems with over-fitting, initialization and hyper-parameter sensitivity of such estimators. We compare our proposed methodology with popular semi- and non-parametric density estimators, underpin its effectiveness in various benchmarks on simulated and Euro Stoxx 50 data and show its superior performance. Our methodology allows to obtain high-quality estimators for statistical expectations of higher moments, quantiles and non-linear return transformations, with very little assumptions about the return dynamic.