# Gaussian Process Conditional Density Estimation

arXiv: https://arxiv.org/abs/1810.12750 · HTML: https://mlsanity.com/paper/1810.12750/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2018.

## Built on by (most cited first, 23 of 23)

- [IB-UQ: Information bottleneck based uncertainty quantification for neural function regression and neural operator learning](https://mlsanity.com/paper/2302.03271/) (2023)
- [GPflux: A Library for Deep Gaussian Processes](https://mlsanity.com/paper/2104.05674/) (2021)
- [Non-Gaussian Gaussian Processes for Few-Shot Regression](https://mlsanity.com/paper/2110.13561/) (2021)
- [Bivariate Causal Discovery using Bayesian Model Selection](https://mlsanity.com/paper/2306.02931/) (2023)
- [Quantifying Epistemic Uncertainty in Deep Learning](https://mlsanity.com/paper/2110.12122/) (2021)
- [Evaluating Aleatoric Uncertainty via Conditional Generative Models](https://mlsanity.com/paper/2206.04287/) (2022)
- [Efficient Uncertainty Quantification and Reduction for Over-Parameterized Neural Networks](https://mlsanity.com/paper/2306.05674/) (2023)
- [Probabilistic Time Series Forecasts with Autoregressive Transformation Models](https://mlsanity.com/paper/2110.08248/) (2021)
- [Conditional Measurement Density Estimation in Sequential Monte Carlo via Normalizing Flow](https://mlsanity.com/paper/2203.08617/) (2022)
- [Effective Bayesian Causal Inference via Structural Marginalisation and Autoregressive Orders](https://mlsanity.com/paper/2402.14781/) (2024)
- [Continuous Bayesian Model Selection for Multivariate Causal Discovery](https://mlsanity.com/paper/2411.10154/) (2024)
- [DeepLSS: breaking parameter degeneracies in large scale structure with deep learning analysis of combined probes](https://mlsanity.com/paper/2203.09616/) (2022)
- [Conditional Density Estimation with Histogram Trees](https://mlsanity.com/paper/2410.11449/) (2024)
- [Continuous Conditional Generative Adversarial Networks (cGAN) with Generator Regularization](https://mlsanity.com/paper/2103.14884/) (2021)
- [Deconvolutional Density Network: Modeling Free-Form Conditional Distributions](https://mlsanity.com/paper/2105.14367/) (2021)
- [Markov Balance Satisfaction Improves Performance in Strictly Batch Offline Imitation Learning](https://mlsanity.com/paper/2408.09125/) (2024)
- [Benchmarking Tabular Foundation Models for Conditional Density Estimation in Regression](https://mlsanity.com/paper/2603.26611/) (2026)
- [Conditional Kernel Imitation Learning for Continuous State Environments](https://mlsanity.com/paper/2308.12573/) (2023)
- [Towards Backwards-Compatible Data with Confounded Domain Adaptation](https://mlsanity.com/paper/2203.12720/) (2022)
- [GGMPs: Generalized Gaussian Mixture Processes](https://mlsanity.com/paper/2603.10442/) (2026)
- [Predicting the probability distribution of bus travel time to move towards reliable planning of public transport services](https://mlsanity.com/paper/2102.02292/) (2021)
- [Gaussian Process Tilted Nonparametric Density Estimation using Fisher Divergence Score Matching](https://mlsanity.com/paper/2504.03485/) (2025)
- [Multivariate quantile regression via Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2609.23906/) (2026)

## Abstract (arXiv)

Conditional Density Estimation (CDE) models deal with estimating conditional distributions. The conditions imposed on the distribution are the inputs of the model. CDE is a challenging task as there is a fundamental trade-off between model complexity, representational capacity and overfitting. In this work, we propose to extend the model's input with latent variables and use Gaussian processes (GP) to map this augmented input onto samples from the conditional distribution. Our Bayesian approach allows for the modeling of small datasets, but we also provide the machinery for it to be applied to big data using stochastic variational inference. Our approach can be used to model densities even in sparse data regions, and allows for sharing learned structure between conditions. We illustrate the effectiveness and wide-reaching applicability of our model on a variety of real-world problems, such as spatio-temporal density estimation of taxi drop-offs, non-Gaussian noise modeling, and few-shot learning on omniglot images.