# GGMPs: Generalized Gaussian Mixture Processes

arXiv: https://arxiv.org/abs/2603.10442 · HTML: https://mlsanity.com/paper/2603.10442/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 58 references that are in the map.
- First posted on arXiv 11 Mar 2026.

## Builds on (most cited first, 22 of 22)

- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [Conditional Density Estimation with Bayesian Normalising Flows](https://mlsanity.com/paper/1802.04908/) (2018)
- [Learning Theory for Distribution Regression](https://mlsanity.com/paper/1411.2066/) (2014)
- [Student-t Processes as Alternatives to Gaussian Processes](https://mlsanity.com/paper/1402.4306/) (2014)
- [Conditional Density Estimation with Neural Networks: Best Practices and Benchmarks](https://mlsanity.com/paper/1903.00954/) (2019)
- [Transforming Gaussian Processes With Normalizing Flows](https://mlsanity.com/paper/2011.01596/) (2020)
- [Gaussian Process Conditional Density Estimation](https://mlsanity.com/paper/1810.12750/) (2018)
- [Distribution-Free Distribution Regression](https://mlsanity.com/paper/1302.0082/) (2013)
- [Bayesian Approaches to Distribution Regression](https://mlsanity.com/paper/1705.04293/) (2017)
- [A Unifying Perspective on Non-Stationary Kernels for Deeper Gaussian Processes](https://mlsanity.com/paper/2309.10068/) (2023)
- [Sharded Bayesian Additive Regression Trees](https://mlsanity.com/paper/2306.00361/) (2023)
- [Regression-based covariance functions for nonstationary spatial modeling](https://mlsanity.com/paper/1410.1494/) (2014)
- [Hybrid Parameter Search and Dynamic Model Selection for Mixed-Variable Bayesian Optimization](https://mlsanity.com/paper/2206.01409/) (2022)
- [Asymptotic Optimism of Random-Design Linear and Kernel Regression Models](https://mlsanity.com/paper/2502.12999/) (2025)
- [Robust Bayesian Optimization via Tempered Posteriors](https://mlsanity.com/paper/2601.07094/) (2026)
- [Compactly-supported nonstationary kernels for computing exact Gaussian processes on big data](https://mlsanity.com/paper/2411.05869/) (2024)
- [On Approximate Inference for Generalized Gaussian Process Models](https://mlsanity.com/paper/1311.6371/) (2013)
- [Anchored Bayesian Gaussian Mixture Models](https://mlsanity.com/paper/1805.08304/) (2018)
- [gp2Scale: A Class of Compactly Supported Non-Stationary Kernels and Distributed Computing for Exact Gaussian Processes on 10 Million Data Points](https://mlsanity.com/paper/2512.06143/) (2025)

## Built on by (most cited first, 1 of 1)

- [Wasserstein-type Gaussian Process Regressions for Input Measurement Uncertainty](https://mlsanity.com/paper/2603.17271/) (2026)

## Abstract (arXiv)

Conditional density estimation is complicated by multimodality, heteroscedasticity, and strong non-Gaussianity. Gaussian processes (GPs) provide a principled nonparametric framework with calibrated uncertainty, but standard GP regression is limited by its unimodal Gaussian predictive form. We introduce the Generalized Gaussian Mixture Process (GGMP), a GP-based method for multimodal conditional density estimation in settings where each input may be associated with a complex output distribution rather than a single scalar response. GGMP combines local Gaussian mixture fitting, cross-input component alignment and per-component heteroscedastic GP training to produce a closed-form Gaussian mixture predictive density. The method is tractable, compatible with standard GP solvers and scalable methods, and avoids the exponentially large latent-assignment structure of naive multimodal GP formulations. Empirically, GGMPs improve distributional approximation on synthetic and real-world datasets with pronounced non-Gaussianity and multimodality.