GGMPs: Generalized Gaussian Mixture Processes

TL;DR

The paper introduces GGMP, a Gaussian process-based method for flexible, multimodal conditional density estimation that effectively models complex output distributions while maintaining computational tractability.

Contribution

GGMP is a novel GP-based approach that combines local Gaussian mixture fitting with heteroscedastic training to handle multimodal, non-Gaussian outputs efficiently.

Findings

Improves distributional approximation on synthetic datasets.

Handles pronounced non-Gaussianity and multimodality effectively.

Compatible with standard GP solvers and scalable methods.

Abstract

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.