GGMPs: Generalized Gaussian Mixture Processes
This addresses the limitation of standard Gaussian processes in handling complex, multimodal output distributions for researchers and practitioners in machine learning, though it appears incremental as it builds on existing GP frameworks.
The paper tackles the problem of multimodal conditional density estimation by introducing Generalized Gaussian Mixture Processes (GGMPs), which combine Gaussian mixture fitting and Gaussian processes to produce closed-form predictive densities, improving distributional approximation on synthetic and real-world datasets with non-Gaussianity and multimodality.
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.