GGMPs: Generalized Gaussian Mixture Processes

• URL: http://arxiv.org/abs/2603.10442v1
• Date: Wed, 11 Mar 2026 05:50:43 GMT
• Title: GGMPs: Generalized Gaussian Mixture Processes
• Abstract summary: Conditional density estimation is complicated by multimodality, heteroscedasticity, and strong non-Gaussianity.<n>We introduce the Generalized Gaussian Mixture Process (GGMP), a GP-based method for multimodal conditional density estimation.
• Score: 1.3066182802188202
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Simplifying Flow Matching Transformations with Low-Rank Mixture Models [58.797704398690165]
  We propose using mixtures of probabilistic principal component analyzers (MPPCA) as the latent density for normalizing flows.<n>We simplify the learned flow transformation by learning a latent distribution that more closely aligns with the data distribution in terms of KL divergence.<n>MPPCA models can be fit quickly and cheaply using the expectation-maximization algorithm, making them a practical choice for initializing latent distributions even in high-dimensional generative tasks.
  arXiv  Detail & Related papers  (2026-06-29T03:03:06Z)
• Toward Global Convergence of Gradient EM for Over-Parameterized Gaussian Mixture Models [47.294535652946095]
  We study the gradient Expectation-Maximization (EM) algorithm for Gaussian Mixture Models (GMM)<n>This is the first global convergence result for Gaussian mixtures with more than $2$ components.
  arXiv  Detail & Related papers  (2024-06-29T16:44:29Z)
• Gaussian Process Regression with Soft Inequality and Monotonicity Constraints [0.0]
  We introduce a new GP method that enforces the physical constraints in a probabilistic manner. This GP model is trained by the quantum-inspired Hamiltonian Monte Carlo (QHMC)
  arXiv  Detail & Related papers  (2024-04-03T17:09:25Z)
• Deep Transformed Gaussian Processes [0.0]
  Transformed Gaussian Processes (TGPs) are processes specified by transforming samples from the joint distribution from a prior process (typically a GP) using an invertible transformation. We propose a generalization of TGPs named Deep Transformed Gaussian Processes (DTGPs), which follows the trend of concatenating layers of processes. Experiments conducted evaluate the proposed DTGPs in multiple regression datasets, achieving good scalability and performance.
  arXiv  Detail & Related papers  (2023-10-27T16:09:39Z)
• Deep Gaussian Mixture Ensembles [9.673093148930874]
  This work introduces a novel probabilistic deep learning technique called deep Gaussian mixture ensembles (DGMEs) DGMEs are capable of approximating complex probability distributions, such as heavy-tailed or multimodal distributions. Our experimental results demonstrate that DGMEs outperform state-of-the-art uncertainty quantifying deep learning models in handling complex predictive densities.
  arXiv  Detail & Related papers  (2023-06-12T16:53:38Z)
• Gaussian Graphical Models as an Ensemble Method for Distributed Gaussian Processes [8.4159776055506]
  We propose a novel approach for aggregating the Gaussian experts' predictions by Gaussian graphical model (GGM) We first estimate the joint distribution of latent and observed variables using the Expectation-Maximization (EM) algorithm. Our new method outperforms other state-of-the-art DGP approaches.
  arXiv  Detail & Related papers  (2022-02-07T15:22:56Z)
• Non-Gaussian Gaussian Processes for Few-Shot Regression [71.33730039795921]
  We propose an invertible ODE-based mapping that operates on each component of the random variable vectors and shares the parameters across all of them. NGGPs outperform the competing state-of-the-art approaches on a diversified set of benchmarks and applications.
  arXiv  Detail & Related papers  (2021-10-26T10:45:25Z)
• Scalable Variational Gaussian Processes via Harmonic Kernel Decomposition [54.07797071198249]
  We introduce a new scalable variational Gaussian process approximation which provides a high fidelity approximation while retaining general applicability. We demonstrate that, on a range of regression and classification problems, our approach can exploit input space symmetries such as translations and reflections. Notably, our approach achieves state-of-the-art results on CIFAR-10 among pure GP models.
  arXiv  Detail & Related papers  (2021-06-10T18:17:57Z)
• Plug-And-Play Learned Gaussian-mixture Approximate Message Passing [71.74028918819046]
  We propose a plug-and-play compressed sensing (CS) recovery algorithm suitable for any i.i.d. source prior. Our algorithm builds upon Borgerding's learned AMP (LAMP), yet significantly improves it by adopting a universal denoising function within the algorithm. Numerical evaluation shows that the L-GM-AMP algorithm achieves state-of-the-art performance without any knowledge of the source prior.
  arXiv  Detail & Related papers  (2020-11-18T16:40:45Z)
• Revisiting the Sample Complexity of Sparse Spectrum Approximation of Gaussian Processes [60.479499225746295]
  We introduce a new scalable approximation for Gaussian processes with provable guarantees which hold simultaneously over its entire parameter space. Our approximation is obtained from an improved sample complexity analysis for sparse spectrum Gaussian processes (SSGPs)
  arXiv  Detail & Related papers  (2020-11-17T05:41:50Z)
• Modulating Scalable Gaussian Processes for Expressive Statistical Learning [25.356503463916816]
  Gaussian process (GP) is interested in learning the statistical relationship between inputs and outputs, since it offers not only the prediction mean but also the associated variability. This article studies new scalable GP paradigms including the non-stationary heteroscedastic GP, the mixture of GPs and the latent GP, which introduce additional latent variables to modulate the outputs or inputs in order to learn richer, non-Gaussian statistical representation.
  arXiv  Detail & Related papers  (2020-08-29T06:41:45Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.