Sparse Gaussian processes for solving nonlinear PDEs
This article proposes an efficient numerical method for solving nonlinear partial differential
equations (PDEs) based on sparse Gaussian processes (SGPs). Gaussian processes (GPs) …
equations (PDEs) based on sparse Gaussian processes (SGPs). Gaussian processes (GPs) …
Trigonometric Quadrature Fourier Features for Scalable Gaussian Process Regression
Fourier feature approximations have been successfully applied in the literature for scalable
Gaussian Process (GP) regression. In particular, Quadrature Fourier Features (QFF) derived …
Gaussian Process (GP) regression. In particular, Quadrature Fourier Features (QFF) derived …
Preventing Model Collapse in Gaussian Process Latent Variable Models
Gaussian process latent variable models (GPLVMs) are a versatile family of unsupervised
learning models, commonly used for dimensionality reduction. However, common …
learning models, commonly used for dimensionality reduction. However, common …
Asymptotic properties of Vecchia approximation for Gaussian processes
Vecchia approximation has been widely used to accurately scale Gaussian-process (GP)
inference to large datasets, by expressing the joint density as a product of conditional …
inference to large datasets, by expressing the joint density as a product of conditional …
Stochastic Gradient Variational Bayes in the Stochastic Blockmodel
P Regueiro, A Rodríguez, J Sosa - arXiv preprint arXiv:2410.02649, 2024 - arxiv.org
Stochastic variational Bayes algorithms have become very popular in the machine learning
literature, particularly in the context of nonparametric Bayesian inference. These algorithms …
literature, particularly in the context of nonparametric Bayesian inference. These algorithms …
Linear-Cost Vecchia Approximation of Multivariate Normal Probabilities
J Cao, M Katzfuss - arXiv preprint arXiv:2311.09426, 2023 - arxiv.org
Multivariate normal (MVN) probabilities arise in myriad applications, but they are analytically
intractable and need to be evaluated via Monte-Carlo-based numerical integration. For the …
intractable and need to be evaluated via Monte-Carlo-based numerical integration. For the …
Scalable Sampling of Truncated Multivariate Normals Using Sequential Nearest-Neighbor Approximation
J Cao, M Katzfuss - arXiv preprint arXiv:2406.17307, 2024 - arxiv.org
We propose a linear-complexity method for sampling from truncated multivariate normal
(TMVN) distributions with high fidelity by applying nearest-neighbor approximations to a …
(TMVN) distributions with high fidelity by applying nearest-neighbor approximations to a …
Sparse Cholesky factorization by greedy conditional selection
Dense kernel matrices resulting from pairwise evaluations of a kernel function arise naturally
in machine learning and statistics. Previous work in constructing sparse approximate inverse …
in machine learning and statistics. Previous work in constructing sparse approximate inverse …