Related papers: Deep Gaussian Process Emulation with gradient Info…
The growing demand for accurate, efficient, and scalable solutions in computational mechanics highlights the need for advanced operator learning algorithms that can efficiently handle large datasets while providing reliable uncertainty…
This paper presents a Gaussian process (GP) model for estimating piecewise continuous regression functions. In scientific and engineering applications of regression analysis, the underlying regression functions are piecewise continuous in…
Deep Gaussian processes have recently been proposed as natural objects to fit, similarly to deep neural networks, possibly complex features present in modern data samples, such as compositional structures. Adopting a Bayesian nonparametric…
Gaussian processes (GPs) are non-parametric Bayesian models that are widely used for diverse prediction tasks. Previous work in adding strong privacy protection to GPs via differential privacy (DP) has been limited to protecting only the…
Gaussian process (GP) models that combine both categorical and continuous input variables have found use in analysis of longitudinal data and computer experiments. However, standard inference for these models has the typical cubic scaling,…
Gaussian processes (GPs) are non-linear probabilistic models popular in many applications. However, na\"ive GP realizations require quadratic memory to store the covariance matrix and cubic computation to perform inference or evaluate the…
Recent research has shown the potential utility of Deep Gaussian Processes. These deep structures are probability distributions, designed through hierarchical construction, which are conditionally Gaussian. In this paper, the current…
Quantifying uncertainties in physical or engineering systems often requires a large number of simulations of the underlying computer models that are computationally intensive. Emulators or surrogate models are often used to accelerate the…
Gaussian processes (GPs), or distributions over arbitrary functions in a continuous domain, can be generalized to the multi-output case: a linear model of coregionalization (LMC) is one approach. LMCs estimate and exploit correlations…
Despite exceptional predictive performance of Deep sequence models (DSMs), the main concern of their deployment centers around the lack of uncertainty awareness. In contrast, probabilistic models quantify the uncertainty associated with…
Parameter retrieval and model inversion are key problems in remote sensing and Earth observation. Currently, different approximations exist: a direct, yet costly, inversion of radiative transfer models (RTMs); the statistical inversion with…
New manufacturing techniques such as 3D printing have recently enabled the creation of previously infeasible chemical reactor designs. Optimizing the geometry of the next generation of chemical reactors is important to understand the…
Off-the-shelf Gaussian Process (GP) covariance functions encode smoothness assumptions on the structure of the function to be modeled. To model complex and non-differentiable functions, these smoothness assumptions are often too…
Gaussian process (GP) is a Bayesian model which provides several advantages for regression tasks in machine learning such as reliable quantitation of uncertainty and improved interpretability. Their adoption has been precluded by their…
The Gaussian process (GP) regression model is a widely employed surrogate modeling technique for computer experiments, offering precise predictions and statistical inference for the computer simulators that generate experimental data.…
Gaussian processes are the leading class of distributions on random functions, but they suffer from well known issues including difficulty scaling and inflexibility with respect to certain shape constraints (such as nonnegativity). Here we…
We present GP-4DGS, a novel framework that integrates Gaussian Processes (GPs) into 4D Gaussian Splatting (4DGS) for principled probabilistic modeling of dynamic scenes. While existing 4DGS methods focus on deterministic reconstruction,…
We consider the use of Gaussian process (GP) priors for solving inverse problems in a Bayesian framework. As is well known, the computational complexity of GPs scales cubically in the number of datapoints. We here show that in the context…
We propose a method (TT-GP) for approximate inference in Gaussian Process (GP) models. We build on previous scalable GP research including stochastic variational inference based on inducing inputs, kernel interpolation, and structure…
Distributed Gaussian processes (DGPs) are prominent local approximation methods to scale Gaussian processes (GPs) to large datasets. Instead of a global estimation, they train local experts by dividing the training set into subsets, thus…