Related papers: Posterior and Computational Uncertainty in Gaussia…
Recently nonparametric functional model with functional responses has been proposed within the functional reproducing kernel Hilbert spaces (fRKHS) framework. Motivated by its superior performance and also its limitations, we propose a…
In this article, we investigate posterior convergence in nonparametric regression models where the unknown regression function is modeled by some appropriate stochastic process. In this regard, we consider two setups. The first setup is…
Variational inference is a powerful tool for approximate inference, and it has been recently applied for representation learning with deep generative models. We develop the variational Gaussian process (VGP), a Bayesian nonparametric…
Gaussian processes (GPs) are a good choice for function approximation as they are flexible, robust to over-fitting, and provide well-calibrated predictive uncertainty. Deep Gaussian processes (DGPs) are multi-layer generalisations of GPs,…
We consider the optimal approximate posterior over the top-layer weights in a Bayesian neural network for regression, and show that it exhibits strong dependencies on the lower-layer weights. We adapt this result to develop a correlated…
Gaussian processes (GPs) are a class of Kernel methods that have shown to be very useful in geoscience and remote sensing applications for parameter retrieval, model inversion, and emulation. They are widely used because they are simple,…
Posterior computation for high-dimensional data with many parameters can be challenging. This article focuses on a new method for approximating posterior distributions of a low- to moderate-dimensional parameter in the presence of a…
Multi-task learning models using Gaussian processes (GP) have been developed and successfully applied in various applications. The main difficulty with this approach is the computational cost of inference using the union of examples from…
In a general class of Bayesian nonparametric models, we prove that the posterior distribution can be asymptotically approximated by a Gaussian process. Our results apply to nonparametric exponential family that contains both Gaussian and…
The posterior variance of Gaussian processes is a valuable measure of the learning error which is exploited in various applications such as safe reinforcement learning and control design. However, suitable analysis of the posterior variance…
In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…
Gaussian processes (GPs) are distributions over functions, which provide a Bayesian nonparametric approach to regression and classification. In spite of their success, GPs have limited use in some applications, for example, in some cases a…
Inverse problems are prevalent in both scientific research and engineering applications. In the context of Bayesian inverse problems, sampling from the posterior distribution can be particularly challenging when the forward models are…
Uncertainty Quantification (UQ) is essential for the reliable application of computational models in engineering and science. Among surrogate modeling techniques, Gaussian Process Regression (GPR) is particularly valuable for its…
Gaussian processes (GPs) with derivatives are useful in many applications, including Bayesian optimization, implicit surface reconstruction, and terrain reconstruction. Fitting a GP to function values and derivatives at $n$ points in $d$…
We address the problem of continual learning in multi-task Gaussian process (GP) models for handling sequential input-output observations. Our approach extends the existing prior-posterior recursion of online Bayesian inference, i.e.\ past…
Mapping with uncertainty representation is required in many research domains, especially for localization. Although there are many investigations regarding the uncertainty of the pose estimation of an ego-robot with map information, the…
Gaussian processes (GPs) are widely-used tools in spatial statistics and machine learning and the formulae for the mean function and covariance kernel of a GP $T u$ that is the image of another GP $u$ under a linear transformation $T$…
Uncertainty quantification based on generalized polynomial chaos has been used in many applications. It has also achieved great success in variation-aware design automation. However, almost all existing techniques assume that the parameters…
Gaussian Processes (GPs) are widely used to model dependencies in spatial statistics and machine learning. However, exact inference is computationally intractable for GP regression, with a time complexity of $O(n^3)$. The Vecchia…