相关论文: Non-separable Dynamic Nearest-Neighbor Gaussian Pr…

This paper introduces deep Gaussian processes (DGPs) for geophysical parameter retrieval. Unlike the standard full GP model, the DGP accounts for complicated (modular, hierarchical) processes, provides an efficient solution that scales well…

Deep Gaussian processes (DGPs) are multi-layer hierarchical generalisations of Gaussian processes (GPs) and are formally equivalent to neural networks with multiple, infinitely wide hidden layers. DGPs are nonparametric probabilistic models…

In this work, we use Deep Gaussian Processes (DGPs) as statistical surrogates for stochastic processes with complex distributions. Conventional inferential methods for DGP models can suffer from high computational complexity as they require…

Deep Gaussian Processes (DGPs) combine the expressiveness of Deep Neural Networks (DNNs) with quantified uncertainty of Gaussian Processes (GPs). Expressive power and intractable inference both result from the non-Gaussian distribution over…

With the growing capabilities of Geographic Information Systems (GIS) and user-friendly software, statisticians today routinely encounter geographically referenced data containing observations from a large number of spatial locations and…

Gaussian Processes (GP) have become popular machine-learning methods for kernel-based learning on datasets with complicated covariance structures. In this paper, we present a novel extension to the GP framework using a contaminated normal…

This thesis is mainly concerned with state-space approaches for solving deep (temporal) Gaussian process (DGP) regression problems. More specifically, we represent DGPs as hierarchically composed systems of stochastic differential equations…

One of the primary aspects of sustainable development involves accurate understanding and modeling of environmental phenomena. Many of these phenomena exhibit variations in both space and time and it is imperative to develop a deeper…

Gaussian process (GP) regression is a powerful probabilistic modeling technique with built-in uncertainty quantification. When one has access to multiple correlated simulations (tasks), it is common to fit a multitask GP (MTGP) surrogate…

Learning mappings between functional spaces, also known as function-on-function regression, is a fundamental problem in functional data analysis with broad applications, including spatiotemporal forecasting, curve prediction, and climate…

This work introduces the concept of parametric Gaussian processes (PGPs), which is built upon the seemingly self-contradictory idea of making Gaussian processes parametric. Parametric Gaussian processes, by construction, are designed to…

Missing values are common in many real-life datasets. However, most of the current machine learning methods can not handle missing values. This means that they should be imputed beforehand. Gaussian Processes (GPs) are non-parametric models…

The periodic Gaussian process (PGP) has been increasingly used to model periodic data due to its high accuracy. Yet, computing the likelihood of PGP has a high computational complexity of $\mathcal{O}\left(n^{3}\right)$ ($n$ is the data…

Gaussian processes (GPs) are important probabilistic tools for inference and learning in spatio-temporal modelling problems such as those in climate science and epidemiology. However, existing GP approximations do not simultaneously support…

Air pollution remains a critical environmental and public health challenge, demanding high-resolution spatial data to better understand its spatial distribution and impacts. This study addresses the challenges of conducting multivariate…

Learning uncertain dynamics models using Gaussian process~(GP) regression has been demonstrated to enable high-performance and safety-aware control strategies for challenging real-world applications. Yet, for computational tractability,…

Large, multi-dimensional spatio-temporal datasets are omnipresent in modern science and engineering. An effective framework for handling such data are Gaussian process deep generative models (GP-DGMs), which employ GP priors over the latent…

This paper presents a probabilistic framework to obtain both reliable and fast uncertainty estimates for predictions with Deep Neural Networks (DNNs). Our main contribution is a practical and principled combination of DNNs with sparse…

Gaussian process state-space models (GP-SSMs) are a very flexible family of models of nonlinear dynamical systems. They comprise a Bayesian nonparametric representation of the dynamics of the system and additional (hyper-)parameters…

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…