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Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate…
We develop a non-parametric multivariate time series model that remains agnostic on the precise relationship between a (possibly) large set of macroeconomic time series and their lagged values. The main building block of our model is a…
Gaussian processes (GPs) are pervasive in functional data analysis, machine learning, and spatial statistics for modeling complex dependencies. Modern scientific data sets are typically heterogeneous and often contain multiple known…
For a learning task, 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. The vanilla GP however struggles…
Gaussian process (GP) priors are non-parametric generative models with appealing modelling properties for Bayesian inference: they can model non-linear relationships through noisy observations, have closed-form expressions for training and…
Gaussian processes (GP) are powerful tools for probabilistic modeling purposes. They can be used to define prior distributions over latent functions in hierarchical Bayesian models. The prior over functions is defined implicitly by the mean…
A multi-output Gaussian process (GP) is introduced as a model for the joint posterior distribution of the local predictive ability of set of models and/or experts, conditional on a vector of covariates, from historical predictions in the…
Gaussian Processes (GPs) are a class of kernel methods that have shown to be very useful in geoscience applications. They are widely used because they are simple, flexible and provide very accurate estimates for nonlinear problems,…
Deep Gaussian process models typically employ discrete hierarchies, but recent advancements in differential Gaussian processes (DiffGPs) have extended these models to infinite depths. However, existing DiffGP approaches often overlook the…
The Gaussian Graphical Model (GGM) is a popular tool for incorporating sparsity into joint multivariate distributions. The G-Wishart distribution, a conjugate prior for precision matrices satisfying general GGM constraints, has now been in…
Differential equations are important mechanistic models that are integral to many scientific and engineering applications. With the abundance of available data there has been a growing interest in data-driven physics-informed models.…
Simulating turbulent fluid flows is a computationally prohibitive task, as it requires the resolution of fine-scale structures and the capture of complex nonlinear interactions across multiple scales. This is particularly the case in direct…
Stochastic volatility models based on Gaussian processes, like fractional Brownian motion, are able to reproduce important stylized facts of financial markets such as rich autocorrelation structures, persistence and roughness of sample…
Gaussian Process (GP) models are a powerful tool in probabilistic machine learning with a solid theoretical foundation. Thanks to current advances, modeling complex data with GPs is becoming increasingly feasible, which makes them an…
Accurate probabilistic prediction of wind power is crucial for maintaining grid stability and facilitating the efficient integration of renewable energy sources. Gaussian process (GP) models offer a principled framework for quantifying…
Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with…
While much research effort has been dedicated to scaling up sparse Gaussian process (GP) models based on inducing variables for big data, little attention is afforded to the other less explored class of low-rank GP approximations that…
Gaussian process (GP) regression has been widely used in supervised machine learning due to its flexibility and inherent ability to describe uncertainty in function estimation. In the context of control, it is seeing increasing use for…
Discrete automated processes in industrial and cyber-physical systems often exhibit a repetitive structure in which successive repetitions follow a common trajectory while differing in duration, amplitude, and fine-scale dynamics. Such…
Despite the widespread utilization of Gaussian process models for versatile nonparametric modeling, they exhibit limitations in effectively capturing abrupt changes in function smoothness and accommodating relationships with heteroscedastic…