Related papers: Numerical Gaussian Processes for Time-dependent an…
In this paper, we introduce the notion of Gaussian processes indexed by probability density functions for extending the Mat\'ern family of covariance functions. We use some tools from information geometry to improve the efficiency and the…
We present an operator learning framework for solving non-perturbative functional renormalization group equations, which are integro-differential equations defined on functionals. Our proposed approach uses Gaussian process operator…
A Gaussian process has been one of the important approaches for emulating computer simulations. However, the stationarity assumption for a Gaussian process and the intractability for large-scale dataset limit its availability in practice.…
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…
In this paper, we study the problem of deriving fast and accurate classification algorithms with uncertainty quantification. Gaussian process classification provides a principled approach, but the corresponding computational burden is…
We introduce fully scalable Gaussian processes, an implementation scheme that tackles the problem of treating a high number of training instances together with high dimensional input data. Our key idea is a representation trick over the…
Spatio-temporal processes in environmental applications are often assumed to follow a Gaussian model, possibly after some transformation. However, heterogeneity in space and time might have a pattern that will not be accommodated by…
The Gaussian process is a powerful and flexible technique for interpolating spatiotemporal data, especially with its ability to capture complex trends and uncertainty from the input signal. This chapter describes Gaussian processes as an…
Gaussian processes are a fully Bayesian smoothing technique that allows for the reconstruction of a function and its derivatives directly from observational data, without assuming a specific model or choosing a parameterization. This is…
Gaussian Process (GP) models provide a flexible framework for prediction and uncertainty quantification. For most covariance functions, however, exact GP prediction with $n$ points scales as $\mathcal{O}(n^3)$, making it prohibitively…
For many applications with multivariate data, random field models capturing departures from Gaussianity within realisations are appropriate. For this reason, we formulate a new class of multivariate non-Gaussian models based on systems of…
In many areas of science and engineering, discovering the governing differential equations from the noisy experimental data is an essential challenge. It is also a critical step in understanding the physical phenomena and prediction of the…
A large collection of time series poses significant challenges for classical and neural forecasting approaches. Classical time series models fail to fit data well and to scale to large problems, but succeed at providing uncertainty…
We consider finite dimensional rough differential equations driven by centered Gaussian processes. Combining Malliavin calculus, rough paths techniques and interpolation inequalities, we establish upper bounds on the density of the…
Stochastic integration \textit{wrt} Gaussian processes has raised strong interest in recent years, motivated in particular by its applications in Internet traffic modeling, biomedicine and finance. The aim of this work is to define and…
We study the problem of identifying unknown processes embedded in time-dependent partial differential equation (PDE) using observational data, with an application to advection-diffusion type PDE. We first conduct theoretical analysis and…
We provide a new approach to approximate emulation of large computer experiments. By focusing expressly on desirable properties of the predictive equations, we derive a family of local sequential design schemes that dynamically define the…
Gaussian processes offer a flexible kernel method for regression. While Gaussian processes have many useful theoretical properties and have proven practically useful, they suffer from poor scaling in the number of observations. In…
With the significant advancement in quantum computation in the past couple of decades, the exploration of machine-learning subroutines using quantum strategies has become increasingly popular. Gaussian process regression is a widely used…
The aim of this work is to define and perform a study of local times of all Gaussian processes that have an integral representation over a real interval (that maybe infinite). Very rich, this class of Gaussian processes, contains Volterra…