Related papers: Time-adaptive functional Gaussian Process regressi…
We consider the problem of constructing Bayesian based confidence sets for linear functionals in the inverse Gaussian white noise model. We work with a scale of Gaussian priors indexed by a regularity hyper-parameter and apply the…
In this work we study the non-parametric reconstruction of spatio-temporal dynamical Gaussian processes (GPs) via GP regression from sparse and noisy data. GPs have been mainly applied to spatial regression where they represent one of the…
We place ourselves in a functional regression setting and propose a novel methodology for regressing a real output on vector-valued functional covariates. This methodology is based on the notion of signature, which is a representation of a…
Non-stationary time series with non-linear trends are frequently encountered in applications. We consider here the feasibility of accurately forecasting the signals of multiple such time series considering jointly when the number of…
In this work, we employ the Bayesian inference framework to solve the problem of estimating the solution and particularly, its derivatives, which satisfy a known differential equation, from the given noisy and scarce observations of the…
This paper presents a new methodology, called AFSSEN, to simultaneously select significant predictors and produce smooth estimates in a high-dimensional function-on-scalar linear model with a sub-Gaussian errors. Outcomes are assumed to lie…
Gaussian process models are commonly used as emulators for computer experiments. However, developing a Gaussian process emulator can be computationally prohibitive when the number of experimental samples is even moderately large. Local…
We study nonparametric Bayesian inference for the intensity function of a covariate-driven point process. We extend recent results from the literature, showing that a wide class of Gaussian priors, combined with flexible link functions,…
We investigate the frequentist guarantees of the variational sparse Gaussian process regression model. In the theoretical analysis, we focus on the variational approach with spectral features as inducing variables. We derive guarantees and…
The Gaussian Process (GP) assumption is often used in functional data analysis. We propose a method to assess departures from the GP assumption, both in terms of the shape of the distribution and its potential dependence on covariates,…
Methods for inference and simulation of linearly constrained Gaussian Markov Random Fields (GMRF) are computationally prohibitive when the number of constraints is large. In some cases, such as for intrinsic GMRFs, they may even be…
The accuracy of Bayesian inference can be negatively affected by the use of inaccurate forward models. In the case of gravitational-wave inference, accurate but computationally expensive waveform models are sometimes substituted with faster…
Calibration is a highly challenging task, in particular in multiple yield curve markets. This paper is a first attempt to study the chances and challenges of the application of machine learning techniques for this. We employ Gaussian…
Gaussian process regression (GPR) is a popular nonparametric Bayesian method that provides predictive uncertainty estimates and is widely used in safety-critical applications. While prior research has introduced various uncertainty bounds,…
We study the theoretical properties of a variational Bayes method in the Gaussian Process regression model. We consider the inducing variables method introduced by Titsias (2009a) and derive sufficient conditions for obtaining contraction…
Surrogate modeling based on Gaussian processes (GPs) has received increasing attention in the analysis of complex problems in science and engineering. Despite extensive studies on GP modeling, the developments for functional inputs are…
In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a…
This paper proposes and analyzes fully data driven methods for inference about the mean function of a stochastic process from a sample of independent trajectories of the process, observed at discrete time points and corrupted by additive…
We introduce a Fourier-based fast algorithm for Gaussian process regression in low dimensions. It approximates a translationally-invariant covariance kernel by complex exponentials on an equispaced Cartesian frequency grid of $M$ nodes.…
Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…