Related papers: Kriging via variably scaled kernels
Kernel-based machine learning approaches are gaining increasing interest for exploring and modeling large dataset in recent years. Gaussian process (GP) is one example of such kernel-based approaches, which can provide very good performance…
We study mesoscopic linear statistics for a class of determinantal point processes which interpolates between Poisson and Gaussian Unitary Ensemble statistics. These processes are obtained by modifying the spectrum of the correlation kernel…
We study learning problems in which the conditional distribution of the output given the input varies as a function of additional task variables. In varying-coefficient models with Gaussian process priors, a Gaussian process generates the…
Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…
It is now common practice in nuclear engineering to base extensive studies on numerical computer models. These studies require to run computer codes in potentially thousands of numerical configurations and without expert individual controls…
We propose a data-driven approach to quantify the uncertainty of models constructed by kernel methods. Our approach minimizes the needed distributional assumptions, hence, instead of working with, for example, Gaussian processes or…
Treeging combines the flexible mean structure of regression trees with the covariance-based prediction strategy of kriging into the base learner of an ensemble prediction algorithm. In so doing, it combines the strengths of the two primary…
Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in…
Recently, 3D Gaussian Splatting has emerged as a promising approach for modeling 3D scenes using mixtures of Gaussians. The predominant optimization method for these models relies on backpropagating gradients through a differentiable…
This work brings together two powerful concepts in Gaussian processes: the variational approach to sparse approximation and the spectral representation of Gaussian processes. This gives rise to an approximation that inherits the benefits of…
Stochastic kriging is a popular metamodeling technique for representing the unknown response surface of a simulation model. However, the simulation model may be inadequate in the sense that there may be a non-negligible discrepancy between…
This article proposes a new kriging that has a rational form. It is shown that the generalized least squares estimate of the mean from rational kriging is much more well behaved than that from ordinary kriging. Parameter estimation and…
The relative balance between physics and data within any physics-informed machine learner is an important modelling consideration to ensure that the benefits of both physics and data-based approaches are maximised. An over reliance on…
In many real-world applications we are interested in approximating costly functions that are analytically unknown, e.g. complex computer codes. An emulator provides a fast approximation of such functions relying on a limited number of…
The Hawkes process (HP) has been widely applied to modeling self-exciting events including neuron spikes, earthquakes and tweets. To avoid designing parametric triggering kernel and to be able to quantify the prediction confidence, the…
We investigate the frequentist coverage properties of credible sets resulting in from Gaussian process priors with squared exponential covariance kernel. First we show that by selecting the scaling hyper-parameter using the maximum marginal…
The interaction between wavelet-like sensors in Divisive Normalization is classically described through Gaussian kernels that decay with spatial distance, angular distance and frequency distance. However, simultaneous explanation of (a)…
We construct flexible likelihoods for multi-output Gaussian process models that leverage neural networks as components. We make use of sparse variational inference methods to enable scalable approximate inference for the resulting class of…
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,…
Many applications in speech, robotics, finance, and biology deal with sequential data, where ordering matters and recurrent structures are common. However, this structure cannot be easily captured by standard kernel functions. To model such…