Related papers: A Kriging procedure for processes indexed by graph…
Gaussian processes are used in machine learning to learn input-output mappings from observed data. Gaussian process regression is based on imposing a Gaussian process prior on the unknown regressor function and statistically conditioning it…
In this paper, we propose a framework for graph signal processing using category theory. The aim is to generalize a few recent works on probabilistic approaches to graph signal processing, which handle signal and graph uncertainties.
This work develops a multivariate extension of the Fixed Rank Kriging (FRK) framework for spatial prediction in settings where multiple spatial processes may provide complementary information. The goal is to preserve the computational…
We present Blitzkriging, a new approach to fast inference for Gaussian processes, applicable to regression, optimisation and classification. State-of-the-art (stochastic) inference for Gaussian processes on very large datasets scales…
In spatial statistics, a common objective is to predict values of a spatial process at unobserved locations by exploiting spatial dependence. Kriging provides the best linear unbiased predictor using covariance functions and is often…
Gaussian processes are a versatile framework for learning unknown functions in a manner that permits one to utilize prior information about their properties. Although many different Gaussian process models are readily available when the…
Gaussian process fitting, or kriging, is often used to create a model from a set of data. Many available software packages do this, but we show that very different results can be obtained from different packages even when using the same…
This paper is motivated by a computer experiment conducted for optimizing residual stresses in the machining of metals. Although kriging is widely used in the analysis of computer experiments, it cannot be easily applied to model the…
The integration of renewable energy sources and distributed generation in the power system calls for fast and reliable predictions of grid dynamics to achieve efficient control and ensure stability. In this work, we present a novel…
The problem of classifying graphs is ubiquitous in machine learning. While it is standard to apply graph neural networks or graph kernel methods, Gaussian processes can be employed by transforming spatial features from the graph domain into…
We introduce a novel edge tracing algorithm using Gaussian process regression. Our edge-based segmentation algorithm models an edge of interest using Gaussian process regression and iteratively searches the image for edge pixels in a…
In this paper, we investigate Gaussian process modeling with input location error, where the inputs are corrupted by noise. Here, the best linear unbiased predictor for two cases is considered, according to whether there is noise at the…
Random data sketching (or projection) is now a classical technique enabling, for instance, approximate numerical linear algebra and machine learning algorithms with reduced computational complexity and memory. In this context, the…
In various industrial contexts, estimating the distribution of unobserved random vectors Xi from some noisy indirect observations H(Xi) + Ui is required. If the relation between Xi and the quantity H(Xi), measured with the error Ui, is…
For estimation and predictions of random fields it is increasingly acknowledged that the kriging variance may be a poor representative of true uncertainty. Experimental designs based on more elaborate criteria that are appropriate for…
Gaussian Processes (\textbf{GPs}) are flexible non-parametric models with strong probabilistic interpretation. While being a standard choice for performing inference on time series, GPs have few techniques to work in a streaming setting.…
This paper presents a novel information value function that can be used in online sensor planning to monitor a spatial phenomenon in which the spatial phenomenon is modeled by nonparametric Gaussian processes. The information value function…
Gaussian Processes (GPs) are highly expressive, probabilistic models. A major limitation is their computational complexity. Naively, exact GP inference requires $\mathcal{O}(N^3)$ computations with $N$ denoting the number of modeled points.…
Approximation of functions satisfying partial differential equations (PDEs) is paramount for simulation of physical fluid flows and other problems in physics. Recently, physics-informed machine learning approaches have proven useful as a…
In semi-supervised learning on graphs, response variables observed at one node are used to estimate missing values at other nodes. The methods exploit correlations between nearby nodes in the graph. In this paper we prove that many such…