Related papers: Large-scale magnetic field maps using structured k…
A key challenge in scaling Gaussian Process (GP) regression to massive datasets is that exact inference requires computation with a dense n x n kernel matrix, where n is the number of data points. Significant work focuses on approximating…
We introduce a new structured kernel interpolation (SKI) framework, which generalises and unifies inducing point methods for scalable Gaussian processes (GPs). SKI methods produce kernel approximations for fast computations through kernel…
Structured kernel interpolation (SKI) accelerates Gaussian process (GP) inference by interpolating the kernel covariance function using a dense grid of inducing points, whose corresponding kernel matrix is highly structured and thus…
We introduce Soft Kernel Interpolation (SoftKI), a method that combines aspects of Structured Kernel Interpolation (SKI) and variational inducing point methods, to achieve scalable Gaussian Process (GP) regression on high-dimensional…
Anomalies in the ambient magnetic field can be used as features in indoor positioning and navigation. By using Maxwell's equations, we derive and present a Bayesian non-parametric probabilistic modeling approach for interpolation and…
Recent work shows that inference for Gaussian processes can be performed efficiently using iterative methods that rely only on matrix-vector multiplications (MVMs). Structured Kernel Interpolation (SKI) exploits these techniques by deriving…
State-of-the-art methods for scalable Gaussian processes use iterative algorithms, requiring fast matrix vector multiplies (MVMs) with the covariance kernel. The Structured Kernel Interpolation (SKI) framework accelerates these MVMs by…
Structured Kernel Interpolation (SKI) (Wilson et al. 2015) helps scale Gaussian Processes (GPs) by approximating the kernel matrix via interpolation at inducing points, achieving linear computational complexity. However, it lacks rigorous…
The application of Gaussian processes (GPs) to large data sets is limited due to heavy memory and computational requirements. A variety of methods has been proposed to enable scalability, one of which is to exploit structure in the kernel…
When an agent, person, vehicle or robot is moving through an unknown environment without GNSS signals, online mapping of nonlinear terrains can be used to improve position estimates when the agent returns to a previously mapped area.…
A fast multilevel algorithm based on directionally scaled tensor-product Gaussian kernels on structured sparse grids is proposed for interpolation of high-dimensional functions and for the numerical integration of high-dimensional…
Learning mappings between functional spaces, also known as function-on-function regression, is a fundamental problem in functional data analysis with broad applications, including spatiotemporal forecasting, curve prediction, and climate…
Gaussian processes (GP) and Kriging are widely used in traditional spatio-temporal mod-elling and prediction. These techniques typically presuppose that the data are observed from a stationary GP with parametric covariance structure.…
A key challenge in spatial statistics is the analysis for massive spatially-referenced data sets. Such analyses often proceed from Gaussian process specifications that can produce rich and robust inference, but involve dense covariance…
Gaussian process regression (GPR) is a useful technique to predict composition--property relationships in glasses as the method inherently provides the standard deviation of the predictions. However, the technique remains restricted to…
Gaussian processes (GPs) provide a gold standard for performance in online settings, such as sample-efficient control and black box optimization, where we need to update a posterior distribution as we acquire data in a sequential fashion.…
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…
We present a scalable Gaussian Process (GP) method called DSoftKI that can fit and predict full derivative observations. It extends SoftKI, a method that approximates a kernel via softmax interpolation, to the setting with derivatives.…
Gaussian processes (GPs) are powerful but computationally expensive machine learning models, requiring an estimate of the kernel covariance matrix for every prediction. In large and complex domains, such as graphs, sets, or images, the…
We present a theoretically grounded Gaussian process framework that leverages neural feature maps to construct expressive kernels. We show that the learned feature map can be interpreted as an optimal low-rank approximation to a Gram matrix…