Related papers: On the Correspondence between Gaussian Processes a…
This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and…
This monograph studies the relations between two approaches using positive definite kernels: probabilistic methods using Gaussian processes, and non-probabilistic methods using reproducing kernel Hilbert spaces (RKHS). They are widely…
In this work, we investigate Gaussian process regression used to recover a function based on noisy observations. We derive upper and lower error bounds for Gaussian process regression with possibly misspecified correlation functions. The…
Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…
Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process…
Kernel-based methods have been recently introduced for linear system identification as an alternative to parametric prediction error methods. Adopting the Bayesian perspective, the impulse response is modeled as a non-stationary Gaussian…
Recently nonparametric functional model with functional responses has been proposed within the functional reproducing kernel Hilbert spaces (fRKHS) framework. Motivated by its superior performance and also its limitations, we propose a…
Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper…
Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…
The expressive power of Bayesian kernel-based methods has led them to become an important tool across many different facets of artificial intelligence, and useful to a plethora of modern application domains, providing both power and…
The rate of convergence of weighted kernel herding (WKH) and sequential Bayesian quadrature (SBQ), two kernel-based sampling algorithms for estimating integrals with respect to some target probability measure, is investigated. Under…
Gaussian Process regression is a kernel method successfully adopted in many real-life applications. Recently, there is a growing interest on extending this method to non-Euclidean input spaces, like the one considered in this paper,…
Gaussian Process (GP) regression is a powerful nonparametric Bayesian framework, but its performance depends critically on the choice of covariance kernel. Selecting an appropriate kernel is therefore central to model quality, yet remains…
Bayesian optimization is a popular formalism for global optimization, but its computational costs limit it to expensive-to-evaluate functions. A competing, computationally more efficient, global optimization framework is optimistic…
Gaussian process regression is a well-established Bayesian machine learning method. We propose a new approach to Gaussian process regression using quantum kernels based on parameterized quantum circuits. By employing a hardware-efficient…
We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data.…
In this paper we investigate a link between state- space models and Gaussian Processes (GP) for time series modeling and forecasting. In particular, several widely used state- space models are transformed into continuous time form and…