Related papers: Gauss-Legendre Features for Gaussian Process Regre…
Forecasting in probabilistic time series is a complex endeavor that extends beyond predicting future values to also quantifying the uncertainty inherent in these predictions. Gaussian process regression stands out as a Bayesian machine…
Kernel-based models such as kernel ridge regression and Gaussian processes are ubiquitous in machine learning applications for regression and optimization. It is well known that a major downside for kernel-based models is the high…
Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…
Gaussian processes (GPs) are ubiquitous tools for modeling and predicting continuous processes in physical and engineering sciences. This is partly due to the fact that one may employ a Gaussian process as an interpolator while facilitating…
The aim of this paper is to develop novel quantum algorithms for Gaussian process quadrature methods. Gaussian process quadratures are numerical integration methods where Gaussian processes are used as functional priors for the integrands…
Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…
Direct quantile regression involves estimating a given quantile of a response variable as a function of input variables. We present a new framework for direct quantile regression where a Gaussian process model is learned, minimising the…
Gaussian processes are flexible function approximators, with inductive biases controlled by a covariance kernel. Learning the kernel is the key to representation learning and strong predictive performance. In this paper, we develop…
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,…
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.…
Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…
Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this…
The increased demand for online prediction and the growing availability of large data sets drives the need for computationally efficient models. While exact Gaussian process regression shows various favorable theoretical properties…
Gaussian process regression is a popular method for non-parametric probabilistic modeling of functions. The Gaussian process prior is characterized by so-called hyperparameters, which often have a large influence on the posterior model and…
Kernel methods are powerful and flexible approach to solve many problems in machine learning. Due to the pairwise evaluations in kernel methods, the complexity of kernel computation grows as the data size increases; thus the applicability…
In this paper, a quantum algorithm based on gaussian process regression model is proposed. The proposed quantum algorithm consists of three sub-algorithms. One is the first quantum subalgorithm to efficiently generate mean predictor. The…
Gaussian process (GP) is a Bayesian model which provides several advantages for regression tasks in machine learning such as reliable quantitation of uncertainty and improved interpretability. Their adoption has been precluded by their…
We propose a lower bound on the log marginal likelihood of Gaussian process regression models that can be computed without matrix factorisation of the full kernel matrix. We show that approximate maximum likelihood learning of model…
Gaussian processes (GP) for machine learning have been studied systematically over the past two decades and they are by now widely used in a number of diverse applications. However, GP kernel design and the associated hyper-parameter…
Fourier feature approximations have been successfully applied in the literature for scalable Gaussian Process (GP) regression. In particular, Quadrature Fourier Features (QFF) derived from Gaussian quadrature rules have gained popularity in…