相关论文: Scalable Gaussian Processes with Billions of Induc…

Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…

We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we…

In this paper, we introduce a probabilistic extension to Kolmogorov Arnold Networks (KANs) by incorporating Gaussian Process (GP) as non-linear neurons, which we refer to as GP-KAN. A fully analytical approach to handling the output…

Gaussian processes (GPs) are typically criticised for their unfavourable scaling in both computational and memory requirements. For large datasets, sparse GPs reduce these demands by conditioning on a small set of inducing variables…

This work introduces the Efficient Transformed Gaussian Process (ETGP), a new way of creating C stochastic processes characterized by: 1) the C processes are non-stationary, 2) the C processes are dependent by construction without needing a…

Gaussian processes (GPs) are frequently used in machine learning and statistics to construct powerful models. However, when employing GPs in practice, important considerations must be made, regarding the high computational burden,…

This work introduces the concept of parametric Gaussian processes (PGPs), which is built upon the seemingly self-contradictory idea of making Gaussian processes parametric. Parametric Gaussian processes, by construction, are designed to…

In their standard form Gaussian processes (GPs) provide a powerful non-parametric framework for regression and classificaton tasks. Their one limiting property is their $\mathcal{O}(N^{3})$ scaling where $N$ is the number of training data…

Latent Gaussian process (GP) models are widely used in neuroscience to uncover hidden state evolutions from sequential observations, mainly in neural activity recordings. While latent GP models provide a principled and powerful solution in…

Multi-robot systems require scalable and federated methods to model complex environments under computational and communication constraints. Gaussian Processes (GPs) offer robust probabilistic modeling, but suffer from cubic computational…

Gaussian processes (GPs), or distributions over arbitrary functions in a continuous domain, can be generalized to the multi-output case: a linear model of coregionalization (LMC) is one approach. LMCs estimate and exploit correlations…

This paper presents a novel approach for approximate integration over the uncertainty of noise and signal variances in Gaussian process (GP) regression. Our efficient and straightforward approach can also be applied to integration over…

Gaussian processes (GPs) offer a flexible class of priors for nonparametric Bayesian regression, but popular GP posterior inference methods are typically prohibitively slow or lack desirable finite-data guarantees on quality. We develop an…

Gaussian Process (GPs) models are a rich distribution over functions with inductive biases controlled by a kernel function. Learning occurs through the optimisation of kernel hyperparameters using the marginal likelihood as the objective.…

Gaussian processes (GPs) are widely used in non-parametric Bayesian modeling, and play an important role in various statistical and machine learning applications. In a variety tasks of uncertainty quantification, generating random sample…

Gaussian processes (GPs) are widely-used tools in spatial statistics and machine learning and the formulae for the mean function and covariance kernel of a GP $T u$ that is the image of another GP $u$ under a linear transformation $T$…

Stochastic gradient descent (SGD) and its variants have established themselves as the go-to algorithms for large-scale machine learning problems with independent samples due to their generalization performance and intrinsic computational…

We propose a Standing Wave Decomposition (SWD) approximation to Gaussian Process regression (GP). GP involves a costly matrix inversion operation, which limits applicability to large data analysis. For an input space that can be…

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…

Many inferential tasks involve fitting models to observed data and predicting outcomes at new covariate values, requiring interpolation or extrapolation. Conventional methods select a single best-fitting model, discarding fits that were…