Related papers: Scalable Gaussian Processes on Discrete Domains
The Gaussian process (GP) is a widely used probabilistic machine learning method with implicit uncertainty characterization for stochastic function approximation, stochastic modeling, and analyzing real-world measurements of nonlinear…
Inference in popular nonparametric Bayesian models typically relies on sampling or other approximations. This paper presents a general methodology for constructing novel tractable nonparametric Bayesian methods by applying the kernel trick…
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 (\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.…
Choosing the most adequate kernel is crucial in many Machine Learning applications. Gaussian Process is a state-of-the-art technique for regression and classification that heavily relies on a kernel function. However, in the Gaussian…
Classical Gaussian processes and Kriging models are commonly based on stationary kernels, whereby correlations between observations depend exclusively on the relative distance between scattered data. While this assumption ensures analytical…
We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
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…
Variable selection for Gaussian process models is often done using automatic relevance determination, which uses the inverse length-scale parameter of each input variable as a proxy for variable relevance. This implicitly determined…
Gaussian process regression is widely applied in computational science and engineering for surrogate modeling owning to its kernel-based and probabilistic nature. In this work, we propose a Bayesian approach that integrates the variability…
Variational autoencoders often assume isotropic Gaussian priors and mean-field posteriors, hence do not exploit structure in scenarios where we may expect similarity or consistency across latent variables. Gaussian process variational…
Gaussian Processes (GPs) are Bayesian models that provide uncertainty estimates associated to the predictions made. They are also very flexible due to their non-parametric nature. Nevertheless, GPs suffer from poor scalability as the number…
We propose a probabilistic enhancement of standard kernel Support Vector Machines for binary classification, in order to address the case when, along with given data sets, a description of uncertainty (e.g., error bounds) may be available…
The log-Gaussian Cox process is a flexible and popular class of point pattern models for capturing spatial and space-time dependence for point patterns. Model fitting requires approximation of stochastic integrals which is implemented…
Gaussian Process (GP) Variational Autoencoders (VAEs) extend standard VAEs by replacing the fully factorised Gaussian prior with a GP prior, thereby capturing richer correlations among latent variables. However, performing exact GP…
We develop a scalable class of models for latent variable estimation using composite Gaussian processes, with a focus on derivative Gaussian processes. We jointly model multiple data sources as outputs to improve the accuracy of latent…
Inference in Gaussian process (GP) models is computationally challenging for large data, and often difficult to approximate with a small number of inducing points. We explore an alternative approximation that employs stochastic inference…
We introduce a fast algorithm for Gaussian process regression in low dimensions, applicable to a widely-used family of non-stationary kernels. The non-stationarity of these kernels is induced by arbitrary spatially-varying vertical and…
The use of Gaussian process models is typically limited to datasets with a few tens of thousands of observations due to their complexity and memory footprint. The two most commonly used methods to overcome this limitation are 1) the…