Related papers: Variational Inference for Gaussian Process Models …
Gaussian processes regression models are an appealing machine learning method as they learn expressive non-linear models from exemplar data with minimal parameter tuning and estimate both the mean and covariance of unseen points. However,…
We present a multivariate Gaussian process regression approach for parameter field reconstruction based on the field's measurements collected at two different scales, the coarse and fine scales. The proposed approach treats the parameter…
Gaussian processes offer a flexible kernel method for regression. While Gaussian processes have many useful theoretical properties and have proven practically useful, they suffer from poor scaling in the number of observations. In…
Gaussian processes are powerful models for probabilistic machine learning, but are limited in application by their $O(N^3)$ inference complexity. We propose a method for deriving parametric families of kernel functions with compact spatial…
The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…
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…
The computational cost for inference and prediction of statistical models based on Gaussian processes with Mat\'ern covariance functions scales cubicly with the number of observations, limiting their applicability to large data sets. The…
Gaussian processes are distributions over functions that are versatile and mathematically convenient priors in Bayesian modelling. However, their use is often impeded for data with large numbers of observations, $N$, due to the cubic (in…
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…
We study learning problems in which the conditional distribution of the output given the input varies as a function of additional task variables. In varying-coefficient models with Gaussian process priors, a Gaussian process generates the…
We develop an automated variational method for inference in models with Gaussian process (GP) priors and general likelihoods. The method supports multiple outputs and multiple latent functions and does not require detailed knowledge of the…
This paper introduces a new sparse spatio-temporal structured Gaussian process regression framework for online and offline Bayesian inference. This is the first framework that gives a time-evolving representation of the interdependencies…
Statistical physics approaches can be used to derive accurate predictions for the performance of inference methods learning from potentially noisy data, as quantified by the learning curve defined as the average error versus number of…
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…
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…
Multivariate categorical data occur in many applications of machine learning. One of the main difficulties with these vectors of categorical variables is sparsity. The number of possible observations grows exponentially with vector length,…
Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…
We introduce fully scalable Gaussian processes, an implementation scheme that tackles the problem of treating a high number of training instances together with high dimensional input data. Our key idea is a representation trick over the…
Gaussian process (GP) regression with 1D inputs can often be performed in linear time via a stochastic differential equation formulation. However, for non-Gaussian likelihoods, this requires application of approximate inference methods…
State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse…