Related papers: Spatio-Temporal Variational Gaussian Processes

Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…

With the rapid advances of data acquisition techniques, spatio-temporal data are becoming increasingly abundant in a diverse array of disciplines. Here we develop spatio-temporal regression methodology for analyzing large amounts of…

Existing spatio-temporal Hawkes process models typically rely on either parametric or semiparametric assumptions, limiting the model's ability to capture complex endogenous and exogenous event dynamics. We propose a fully Bayesian…

Variable selection in Gaussian processes (GPs) is typically undertaken by thresholding the inverse lengthscales of automatic relevance determination kernels, but in high-dimensional datasets this approach can be unreliable. A more…

We introduce a new scalable approximation for Gaussian processes with provable guarantees which hold simultaneously over its entire parameter space. Our approximation is obtained from an improved sample complexity analysis for sparse…

Conventional variational autoencoders fail in modeling correlations between data points due to their use of factorized priors. Amortized Gaussian process inference through GP-VAEs has led to significant improvements in this regard, but is…

The aim of this article is to present a novel parallelization method for temporal Gaussian process (GP) regression problems. The method allows for solving GP regression problems in logarithmic O(log N) time, where N is the number of time…

Recent years have seen a huge development in spatial modelling and prediction methodology, driven by the increased availability of remote-sensing data and the reduced cost of distributed-processing technology. It is well known that…

Approximations to Gaussian processes based on inducing variables, combined with variational inference techniques, enable state-of-the-art sparse approaches to infer GPs at scale through mini batch-based learning. In this work, we address…

Making predictions and quantifying their uncertainty when the input data is sequential is a fundamental learning challenge, recently attracting increasing attention. We develop SigGPDE, a new scalable sparse variational inference framework…

We propose a parallelizable sparse inverse formulation Gaussian process (SpInGP) for temporal models. It uses a sparse precision GP formulation and sparse matrix routines to speed up the computations. Due to the state-space formulation used…

Standard GPs offer a flexible modelling tool for well-behaved processes. However, deviations from Gaussianity are expected to appear in real world datasets, with structural outliers and shocks routinely observed. In these cases GPs can fail…

A generator of spatio-temporal pseudo-random Gaussian fields that satisfy the "proportionality of scales" property (Tsyroulnikov, 2001) is presented. The generator is based on a third-order in time stochastic differential equation with a…

Spatio-temporal point process models play a central role in the analysis of spatially distributed systems in several disciplines. Yet, scalable inference remains computa- tionally challenging both due to the high resolution modelling…

We consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve…

Gaussian process (GP) models form a core part of probabilistic machine learning. Considerable research effort has been made into attacking three issues with GP models: how to compute efficiently when the number of data is large; how to…

Gaussian processes (GPs) are an important tool in machine learning and statistics with applications ranging from social and natural science through engineering. They constitute a powerful kernelized non-parametric method with…

Scalable spatial GPs for massive datasets can be built via sparse Directed Acyclic Graphs (DAGs) where a small number of directed edges is sufficient to flexibly characterize spatial dependence. The DAG can be used to devise fast algorithms…

We develop a fast variational approximation scheme for Gaussian process (GP) regression, where the spectrum of the covariance function is subjected to a sparse approximation. Our approach enables uncertainty in covariance function…

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…