Related papers: Efficiently Sampling Functions from Gaussian Proce…
Gaussian Process state-space models capture complex temporal dependencies in a principled manner by placing a Gaussian Process prior on the transition function. These models have a natural interpretation as discretized stochastic…
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…
Recently there have been exciting developments in Monte Carlo methods, with the development of new MCMC and sequential Monte Carlo (SMC) algorithms which are based on continuous-time, rather than discrete-time, Markov processes. This has…
Gaussian processes (GPs) are widely used metamodels for approximating expensive computer simulations, particularly in engineering design and spatial prediction. However, their performance can deteriorate significantly when covariance…
A key quantity of interest in Bayesian inference are expectations of functions with respect to a posterior distribution. Markov Chain Monte Carlo is a fundamental tool to consistently compute these expectations via averaging samples drawn…
Monte Carlo methods, Variational Inference, and their combinations play a pivotal role in sampling from intractable probability distributions. However, current studies lack a unified evaluation framework, relying on disparate performance…
Uncertainty quantification for large-scale inverse problems remains a challenging task. For linear inverse problems with additive Gaussian noise and Gaussian priors, the posterior is Gaussian but sampling can be challenging, especially for…
The posterior probability distribution for a set of model parameters encodes all that the data have to tell us in the context of a given model; it is the fundamental quantity for Bayesian parameter estimation. In order to infer the…
Gaussian processes (GPs) with derivatives are useful in many applications, including Bayesian optimization, implicit surface reconstruction, and terrain reconstruction. Fitting a GP to function values and derivatives at $n$ points in $d$…
We present a Hamiltonian Monte Carlo algorithm to sample from multivariate Gaussian distributions in which the target space is constrained by linear and quadratic inequalities or products thereof. The Hamiltonian equations of motion can be…
We present two data-driven methods for estimating reachable sets with probabilistic guarantees. Both methods make use of a probabilistic formulation allowing for a formal definition of a data-driven reachable set approximation that is…
Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…
In a general class of Bayesian nonparametric models, we prove that the posterior distribution can be asymptotically approximated by a Gaussian process. Our results apply to nonparametric exponential family that contains both Gaussian and…
We study the problem of posterior sampling in the context of score based generative models. We have a trained score network for a prior $p(x)$, a measurement model $p(y|x)$, and are tasked with sampling from the posterior $p(x|y)$. Prior…
Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate…
The Gaussian process is a powerful and flexible technique for interpolating spatiotemporal data, especially with its ability to capture complex trends and uncertainty from the input signal. This chapter describes Gaussian processes as an…
Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple…
Many functions have approximately-known upper and/or lower bounds, potentially aiding the modeling of such functions. In this paper, we introduce Gaussian process models for functions where such bounds are (approximately) known. More…
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…
Missing values with mixed data types is a common problem in a large number of machine learning applications such as processing of surveys and in different medical applications. Recently, Gaussian copula models have been suggested as a means…