Related papers: Bayesian inference for high-dimensional nonstation…
Inverse problems are prevalent in both scientific research and engineering applications. In the context of Bayesian inverse problems, sampling from the posterior distribution can be particularly challenging when the forward models are…
Bayesian optimization has shown to be a fundamental global optimization algorithm in many applications: ranging from automatic machine learning, robotics, reinforcement learning, experimental design, simulations, etc. The most popular and…
Even though Nearest Neighbor Gaussian Processes (NNGP) alleviate considerably MCMC implementation of Bayesian space-time models, they do not solve the convergence problems caused by high model dimension. Frugal alternatives such as response…
Gaussian process (GP) regression is a non-parametric, Bayesian framework to approximate complex models. Standard GP regression can lead to an unbounded model in which some points can take infeasible values. We introduce a new GP method that…
Approximate Bayesian computation (ABC) methods are used to approximate posterior distributions using simulation rather than likelihood calculations. We introduce Gaussian process (GP) accelerated ABC, which we show can significantly reduce…
Analysing non-Gaussian spatial-temporal data requires introducing spatial as well as temporal dependence in generalised linear models through the link function of an exponential family distribution. Unlike in Gaussian likelihoods, inference…
Inspired by recent advances in the field of expert-based approximations of Gaussian processes (GPs), we present an expert-based approach to large-scale multi-output regression using single-output GP experts. Employing a deeply structured…
We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…
Gaussian processes have become a popular tool for nonparametric regression because of their flexibility and uncertainty quantification. However, they often use stationary kernels, which limit the expressiveness of the model and may be…
Recent advances in big data and analytics research have provided a wealth of large data sets that are too big to be analyzed in their entirety, due to restrictions on computer memory or storage size. New Bayesian methods have been developed…
Recently, there has been an increasing interest in performing post-hoc uncertainty estimation about the predictions of pre-trained deep neural networks (DNNs). Given a pre-trained DNN via back-propagation, these methods enhance the original…
In geostatistics, traditional spatial models often rely on the Gaussian Process (GP) to fit stationary covariances to data. It is well known that this approach becomes computationally infeasible when dealing with large data volumes,…
Missing values are common in many real-life datasets. However, most of the current machine learning methods can not handle missing values. This means that they should be imputed beforehand. Gaussian Processes (GPs) are non-parametric models…
In this article, we primarily propose a novel Bayesian characterization of stationary and nonstationary stochastic processes. In practice, this theory aims to distinguish between global stationarity and nonstationarity for both parametric…
Identifying dynamical system (DS) is a vital task in science and engineering. Traditional methods require numerous calls to the DS solver, rendering likelihood-based or least-squares inference frameworks impractical. For efficient parameter…
Gaussian Process (GP) models are a powerful tool in probabilistic machine learning with a solid theoretical foundation. Thanks to current advances, modeling complex data with GPs is becoming increasingly feasible, which makes them an…
Understanding the properties of transient gravitational waves and their sources is of broad interest in physics and astronomy. Bayesian inference is the standard framework for astro-physical measurement in transient gravitational-wave…
Deep Gaussian processes (DGP) have appealing Bayesian properties, can handle variable-sized data, and learn deep features. Their limitation is that they do not scale well with the size of the data. Existing approaches address this using a…
Gaussian processes (GPs) are a popular model for spatially referenced data and allow descriptive statements, predictions at new locations, and simulation of new fields. Often a few parameters are sufficient to parameterize the covariance…
We present a scalable approach to performing approximate fully Bayesian inference in generic state space models. The proposed method is an alternative to particle MCMC that provides fully Bayesian inference of both the dynamic latent states…