Related papers: Robust Gaussian Stochastic Process Emulation
Engineers widely use Gaussian process regression framework to construct surrogate models aimed to replace computationally expensive physical models while exploring design space. Thanks to Gaussian process properties we can use both samples…
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 (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…
Many fields of science and engineering rely on running simulations with complex and computationally expensive models to understand the involved processes in the system of interest. Nevertheless, the high cost involved hamper reliable and…
In this paper we introduce a novel model for Gaussian process (GP) regression in the fully Bayesian setting. Motivated by the ideas of sparsification, localization and Bayesian additive modeling, our model is built around a recursive…
Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…
Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…
Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…
Logistic Gaussian process (LGP) priors provide a flexible alternative for modelling unknown densities. The smoothness properties of the density estimates can be controlled through the prior covariance structure of the LGP, but the challenge…
In the gravitational-wave analysis of pulsar-timing-array datasets, parameter estimation is usually performed using Markov Chain Monte Carlo methods to explore posterior probability densities. We introduce an alternative procedure that…
A new methodology for model determination in decomposable graphical Gaussian models is developed. The Bayesian paradigm is used and, for each given graph, a hyper inverse Wishart prior distribution on the covariance matrix is considered.…
Gaussian Process (GP) regression is a flexible non-parametric approach to approximate complex models. In many cases, these models correspond to processes with bounded physical properties. Standard GP regression typically results in a proxy…
Non-conjugate Gaussian processes (NCGPs) define a flexible probabilistic framework to model categorical, ordinal and continuous data, and are widely used in practice. However, exact inference in NCGPs is prohibitively expensive for large…
The ability to obtain reliable point estimates of model parameters is of crucial importance in many fields of physics. This is often a difficult task given that the observed data can have a very high number of dimensions. In order to…
Several machine learning problems arising in natural language processing can be modeled as a sequence labeling problem. We provide Gaussian process models based on pseudo-likelihood approximation to perform sequence labeling. Gaussian…
We introduce constrained Gaussian process (CGP), a Gaussian process model for random functions that allows easy placement of mathematical constrains (e.g., non-negativity, monotonicity, etc) on its sample functions. CGP comes with…
Gaussian process regression (GPR) is a popular nonparametric Bayesian method that provides predictive uncertainty estimates and is widely used in safety-critical applications. While prior research has introduced various uncertainty bounds,…
In spite of the diverse literature on nonstationary spatial modeling and approximate Gaussian process (GP) methods, there are no general approaches for conducting fully Bayesian inference for moderately sized nonstationary spatial data sets…
Optical scatterometry is a method to measure the size and shape of periodic micro- or nanostructures on surfaces. For this purpose the geometry parameters of the structures are obtained by reproducing experimental measurement results…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…