Related papers: Efficient Marginal Likelihood Computation for Gaus…
The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the…
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 present a continuation method that entails generating a sequence of transition probability density functions from the prior to the posterior in the context of Bayesian inference for parameter estimation problems. The characterization of…
In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…
A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…
We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for…
Maximum likelihood estimation is an important statistical technique for estimating missing data, for example in climate and environmental applications, which are usually large and feature data points that are irregularly spaced. In…
Using quasi-Newton methods in stochastic optimization is not a trivial task given the difficulty of extracting curvature information from the noisy gradients. Moreover, pre-conditioning noisy gradient observations tend to amplify the noise.…
Gaussian Process (GP) models provide a flexible framework for prediction and uncertainty quantification. For most covariance functions, however, exact GP prediction with $n$ points scales as $\mathcal{O}(n^3)$, making it prohibitively…
Gaussian process (GP) regression is a powerful probabilistic modeling technique with built-in uncertainty quantification. When one has access to multiple correlated simulations (tasks), it is common to fit a multitask GP (MTGP) surrogate…
Bayesian optimization (BO) has become a popular strategy for global optimization of expensive real-world functions. Contrary to a common expectation that BO is suited to optimizing black-box functions, it actually requires domain knowledge…
Bayesian optimization has proven to be a highly effective methodology for the global optimization of unknown, expensive and multimodal functions. The ability to accurately model distributions over functions is critical to the effectiveness…
Optimization constrained by high-fidelity computational models has potential for transformative impact. However, such optimization is frequently unattainable in practice due to the complexity and computational intensity of the model. An…
The use of Gaussian processes (GPs) is supported by efficient sampling algorithms, a rich methodological literature, and strong theoretical grounding. However, due to their prohibitive computation and storage demands, the use of exact GPs…
Sparse variational Gaussian processes (GPs) construct tractable posterior approximations to GP models. At the core of these methods is the assumption that the true posterior distribution over training function values ${\bf f}$ and inducing…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
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…
Gaussian process priors are a popular choice for Bayesian analysis of regression problems. However, the implementation of these models can be complex, and ensuring that the implementation is correct can be challenging. In this paper we…
A number of problems in probability and statistics can be addressed using the multivariate normal (Gaussian) distribution. In the one-dimensional case, computing the probability for a given mean and variance simply requires the evaluation…
In applications of Gaussian processes where quantification of uncertainty is a strict requirement, it is necessary to accurately characterize the posterior distribution over Gaussian process covariance parameters. Normally, this is done by…