Related papers: Manifold Optimization Assisted Gaussian Variationa…
Gaussian processes are powerful non-parametric probabilistic models for stochastic functions. However, the direct implementation entails a complexity that is computationally intractable when the number of observations is large, especially…
Deep feedforward neural networks (DFNNs) are a powerful tool for functional approximation. We describe flexible versions of generalized linear and generalized linear mixed models incorporating basis functions formed by a DFNN. The…
In the Bayesian approach to inverse problems, data are often informative, relative to the prior, only on a low-dimensional subspace of the parameter space. Significant computational savings can be achieved by using this subspace to…
We deal with the efficient parallelization of Bayesian global optimization algorithms, and more specifically of those based on the expected improvement criterion and its variants. A closed form formula relying on multivariate Gaussian…
We introduce Bayesian optimization, a technique developed for optimizing time-consuming engineering simulations and for fitting machine learning models on large datasets. Bayesian optimization guides the choice of experiments during…
In this study, two classes of methods including statistical and variational data assimilation algorithms will be described. In statistical methods, the model state is updated sequentially based on the previous estimate. Variational methods,…
The main computational challenge in Bayesian inference is to compute integrals against a high-dimensional posterior distribution. In the past decades, variational inference (VI) has emerged as a tractable approximation to these integrals,…
Due to the increasing demand for high performance and cost reduction within the framework of complex system design, numerical optimization of computationally costly problems is an increasingly popular topic in most engineering fields. In…
Bayesian methods estimate a measure of uncertainty by using the posterior distribution. One source of difficulty in these methods is the computation of the normalizing constant. Calculating exact posterior is generally intractable and we…
We consider the optimal approximate posterior over the top-layer weights in a Bayesian neural network for regression, and show that it exhibits strong dependencies on the lower-layer weights. We adapt this result to develop a correlated…
Centered Gaussian random fields (GRFs) indexed by compacta such as smooth, bounded Euclidean domains or smooth, compact and orientable manifolds are determined by their covariance operators. We consider centered GRFs given as variational…
The problem of low rank matrix completion is considered in this paper. To exploit the underlying low-rank structure of the data matrix, we propose a hierarchical Gaussian prior model, where columns of the low-rank matrix are assumed to…
Variational inference offers scalable and flexible tools to tackle intractable Bayesian inference of modern statistical models like Bayesian neural networks and Gaussian processes. For largely over-parameterized models, however, the…
This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…
Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…
This paper tackles the challenge presented by small-data to the task of Bayesian inference. A novel methodology, based on manifold learning and manifold sampling, is proposed for solving this computational statistics problem under the…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Approximating complex probability distributions, such as Bayesian posterior distributions, is of central interest in many applications. We study the expressivity of geometric Gaussian approximations. These consist of approximations by…
Posterior sampling by Monte Carlo methods provides a more comprehensive solution approach to inverse problems than computing point estimates such as the maximum posterior using optimization methods, at the expense of usually requiring many…