Related papers: A Locally Adaptive Bayesian Cubature Method
We discuss efficient Bayesian estimation of dynamic covariance matrices in multivariate time series through a factor stochastic volatility model. In particular, we propose two interweaving strategies (Yu and Meng, Journal of Computational…
Calibration or parameter identification is used with computational mechanics models related to observed data of the modeled process to find model parameters such that good similarity between model prediction and observation is achieved. We…
In high-dimensional settings, Bayesian optimization (BO) can be expensive and infeasible. The random embedding Bayesian optimization algorithm is commonly used to address high-dimensional BO challenges. However, this method relies on the…
Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model…
Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is…
In Bayesian inverse problems sampling the posterior distribution is often a challenging task when the underlying models are computationally intensive. To this end, surrogates or reduced models are often used to accelerate the computation.…
Bayesian inference can often be sensitive to the choice of hyperparameters of the prior or likelihood, yet defining and quantifying this sensitivity in a principled and computationally feasible way remains challenging in practice.…
While MCMC methods have become a main work-horse for Bayesian inference, scaling them to large distributed datasets is still a challenge. Embarrassingly parallel MCMC strategies take a divide-and-conquer stance to achieve this by writing…
Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e.…
Bayesian optimization involves "inner optimization" over a new-data acquisition criterion which is non-convex/highly multi-modal, may be non-differentiable, or may otherwise thwart local numerical optimizers. In such cases it is common to…
Mixture models are becoming a popular tool for the clustering and classification of high-dimensional data. In such high dimensional applications, model selection is problematic. The Bayesian information criterion, which is popular in lower…
A local optimization method based on Bayesian Gaussian Processes is developed and applied to atomic structures. The method is applied to a variety of systems including molecules, clusters, bulk materials, and molecules at surfaces. The…
Bayesian optimization (BO) for high-dimensional constrained problems remains a significant challenge due to the curse of dimensionality. We propose Local Constrained Bayesian Optimization (LCBO), a novel framework tailored for such…
Uncertainty quantification is critical for ensuring adequate predictive power of computational models used in biology. Focusing on two anaerobic digestion models, this article introduces a novel generalized Bayesian procedure, called…
Computer models are used as replacements for physical experiments in a large variety of applications. Nevertheless, direct use of the computer model for the ultimate scientific objective is often limited by the complexity and cost of the…
Local optimization presents a promising approach to expensive, high-dimensional black-box optimization by sidestepping the need to globally explore the search space. For objective functions whose gradient cannot be evaluated directly,…
Bayesian optimization is a popular method for optimizing expensive black-box functions. Yet it oftentimes struggles in high dimensions where the computation could be prohibitively heavy. To alleviate this problem, we introduce Coordinate…
Developing efficient MCMC algorithms is indispensable in Bayesian inference. In parallel tempering, multiple interacting MCMC chains run to more efficiently explore the state space and improve performance. The multiple chains advance…
In this paper, we modify the adaptive cubic regularization method for large-scale unconstrained optimization problem by using a real positive definite scalar matrix to approximate the exact Hessian. Combining with the nonmonotone technique,…
We introduce a new type of cubature formula for the evaluation of an integral over the disk with respect to a weight function. The method is based on an analysis of the Fourier series of the weight function and a reduction of the bivariate…