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Matrix completion and robust principal component analysis have been widely used for the recovery of data suffering from missing entries or outliers. In many real-world applications however, the data is also time-varying, and the naive…
A fully Bayesian approach is proposed for ultrahigh-dimensional nonparametric additive models in which the number of additive components may be larger than the sample size, though ideally the true model is believed to include only a small…
Gaussian processes are a fully Bayesian smoothing technique that allows for the reconstruction of a function and its derivatives directly from observational data, without assuming a specific model or choosing a parameterization. This is…
Bayesian optimization (BO) is an effective technique for black-box optimization. However, its applicability is typically limited to moderate-budget problems due to the cubic complexity of fitting the Gaussian process (GP) surrogate model.…
The increased demand for online prediction and the growing availability of large data sets drives the need for computationally efficient models. While exact Gaussian process regression shows various favorable theoretical properties…
Complex computer codes are often too time expensive to be directly used to perform uncertainty propagation studies, global sensitivity analysis or to solve optimization problems. A well known and widely used method to circumvent this…
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 inverse problems, the parameters of a model are estimated based on observations of the model response. The Bayesian approach is powerful for solving such problems; one formulates a prior distribution for the parameter state that is…
The estimation of unknown values of parameters (or hidden variables, control variables) that characterise a physical system often relies on the comparison of measured data with synthetic data produced by some numerical simulator of the…
Construction of kinetic models has become an indispensable step in the development and scale up of processes in the industry. Model-based design of experiments (MBDoE) has been widely used for the purpose of improving parameter precision in…
Gaussian processes (GPs) with derivatives are useful in many applications, including Bayesian optimization, implicit surface reconstruction, and terrain reconstruction. Fitting a GP to function values and derivatives at $n$ points in $d$…
We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on…
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…
Bayesian Optimization (BO) is a method for globally optimizing black-box functions. While BO has been successfully applied to many scenarios, developing effective BO algorithms that scale to functions with high-dimensional domains is still…
Bayesian deep learning all too often underfits so that the Bayesian prediction is less accurate than a simple point estimate. Uncertainty quantification then comes at the cost of accuracy. For linearized models, the null space of the…
Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…
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…
Several fundamental problems in science and engineering consist of global optimization tasks involving unknown high-dimensional (black-box) functions that map a set of controllable variables to the outcomes of an expensive experiment.…
Many expensive black-box optimisation problems are sensitive to their inputs. In these problems it makes more sense to locate a region of good designs, than a single-possibly fragile-optimal design. Expensive black-box functions can be…
Bayesian experimental design is a technique that allows to efficiently select measurements to characterize a physical system by maximizing the expected information gain. Recent developments in deep neural networks and normalizing flows…