Related papers: ANOVA decomposition of conditional Gaussian proces…
In this paper we present a novel analysis of variance Gaussian process (ANOVA-GP) emulator for models governed by partial differential equations (PDEs) with high-dimensional random inputs. Gaussian process (GP) is a widely used surrogate…
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…
Sensitivity analysis is an important tool used in many domains of computational science to either gain insight into the mathematical model and interaction of its parameters or study the uncertainty propagation through the input-output…
Running a reliability analysis on engineering problems involving complex numerical models can be computationally very expensive, requiring advanced simulation methods to reduce the overall numerical cost. Gaussian process based active…
Variable selection for Gaussian process models is often done using automatic relevance determination, which uses the inverse length-scale parameter of each input variable as a proxy for variable relevance. This implicitly determined…
We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to…
Gaussian processes constitute a very powerful and well-understood method for non-parametric regression and classification. In the classical framework, the training data consists of deterministic vector-valued inputs and the corresponding…
Sensitivity analysis is an important concept to analyze the influences of parameters in a system, an equation or a collection of data. The methods used for sensitivity analysis are divided into deterministic and statistical techniques.…
The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models…
Complex computer codes are widely used in science and engineering to model physical phenomena. Furthermore, it is common that they have a large number of input parameters. Global sensitivity analysis aims to identify those which have the…
Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…
High dimensional time series are endemic in applications of machine learning such as robotics (sensor data), computational biology (gene expression data), vision (video sequences) and graphics (motion capture data). Practical nonlinear…
Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator.…
Complex computer codes are often too time expensive to be directly used to perform uncertainty, sensitivity, optimization and robustness analyses. A widely accepted method to circumvent this problem consists in replacing cpu-time expensive…
Global sensitivity analysis of complex numerical simulators is often limited by the small number of model evaluations that can be afforded. In such settings, surrogate models built from a limited set of simulations can substantially reduce…
With the rapid development of modern technology, massive amounts of data with complex pattern are generated. Gaussian process models that can easily fit the non-linearity in data become more and more popular nowadays. It is often the case…
The global sensitivity analysis method, used to quantify the influence of uncertain input variables on the response variability of a numerical model, is applicable to deterministic computer code (for which the same set of input variables…
Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…
Sensitivity analysis is a process of computing sensitivity indices, which are certain measures of importance of parameters in influencing the outputs of mathematical models. Sensitivity indices computed in variance-based sensitivity…
Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process…